Searching for Exotic Weak Currents with the WITCH Experiment

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1 FACULTY OF SCIENCE Searching for Exotic Weak Currents with the WITCH Experiment Elisabeth WURSTEN Supervisor: Prof. N. Severijns Thesis presented in fulfillment of the requirements for the degree of Master of Science in Physics Academic year

2 c Copyright by KU Leuven Without written permission of the promotors and the authors it is forbidden to reproduce or adapt in any form or by any means any part of this publication. Requests for obtaining the right to reproduce or utilize parts of this publication should be addressed to KU Leuven, Faculteit Wetenschappen, Geel Huis, Kasteelpark Arenberg 11 bus 21, 31 Leuven (Heverlee), Telephone A written permission of the promotor is also required to use the methods, products, schematics and programs described in this work for industrial or commercial use, and for submitting this publication in scientific contests.

3 Preface The Standard Model of Particle Physics was finalized in the 197 s and has stood the test of time ever since. It has known many successes, predicting experimentally observed quantities to many decimal places. However, it certainly cannot be all there is to know about the world. Indeed, it does not explain gravity, nor does it explain dark matter and energy, why neutrino s have such low masses or why there was an asymmetry in the quantity of matter and antimatter in the early universe. As such, physicists are constantly hunting for new physics: probing the predictions of the Standard Model to see where they fail. There are, roughly speaking, two main approaches to finding new physics. One can go to very high energies and try to discover evidence of new particles in collision experiments. Or, one can try to measure a certain physical quantity with a very high precision, to check with the Standard Model prediction. The WITCH experiment at ISOLDE/CERN takes this second, high precision approach. The question that it tries to answer is the following: does the Standard Model adequately describe the weak interaction, or are there some exotic components that are not yet incorporated? More concretely, we look at the β-ν angular correlation a, between the positron and neutrino that get emitted in the β decay of radioactive 35 Ar isotopes. For this process, the Standard Model predicts a value of a =.94(16). In November 212, the WITCH experiment made its first set of measurements with radioactive argon that gathered enough statistics to be physically relevant. The goal of this thesis is to perform a systematic and scrutinized yet preliminary analysis of the resulting data. Because it is a precision experiment, meticulous care was taken to track down systematic effects and to gain as complete an understanding of the data as possible. With this understanding, procedures to remove as much noise as possible were suggested to improve the quality of the data. Finally, a novel fit procedure was developed that incorporates all discovered effects. From the insights gained during this investigation, several future recommendations and remaining open problems were formulated. I would like to thank my promotor, Nathal Severijns, for his guidance in the creation of this thesis. I m grateful to Gergelj Soti and Simon Van Gorp for always being available when assistance was needed with Simbuca or ROOT. Moreover, my thanks go out to i

4 PREFACE ii all the team members of the WITCH experiment for their support: Martin Breitenfeldt, Tomica Porobic, Paul Finlay and Andreas Knecht. And last but not least, I m grateful to Roald Frederickx for the lively discussions.

5 Abstract (English) A measurement of the β-ν angular correlation coefficient a in nuclear β decay provides a good probe to test for exotic weak currents and hence physics beyond the Standard Model. The WITCH experiment at ISOLDE/CERN aims to precisely measure the energy distribution of the recoiling daughter nucleus after β decay of radioactive 35 Ar isotopes. From the shape of this spectrum, the coefficient a can be determined and compared to the Standard Model prediction of a =.94(16). Concretely, 1.4 GeV proton beams are sent onto a CaO target at ISOLDE. From the produced elements, the General Purpose Separator then selects the 35 Ar ions which are bunched in REXtrap. These bunches then get injected into the WITCH setup, where they enter a first Penning trap. Here, they are cooled by a buffer gas before being sent to a second Penning trap in which the pressure is of order 1 8 mbar. There, the ion cloud acts as a radioactive source that is essentially free from scattering. The recoil energy of the daughter nuclei is probed by a retardation spectrometer and an MCP detector. In November 212, the WITCH experiment made its first set of measurements with radioactive argon that gathered enough statistics to be physically relevant. The goal of this thesis was to perform the first systematic analysis of the resulting data to gain as much insight as possible into the observed (background) effects, to track down occurring systematic effects and to explore ways of reducing noise. An important aspect of this analysis was relating experimental data to results simulated with Simbuca, a simulation framework specifically crafted for the WITCH experiment. We observed several effects in the data of which the origin could be determined. These include, of course, the actual recoil ions that we want to analyse. On the other hand, also a number of other, unwanted and sometimes unforeseen background effects were identified. For instance, a large fraction of the beta particles that are emitted during the decay of the trapped ions ended up reaching the detector as well. The retardation voltage and switching of the pulsed drift tube also had a measurable influence on the static background level. Furthermore, the steerer, which was switched to decrease the background level that entered the trap, is found to quite possibly have the opposite effect. We also observed persistent magnetron oscillations, showing that the ion cloud is not perfectly centred in the decay trap, but is coherently circling around the centre. In an off-line measurement, coherent axial oscillations of the ion cloud in the decay trap were iii

6 ABSTRACT (ENGLISH) iv also observed. The Coulomb repulsion between the ions is essential to keep the cloud coherent, in an effect called phase locking. Simulations confirmed its necessity and agreed with the observed behaviour. Additional background due to neutralised argon atoms was noted. When the trap is cleared, the argon ions are sent towards the walls of the trap. Here, they can neutralise due to charge exchange with the walls. Because of their noble gas nature, the neutralised argon atoms are unlikely to stick to the walls for prolonged time. Instead, they diffuse back into the trap, where they can still decay and send β + particles towards the detector. Furthermore, during the filling of the cooler trap, high energy ions apparently make their way through the trap and retardation section and get implanted in the detector. There, they create another unwanted background level as they decay. A conjectured explanation for the high energy ions is an improper working of the pulsed drift tube, possibly due to incoming ion bunches from REXtrap that are too spread out longitudinally. A fitting procedure that handles the recoil ions and takes into account all listed background effects was developed and used for an exploratory initial investigation. Some peculiarities arise from the data. Firstly, the half-lives for the betas and the ions coming from the decay trap are consistently smaller than the nuclear half-live of argon-35. Moreover, the beta and ion half-life are not equal, although they arise from the same radioactive source, i.e. the ion cloud in the decay trap. Hence, there must be loss mechanisms at play in the decay trap which are different for betas and ions. One possibility is that neutralisation occurs there as well. Secondly, the obtained preliminary energy distribution of the recoiling nuclei deviates too strongly from the Standard Model prediction to be considered credible. This seems to indicate that there is a retardation voltage dependent effect that was not accounted for yet. As this was the first time that data with sufficient statistics is available, its analysis was bound to stumble upon unforeseen and unwanted effects as those characterised above. Furthermore, there are some additional open problems that resulted from this research and that require further investigation. For example, what causes the ion losses in the decay trap? Does neutralisation happen in the decay trap, and is the signal due to neutralised argon atoms retardation voltage dependent? Can implantation be avoided? The measurements of the first 5 V retardation bin is too flat for some hitherto unknown reason. The shape of the recoil ion spot on the detector looks to be retardation voltage dependent, hence the efficiency map of the MCP needs to be characterized and calibrated. The tracking software SimWITCH currently assumes axial symmetry and should be extended to enable full 3D calculations, because observed magnetron oscillations indicate that axial symmetry is broken. And of course: is the problem of the incorrect recoil ion energy distribution solved if the previous points are attended to? Or are there other retardation voltage dependent effects that are not yet taken into account?

7 Abstract (Nederlands) Metingen van de β-ν angulaire correlatie coëfficiënt a bij nucleair β verval vormen een goede test voor het mogelijke bestaan van exotische zwakke stromen en dus voor fysica buiten het Standaardmodel. Het WITCH experiment in ISOLDE/CERN probeert om de energiedistributie van de terugstotende dochterkern na β verval van een radioactief 35 Ar isotoop te meten. Uit de vorm van dit spectrum kan de coëfficiënt a worden bepaald. Deze kan dan worden vergeleken met de waarde a =.94(16) die het Standaardmodel voorspelt. Concreet worden 1.4 GeV proton bundels op een CaO target van ISOLDE gericht. De GPS separator selecteert dan de gewenste 35 Ar ionen uit de geproduceerde elementen. Deze ionen worden verzameld in REXtrap, dewelke ze als een pakketje injecteert in de WITCH opstelling. Daar komen ze de eerste penningval binnen, waar ze gekoeld worden door een buffergas. Wanneer de ionenwolk voldoende gethermaliseerd is, wordt ze naar een tweede penningval gestuurd waar een lage druk heerst van orde 1 8 mbar. Als dusdanig gedraagt de ionenwolk zich als een verstrooiingsvrije radioactieve bron. De terugstootenergie van de dochterkern wordt dan opgemeten door een retardatiespectrometer en een MCP detector. In november 212 deed het WITCH experiment zijn eerste metingen met radioactief argon die voldoende statistiek hadden vergaard om fysisch relevant te zijn. Het doel van deze thesis was om een systematische analyse van de resulterende data te maken. Dit om zoveel mogelijk inzicht te krijgen in de geobserveerde (achtergrond-) effecten om aldus optredende systematische effecten op te sporen en om de mogelijkheid tot ruisonderdrukking te verkennen. Een belangrijk aspect van deze analyse hield in om experimentele data te linken aan resultaten die bekomen werden door simulaties uit Simbuca, een simulatieraamwerk dat speciaal werd gemaakt voor het WITCH project. We hebben meerdere effecten geobserveerd waarvan we de oorsprong hebben kunnen bepalen. Naast de terugstootionen die we wilden onderzoeken, hebben we echter ook een aantal andere en soms onvoorziene achtergrondeffecten geïdentificeerd. Bij het verval van een gevangen ion worden bijvoorbeeld beta deeltjes uitgestuurd, waarvan een grote fractie op de detector eindigt. Het schakelen van de retardatiespanning en de pulsed drift tube had ook meetbare effecten op het statische achtergrondsniveau. Verder bleek dat het schakelen van één van de sturende elektrodes voor de eerste penningval niet het gewenste effect van achtergrond vermindering had. We hebben ook een persistente magnetronoscillatie waargenomen, dewelke aantoont dat de ionenwolk niet perfect gecentreerd is in de v

8 ABSTRACT (NEDERLANDS) vi tweede val, maar coherent rondom het centrum cirkelt. In een off-line meting werden tevens coherente axiale oscillaties van de ionenwolk in de tweede penningval geobserveerd. De coulombafstoting tussen de ionen is hierbij essentieel om de wolk coherent te houden, in een effect dat phase locking wordt genoemd. Simulaties hebben de noodzaak hiervan bevestigd, alsook het geobserveerde gedrag nagebootst. Extra achtergrondsignaal afkomstig van neutrale argon atomen werd ook geobserveerd. Indien de val wordt leeggemaakt, worden argon ionen richting de wanden van de val gestuurd. Daar kunnen ze neutraliseren door ladingsoverdracht met de wanden. Wegens hun edelgasstructuur is het onwaarschijnlijk dat de geneutraliseerde argon atomen voor lange tijd aan de wanden blijven plakken. In plaats daarvan diffunderen ze terug naar de val, waar ze nog steeds kunnen vervallen en β + straling uitzenden richting detector. Daarenboven, bij het vullen van de eerste penningval zijn er ogenschijnlijk hoge-energie ionen die, ondanks de val en hoge retardatiepotentiaal, toch hun weg vinden tot aan de detector. Deze ionen worden dan geïmplanteerd in de MCP alwaar ze een ongewenst achtergrond niveau creeren terwijl ze vervallen. Een vermoedelijke verklaring voor de hoge-energie ionen is een suboptimaal werkende pulsed drift tube, mogelijk omdat de ionenpakketjes vanuit REXtrap te sterk zijn uitgesmeerd in de longitudinale richting. Een fitting-procedure werd ontwikkeld die zowel de terugstoot ionen als alle hierboven genoemde achtergrondeffecten behandelt. Deze procedure werd gebruikt voor een preliminair onderzoek. Deze analyse leverde eigenaardige resultaten op. Eerst en vooral zijn de halfwaardetijden voor de verschillende vervallende componenten (waaronder ook de terugstootionen) allen consistent kleiner dan de nucleaire halfwaardetijd van argon. Bijgevolg moeten er dus ionverliezen zijn in de val. Het is bijvoorbeeld mogelijk dat hier ook neutralisatie optreedt. Ten tweede wijkt de bekomen terugstootenergiedistributie te sterk af van de Standaardmodel voorspelling om geloofwaardig te worden geacht. Dit lijkt te wijzen op een retardatiespanning-afhankelijk effect dat nog niet in rekening werd gebracht. Aangezien dit de eerste keer is waarbij data met voldoende statistiek beschikbaar is, is het niet verwonderlijk dat de analyse hiervan stuit op enkele onvoorziene en ongewenste effecten zoals hierboven beschreven. Meer nog, uit dit onderzoek zijn nog extra open vragen gevloeid die verder onderzoek vereisen. Bijvoorbeeld, wat is de oorzaak van de ionverliezen in de val? Vindt er ook neutralisatie plaats van de gevangen ionen, en is het signaal van de geneutraliseerde argon atomen retardatiespanning-afhankelijk? Kan implantatie worden vermeden? Bovendien lijkt het tijdsspectrum in de eerste 5 V retardatie periode te vlak, waarom is dit? De vorm van de terugstootionenvlek op de MCP lijkt afhankelijk te zijn van de retardatiespanning, dus de efficientiekaart van de MCP moet nog in rekening worden gebracht. De simulatiesoftware SimWITCH gebruikt momenteel de aanname van axiale symmetrie en moet worden uitgebreid om volledige 3D berekeningen aan te kunnen, aangezien de geobserveerde magnetronoscillaties aantonen dat de axiale symmetrie gebroken is. En uiteraard: is het probleem van de incorrecte terugstootenergiedistributie opgelost indien de vorige punten onder handen worden genomen? Of is er nog een ander retardatiespanning-afhankelijk effect dat nog niet in rekening werd gebracht?

9 Contents Preface i Abstract (English) iii Abstract (Nederlands) v Introduction 1 1 The Weak Interaction Goal Historical Introduction to Weak Interaction Theory Fermi Theory Gamow-Teller Extention Parity Violation Chirality Invariance and the Standard Model How to Look for Physics Beyond the Standard Model? β-ν Angular Correlation Physics Case for WITCH State of the Art Experimental Setup ISOLDE Radioactive Beam Production at ISOLDE Argon Production and Beam Preparation for the WITCH Experiment WITCH Horizontal Beamline Vertical Beamline Penning Traps Retardation Spectrometer vii

10 CONTENTS viii MCP detector Simulations with Simbuca Introduction Simbuca Axial Motion Optimal Transfer Time Measuring the Axial Motion Qualitative Investigation Reproduction of the Measurement Conclusion Data Analysis General Overview Events Cycles Runs Data Selection Background Cycles Noise Reduction Fitting Modelling the Data Fit Results Outlook Conclusion and Outlook Conclusions Open Questions and Future Work Future Improvements Software Changes Background Reduction Beta Reduction A Simulation Results 8 B Position and Pulse Height Distributions 92

11 Introduction There are two ways to look for physics beyond the Standard Model of Particle Physics. One possibility consists of climbing up the energy ladder by performing high energy collision experiments. The collision products are then analysed for evidence of new particles. This is for instance the approach taken by the LHC experiment at CERN. A second way of probing for new physics is by performing high precision measurements, and checking the results against the Standard Model predictions. This thesis is concerned with the WITCH project at ISOLDE/CERN, which takes the second, high precision approach. The question that it tries to answer is: does the Standard Model adequately describe the weak interaction, or are there some exotic components that are not yet incorporated? This thesis will give an introduction to weak interaction theory and to the WITCH experiment itself. Furthermore, the majority of this document will thoroughly explain the analysis that was performed during the span of this thesis on the November 212 data. This data set was the very first batch of data from the experiment that gathered enough statistics to be physically relevant. As such, this analysis entails truly novel work and discovered quite a few unforeseen effects. From the insights gained during this investigation, several future recommendations and remaining open problems were formulated at the end of this document. Concretely, Chapter 1 introduces the WITCH experiment within the field of high precision weak interaction studies. The specific goal of the WITCH experiment is explained in Section 1.1, followed by a historical introduction to weak interaction theory in Section 1.2. Section 1.3 elaborates on the position of the WITCH experiment within the search for physics beyond the Standard Model and compares it with the current state of the art. In Chapter 2, the experimental WITCH setup at ISOLDE/CERN is described. We start with a general overview in Section 2.1 of isotope production and ion beam preparation at ISOLDE. The second part of that sections deals with the specific approach taken for 35 Ar, the isotope of interest for the WITCH experiment. In Section 2.2, the WITCH setup itself is presented. Each critical element of the experimental setup is highlighted, which is vital for a thorough understanding of the data analysis in Chapter 4. Chapter 3 deals with Simbuca: the simulation framework for the behaviour of ion clouds in the WITCH Penning traps. First, the role of Simbuca in the full simulation procedure is presented in Section 3.1, where it is explained how the angular correlation coefficient a 1

12 CONTENTS 2 can be obtained from the experimental measurements. Next, an introduction to the main features of Simbuca is given in Section 3.2. Lastly, the code is used to reproduce a measurement that showed somewhat unexpected results in Section 3.3. From the simulations, the origin of the observed effect is made clear. A discussion of the analysis of the experimental data that was taken during the run in November 212 is given in Chapter 4. A general overview of the type of data handled in that chapter is given in Section 4.1. Section 4.2 gives a detailed account of the selection procedure that was used to remove as much background effects as possible. Section 4.3 pertains to the fitting of the selected data. The different aspects of the fitting procedure are presented and the fit results are carefully scrutinized. Finally, effects that require more investigation are summarized in the outlook at the end of this chapter. Lastly, Chapter 5 lists the major conclusions of the research performed in the context of this thesis. It also compiles a set of open problems that need further attention and ends with suggestions for future improvements which might be implemented in the WITCH setup.

13 Chapter 1 The Weak Interaction This chapter introduces the WITCH experiment within the field of high precision weak interaction studies. The goal of the WITCH experiment is explained in Section 1.1. Next, a historical introduction to weak interaction theory is presented in Section 1.2. From this point of view, the position of high precision nuclear beta decay experiments within the search for physics beyond the Standard Model will become clear. Section 1.3 further elaborates on this. The specific physics case of the WITCH experiment is presented and an overview is given of similar experiments. 1.1 Goal There are many unanswered questions in the domain of fundamental physics. Why is there more matter than antimatter? How can we unify gravity with the other fundamental forces? Is there such a thing as supersymmetry? What about dark matter and the expansion of the universe? The Standard Model of Particle Physics is our current attempt at trying to describe what we know about particle physics in particular, but it is far from complete. It does not provide any answers to the previous questions. Hence, there are a lot of initiatives that try to bring us one step closer at understanding nature, both on the theoretical and the experimental side. High energy experiments such as those performed at the Large Hadron Collider at CERN are looking for physics beyond the Standard Model by colliding protons (or lead atoms) at high energy and looking for traces of new particles and interactions in the resulting debris. Another strategy is to study one of the fundamental interactions with high precision. In the latter case, deviations from the Standard Model prediction are the indicator of new physics. This is the domain in which the WITCH experiment is situated. The acronym WITCH stands for Weak Interaction Trap for CHarged particles. This experiment is designed to study the weak interaction by trapping radioactive ions and carefully observing their decay. The question we try to answer is whether the Standard 3

14 CHAPTER 1. THE WEAK INTERACTION 4 Model is adequate in describing the weak interaction or whether some exotic components exist which were not yet incorporated into the Standard Model. In order to explain exactly how the WITCH experiment is planning to do this, a basis of weak interaction theory is required. 1.2 Historical Introduction to Weak Interaction Theory In order to explain the necessity of high precision experiments in nuclear beta decay, a historical introduction to the weak interaction seems appropriate. This section illustrates the evolution of weak interaction theory and indicates where the Standard Model makes an assumption which might not be 1% correct Fermi Theory The first theory of beta decay was proposed in 1933 by Enrico Fermi [Wilson, 1968]. Around 193, little was known about beta decay. So-called beta rays were observed for certain nuclei and it was known that the beta spectrum was continuous, but there was no satisfying explanation for this. At that time, the theory of nuclear electrons was still popular [Amaldi, 1982]. It was assumed that the nucleus consisted of protons and electrons. The observed beta rays were interpreted as electrons escaping from the nucleus. It was noted in Fermi s paper that this theory was incapable of explaining why the betas have a continuous spectrum. Moreover, relativistic theories of light particles were not able to explain why an electron could be bound in orbits of nuclear sizes [Wilson, 1968]. Several theories were put forward to account for these discrepancies. Bohr suggested that the principle of conservation of energy should be abandoned [Amaldi, 1982]. Pauli, on the contrary, postulated a neutral particle which he called the neutron 1 (in 193). The whole theory of nuclear electrons was discredited with the discovery of the neutron 2 in 1932 [Chadwick, 1932]. The view on the nuclear structure changed to the one we know today: that of protons and neutrons. Using the newly accepted picture of the nucleus and the particle proposed by Pauli (which Fermi renamed to neutrino), Fermi came up with a new theory of beta decay. In analogy with the radiation theory of photon emission from atoms, he proposed that electrons and neutrinos can be created and destroyed. This might seem trivial now, but at that time, this was a controversial idea 3. Back then the photon was the only type of particle for which the particle number was not conserved, but this was considered to be a special case because of its zero mass. 1 This particle is now called the neutrino. 2 Meaning: the particle that we now know as the neutron. 3 Fermi s paper on the theory of beta decay was rejected in 1933 by Nature magazine because it contained speculations too remote from physical reality to be of interest to readers [Bernardini and Bonolis, 24].

15 CHAPTER 1. THE WEAK INTERACTION 5 Fermi included a term in the nuclear Hamiltonian which contains creation and annihilation operators for the light (leptonic) particles: the electron and neutrino. He also introduced an isospin operator which turns the proton into a neutron and vice versa. In his paper, Fermi mentioned that the amplitude of this interaction can depend on the coordinates, momenta, etc. of the heavy particles [Wilson, 1968]. Guided by conservation of momentum and Lorentz invariance; Fermi investigated the simplest choice: take the amplitude proportional to the wave functions of the light particles evaluated at the position of the nucleus. Using a relativistic approach for the light particles, he concluded that the amplitude should be described by a bilinear combination of the Dirac spinors for electron and neutrino 4. Since Dirac spinors have 4 components, there are 16 independent bilinear combinations. Using the properties under Lorentz transformations of these bilinears, they can be divided into 5 groups. These are given in Table 1.1. The γ µ represent the Dirac gamma matrices which obey the following anticommutation relation: {γ µ, γ ν } = γ µ γ ν + γ ν γ µ = 2η µν I 4, with η µν the Minkowski metric. The fifth matrix is defined in function of the four others: γ 5 = iγ γ 1 γ 2 γ 3. The ψ a and ψ b are Dirac 4-spinors, with ψ a = ψ aγ. Bilinear combination ψ a ψ b ψ a γ µ ψ b ψ a γ µ γ ν ψ b ψ a γ µ γ ν γ λ ψ b = ψ a γ σ γ 5 ψ b ψ a γ 5 ψ b Transforms as a... under Lorentz transformations Scalar (1 comp.) Vector (4 comp.) Tensor of rank 2 (antisymmetric, 6 comp.) Axial (or pseudo) vector (4 comp.) Pseudoscalar (1 comp.) Table 1.1: Classes of bilinears. Here, µ, ν and λ range from to 3 and µ ν λ. Since Fermi based his theory on the interaction of a photon (which is a vector-type interaction), Fermi also assumed a vector-type interaction for beta decay. Using relativistic notation for the nucleons as well, Fermi s interaction Hamiltonian would look like this: H = g F ( ψp γ µ ψ n ) ( ψe γ µ ψ ν ) + h.c. where h.c. stands for the Hermitian conjugate. The first term describes β decay, its Hermitian conjugate describes β + decay. Decay rates and distributions can be calculated with the usual perturbation theoretical formulae by treating the interaction Hamiltonian as a perturbation to the nuclear Hamiltonian. The following formula for the transition probability per unit time W has the commemorative name Fermi s Golden Rule: W = 2π H if 2 ρ f 4 For more information on Dirac spinors, gamma matrices and bilinears, see the textbook of David Griffiths on particle physics [Griffiths, 28]

16 CHAPTER 1. THE WEAK INTERACTION 6 with H if the matrix element between initial and final state of the interaction Hamiltonian; and ρ f the density of final states [Amaldi, 1982]. Assuming no orbital angular momentum is transferred to the leptons (i.e. assuming allowed decay), Fermi s selection rules are I = and π i = π f with I the difference in spin of the initial and final nucleus, π i the parity of the initial state and π f the parity of the final state Gamow-Teller Extention Fermi s simple model actually works quite well for the fastest type of decays (superallowed decays), but completely breaks down for some others. There were processes known in nature which violate its selection rules. The problem with Fermi s theory is that it only incorporates decays with combined lepton spin of zero, whereas fast decays (indicating no orbital angular momentum transfer to the light particles) with nuclear spin flips had actually been observed. To incorporate these observations into the theory, Gamow and Teller expanded Fermi s Hamiltonian in 1936 [Amaldi, 1982]: [ ( ) ( ) H =g F C S ψp ψ n ψe ψ ν ( ) ( ) + C V ψp γ µ ψ n ψe γ µ ψ ν 1 ( ) ( ) + C T ψp σ µλ ψ n ψe σ µλ ψ ν 2 ( ) ( ) C A ψp γ µ γ 5 ψ n ψe γ µ γ 5 ψ ν ( ) ( ) ] + C p ψp γ 5 ψ n ψe γ 5 ψ ν + h.c. ( ) ( ) ] =g F [C i ψp O i ψ n ψe O i ψ ν + h.c. i=s,v,t,a,p with σ µλ = i (γ 2 µγ λ γ λ γ µ ). In the last line, O S = 1 4x4, O V = γ µ, O T = 1 2 σ µλ, O A = iγ µ γ 5 and O P = γ 5. The numerical constants C i are called coupling constants and have to be determined by experiment. In this general Hamiltonian, the Scalar and Vector type of transitions have combined lepton spin. The Tensor and Axial-vector terms incorporate parallel lepton spins. The Pseudoscalar term does not play an important role in beta decay because it is negligible for non-relativistic nucleons [Amaldi, 1982]. The names of Fermi, Gamow and Teller are still known today in the field of nuclear physics. A decay with lepton spins combined to is called a Fermi transition, whereas a decay with lepton spins combined to 1 is called a Gamow-Teller transition Parity Violation This Hamiltonian remained unchanged for about 2 years. Many experiments were performed in order to determine the C i coefficients, but the results seemed to contradict each other due to faulty measurements. It was only until 1956 that there was a breakthrough

17 CHAPTER 1. THE WEAK INTERACTION 7 in weak interaction theory. Lee and Yang recognised that the θ π puzzle (regarding the strange behaviour of newly discovered particles in cosmic rays) could be explained by assuming that the weak interaction violates parity. They proposed the following Hamiltonian [Amaldi, 1982]: [ (ψp ) ( ) ] H = g F O i ψ n ψe O i (C i + C iγ 5 )ψ ν + h.c. (1.1) i=s,v,t,a,p A whole series of experiments was set up to test this hypothesis; not much later Madame Wu and her co-workers found that parity is indeed violated in beta decay [Wu et al., 1957] Chirality Invariance and the Standard Model Soon, experimental evidence began to point to maximal parity violation, meaning that C i = ±C i. Rewriting (1.1) gives ( ) ( ) ] H = g F [C i ψp O i ψ n ψe O i (1 ± γ 5 )ψ ν + h.c.. i=s,v,t,a,p Furthermore, after re-examining the experimental results, Marshak and Sudarshan proposed the chirality principle in 1958 [Sudarshan and Marshak, 1958]. This principle states that the weak interaction is of the V-A form, meaning that C i = C i, C V = C A and the others coefficients equal zero: [ (ψp ) ( ) ] H γ µ (1 + γ 5 )ψ n ψe γ µ (1 + γ 5 )ψ ν + h.c.. Feynman and Gell-Mann reached the same conclusion despite starting from a different point of view [Feynman and Gell-Mann, 1958]. Do note that the measured values of C V and C A are not equal, because the strong interaction between the quarks in a nucleon or nucleus influences the effective weak interaction. This is why form factors have to be included for each type of nuclear beta decay. The name chirality invariance comes from the (1 + γ 5 ) term is the Hamiltonian. This particular term is a projection operator. For massless particles it projects onto the lefthanded helicity state. For a massive particle, this statement is no longer holds and (1+γ 5 ) is said to project onto the left-handed chiral state. The proposal of the chirality principle was crucial in the development of electroweak theory and hence the Standard Model [Weinberg, 29]. The Standard Model describes the weak interaction as the interaction of a W-boson with the left-handed chiral states of leptons and quarks. The difference between the 4-fermion point interaction and the Standard Model interaction is clearly shown in Figure 1.1. The 4-fermion vertex is smeared out in the Standard Model and replaced with 2 vertices and a W-boson propagator.

18 CHAPTER 1. THE WEAK INTERACTION 8 Figure 1.1: Feynman diagrams for the Fermi interaction (left) and the Standard Model charged weak interaction (right). It is important to note that the determination of the weak interaction Hamiltonian was based on a lot of experimental input. However, experiments can never prove a certain theory, they can only make assumptions probable. There is still room for non Standard Model physics in nuclear beta decay, i.e. it is not certain that the S, T and P coupling constants are zero. The current limits on the norm of the Tensor and Scalar coupling constants are [Severijns and Naviliat-Cuncic, 213]: ) C( S C( ) T <.7 and <.9 (1.2) C V C A 1.3 How to Look for Physics Beyond the Standard Model? As mentioned in the previous section, the values of the coupling constants C i in 1.1 have to be determined experimentally. The current limits on these parameters are given in (1.2). They are still in agreement with the Standard Model prediction of, but that does not mean they actually are zero. The goal of the WITCH experiment is to improve the experimental constraints on these parameters. How exactly the WITCH experiment in particular is planning to achieve this will be explained in Sections and In Section 1.3.3, other recent endeavours at investigating the Standard Model using nuclear beta decay will briefly be summarized.

19 CHAPTER 1. THE WEAK INTERACTION β-ν Angular Correlation From (1.1), the distribution in electron and neutrino directions, electron polarization and energy for a β-transition can be determined using Fermi s Golden Rule (only the most important terms are included) [Jackson et al., 1957]: ω ( I, ) σ E e, Ω e, Ω ν de e dω e dω ν F (±Z, E e )p e E e (E E e ) 2 de e dω e dω ν { ξ 1 + p e p ν a + m b + [ I E e E ν E e I pe A + p ν B + p ] e p ν D + E e E ν σ [ p e E e G + I I N + p e E e + m ( I I p e E e ) Q + E e E ν ( I I p e E e ) R ]}. (1.3) E, p and Ω denote the total energy, the momentum and the angular coordinates of the β-particle and the neutrino, I is the nuclear polarization of the state with spin I, E is the total spectrum endpoint energy, m is the rest mass of the electron, σ is the spin vector of the β-particle and F (±Z, E e ) is the Fermi function which takes the interaction between the charged daughter nucleus and the β-particle into account. The upper sign is always reserved for β decay whilst the lower one is for β +. The parameters a (β-ν angular correlation), b (Fierz interference term), A (β-asymmetry), etc. are called correlation coefficients and are a function of the coupling constants C i. The choice of setup determines which correlation coefficient(s) can be measured. The goal of the WITCH experiment is to determine the β-ν angular correlation coefficient a. This means that oriented nuclei are not necessary ( I = ) and the polarization of the beta particle does not have to be measured. All terms with I then drop out and a sum has to be taken over all polarization states σ of the beta particle. The resulting decay rate is given by ω (E e, Ω e, Ω ν ) de e dω e dω ν F (±Z, E e )p e E e (E E e ) 2 de e dω e dω ν ξ { 1 + p e p ν a + m } b. (1.4) E e E ν E e As mentioned before, the correlation coefficients are functions of the coupling constants. The particular expressions are given below. ξ = M F 2 ( C S 2 + C S 2 + C V 2 + C V 2) ( + M GT 2 C A 2 + C A 2 + C T 2 + C T 2) (1.5) [ aξ = M F 2 C S 2 C S 2 + C V 2 + C V 2 2 αzm ] Im(C S C V + C p SC V ) e + M GT 2 [ C A 2 C 3 A 2 + C T 2 + C T 2 ± 2 αzm ] Im(C T C A + C p TC A ) (1.6) e bξ = ± 2γRe [ M F 2 ( C S C V + C SC V ) + M GT 2 ( C T C A + C TC A )] (1.7)

20 CHAPTER 1. THE WEAK INTERACTION (a) Small angle 1 (b) Large angle Figure 1.2: Recoil energy of the daughter nucleus in function of the angle between the β-particle and the neutrino. Here, MF and MGT are the Fermi and Gamow-Teller nuclear matrix elements and γ = p 2 1 (αz)2 with α = e~c the fine-structure constant. If the decay rate can be measured in function of the angle of emission between beta and neutrino, the correlation coefficients a and b can be constrained and a limit can be found on the relevant coupling constants. From (1.6) it becomes clear that the vector and tensor interactions on one side; and the scalar and axial vector interactions on the other side have a similar effect on the angular correlation coefficient. Indeed, V and T make a more positive and hence result in a higher probability of small angles ( Ep~ee ~Epνν a is largest when beta and neutrino are emitted in the same direction). On the other hand, S and A have the opposite effect. They make a more negative and thus favour emission of beta and neutrino in opposite direction Physics Case for WITCH There are several ways of testing the Standard Model. One of them is determining the β-ν angular correlation coefficient for a certain beta decay process and checking if it agrees with the Standard Model prediction. However, directly determining the angle between β-particle and neutrino is not so straightforward, as the neutrino is very hard to detect. That is why the WITCH experiment resorts to an indirect measurement of this angular correlation by determining the recoil energy distribution of the daughter nuclei. As shown in Figure 1.2, the recoil energy is large if the angle between beta and neutrino is small (1.2a), whereas the recoil energy is small if the angle is large (1.2b). The angular correlation coefficient can be determined from this energy spectrum through simulations (see Chapter 3). It is imperative to note here that the Standard Model is actually quite good at describing the weak interaction. In terms of the recoil energy distribution: the deviation from Standard Model values is smaller than 1/1 (this upper limit was determined by similar experiments). This means that the measurements of the recoil distribution have to be very precise. Hence not only high statistics are needed, but also all systematic effects which influence the energy distribution have to be taken into account.

21 CHAPTER 1. THE WEAK INTERACTION 11 It is of the utmost importance to choose the right beta decay process. There are certain experimental constraints to the choice of isotope. First of all, the production yield of the isotope has to be high enough to meet the statistics requirement. This means that yields of particles/s or higher should be attained [Gorp, 212]. In addition, the half-life should be neither too short nor too long. Optimally between.5 s and 3 s. If the half-life is too short, most of the ions will decay during the preparation of the ion cloud before the measurement can take place. If the half-life is too long, the count rate would be low and require more ions to be produced and stored in the setup. Furthermore, isobaric contamination should be avoided as much as possible. The decay scheme of the isotope should be well known, as well as the charge state distribution of the daughter nucleus. Preferably, the positive charge states should be populated, as the energy of neutral atoms can not be probed with the WITCH setup. Finally, the daughter nucleus should be preferentially stable in order to avoid unwanted counts from these decays. Besides experimental limitations, there are also some preferences from a physical point of view. As can be seen from formulae (1.6) and (1.7), the constraints that can be set on the correlation coefficients are influenced by the precision of the Fermi and Gamow-Teller nuclear matrix elements, which have to be determined experimentally. Therefore, it would be best if the transition is purely Fermi or purely Gamow-Teller, so that the matrix elements drop out of the expression for a (remember that the expression for a is given by dividing (1.6) with (1.5)). If a pure process is not possible, the next best thing would be to find a process for which the mixing ratio is accurately known. The specific beta decay process that was chosen for the WITCH experiment is the positron decay of Ar-35: 35 18Ar Cl 18 + e + + ν e. It is a mirror transition 5, which means that the matrix elements can be determined more accurately due to the proton/neutron symmetry. It has a half-life of (1) s [Chen et al., 211] which is compatible with the time structure of the experiment and the production yield that can be delivered by ISOLDE. The decay scheme is simple and very well known, with a maximum recoil energy of 452 ev. The charge state distribution was measured recently with the LPC trap setup in GANIL, Caen and is given in Table 1.2. The Standard Model prediction of a for this decay process is.94(16) State of the Art This section contains a short description of both completed and ongoing experiments designed to measure the beta-neutrino angular correlation of various beta decays. 5 The number of protons and the number of neutrons in the mother nucleus are switched in the daughter nucleus.

22 CHAPTER 1. THE WEAK INTERACTION 12 Charge state Contribution (%) (1.) (4) (3) (21) >4.71(18) Table 1.2: Charge state distribution of the 35 Cl daughter ions after 35 Ar decay. About 28(1)% of the recoils is charged. The remainder is neutral. From [Couratin, 213]. Experiments Without Particle Traps 6 He In 1963, Johnson et al. studied the β decay of 6 He [Johnson et al., 1963]. It is an allowed, pure Gamow-Teller transition ( ), hence the beta-neutrino correlation is only sensitive to axial vector and tensor interactions. The correlation coefficient was determined by measuring the energy spectrum of the recoiling 6 Li ions. The result of this experiment was a =.3343 ±.3 (assuming that the Fierz term is negligible). This value agrees well with the Standard Model value of -1/3. 32 Ar The β + decay of 32 Ar was investigated by [Adelberger et al., 1999]. This decay is a pure Fermi transition ( + + ), thus the positron-neutrino correlation could provide a signature of scalar weak interactions. The method that was used to measure the correlation coefficient is based on the instability of the 32 Cl daughter nucleus which emits a proton shortly after the beta decay (the 32 Cl daughter state has a width of 2 ± 1 ev [Adelberger et al., 1999]). The kinematics of the β decay is reflected in the energy of these protons (broadening of the proton peaks due to the Doppler effect) and hence the positron-neutrino correlation coefficient can be determined. The value of ã = a/( b) =.9989 ±.52(stat) ±.39(syst) at 68% confidence level was obtained. However, in 23, a more precise measurement of the 32 Ar mass was performed at ISOLTRAP (ISOLDE) [Blaum et al., 23]. Since the determination of ã is dependent on the Q-value of the beta decay and thus on the mass of argon-32, the value of ã had to be updated, resulting in 1.5 ±.52(stat) [Blaum et al., 23]. In order to evaluate the new systematic error, a re-analysis of the data is necessary. Nevertheless, the Standard Model value of 1 already lies within the (statistical) error bars of ã. Neutron Another isotope of interest for weak interaction studies is the neutron. Its decay is a mixed Fermi/Gamow-Teller transition, so it is sensitive to both scalar and tensor type interactions. Moreover, no nuclear structure effects have to be taken into account since it is a single nucleon. Recently, a new retardation spectrometer aspect was developed to measure the recoil proton spectrum after free neutron decay [Gluck et al., 25]. In order to study the properties of this spectrometer, the neutron beam MEPHISTO at the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (Research reactor

23 CHAPTER 1. THE WEAK INTERACTION 13 Munich II, also called FRM II) was used. The result of the first beam time in 26 is ã =.1151 ±.4(stat) [Baeßler et al., 28]. Systematic effects are still under investigation. After this proof of principle, another measurement was performed at the Institute Laue-Langevin in 28. The analysis of the acquired data is still ongoing and a final data-taking run is presently ongoing there as well. Nevertheless, a prominent factor of uncertainty in this experiment stems from the issues with the determination of the half-life of the neutron [Serebrov and Fomin, 21] which should be settled first in order to extract the best possible information on possible new weak interaction components from the aspect results. A few neutron half-life measurements are currently ongoing and planned (e.g. [Paul, 29]). Experiments Using Particle Traps With the development of atom and ion traps, a new series of beta-neutrino correlation experiments has emerged. Indeed, these traps enable the investigation of decay kinematics with minimal interference of scattering effects. The majority of these experiments are still ongoing and improvements are planned. 21 Na The decay of 21 Na was studied in 24 with a magneto-optical trap [Scielzo et al., 24]. 21 Na decays via a β + mirror transition: 21 Na(3/2 + ) 21 Ne(3/2 + ). This transition is mixed Fermi/Gamow-Teller, with the Fermi matrix element being unity due to isospin symmetry [Scielzo et al., 24]. The result of the measurement was ã =.5243 ±.91 which deviates 3σ from the Standard Model value of.5587±.27 [Severijns et al., 28]. The authors of [Scielzo et al., 24] already mentioned in their paper that there might have been a dependence on the trapped atom population. Therefore, further investigation was necessary. It turned out that the measurements were disturbed by photoassociation of molecular sodium in the trap. In order to reduce the effect of this molecular sodium, an improved experiment was performed [Vetter et al., 28]. This measured the ions in coincidence with shake-off electrons instead of positrons, which made the detection efficiency higher and thus allowed lower trap densities. The result of this measurement was ã =.552 ±.6, which nicely agrees with the Standard Model prediction. 38 K m A similar experiment was carried out at TRIUMF to determine the beta-neutrino correlation in 38 K m decay [Gorelov et al., 25]. Being a + + pure Fermi decay, it is sensitive to scalar weak interactions. Gorelov et al. obtained a value of ã =.9981 ± [Gorelov et al., 25]. In agreement with the Standard Model prediction of unity. 6 He + Recently, an experiment was designed to measure the beta-neutrino correlation coefficient of 6 He + decay using a Paul trap [Fléchard et al., 211]. As mentioned before in Section 1.3.3, 6 He + is a suitable candidate for beta-neutrino correlation measurements since it entirely decays to the ground state of 6 Li via a pure Gamow-Teller transition.

24 CHAPTER 1. THE WEAK INTERACTION 14 The experiment, called LPCtrap, is set up at the LIRAT beamline in GANIL Caen, France. During the run described in [Fléchard et al., 211], an average of 7 ions in the trap was reached. The obtained beta-neutrino correlation coefficient is ã =.3335 ±.73(stat) ±.75(sys). This agrees nicely with the Standard Model value of -1/3. Later new, higher-statistics data were taken (corresponding to a statistical precision of about.5%) which are still under analysis. 35 Ar With the LPCtrap setup a measurement with 35 Ar has been performed in June 212. These data are also still being analysed. This experiment has also provided the charge state distribution results that were listed in Table 1.2 [Couratin, 213].

25 Chapter 2 Experimental Setup This chapter describes the WITCH setup at ISOLDE, CERN. Section 2.1 starts with a general overview of isotope production and ion beam preparation at ISOLDE, followed by the specific approach taken for 35 Ar. In Section 2.2, the WITCH setup itself is presented. Each critical element of the experimental setup is highlighted, which is vital for a thorough understanding of the data analysis in Chapter ISOLDE The WITCH experiment is located at the ISOLDE hall 1 in CERN. This facility is designed to produce a vast range of radioactive isotopes using OnLine Isotope Separation techniques. The ISOLDE layout is given in Figure Radioactive Beam Production at ISOLDE Proton bunches are first accelerated to 1.4 GeV with a linear accelerator and the Proton- Synchrotron Booster. Intensities up to 2 µa can be reached per bunch and the repetition rate is 1.2 s. These proton pulses are then sent onto a target. The impact creates a broad range of isotopes through spallation, fragmentation or fission reactions. The elemental composition of the target determines which isotopes can be produced. Reaction products that are sufficiently volatile can diffuse out of the target, and are guided towards an ion source. The efficiency of diffusion and effusion depends on the physical and chemical properties of the element, the target, the transfer line and the target container [Duppen and Riisager, 211]. Typically, the target is heated to some 1 C to accelerate this process. 1 All information can be found on the ISOLDE website: 15

26 CHAPTER 2. EXPERIMENTAL SETUP 16 Figure 2.1: Overview of the ISOLDE hall. The created nuclei are then ionised by either electron impact ionisation in a high temperature plasma or by surface and resonant laser ionisation in a hot cavity [Duppen and Riisager, 211]. The mixture of ions is then accelerated to 3 kev or 6 kev (depending on the experimental requirements) and sent through a mass separator. Two such mass separators are available, each with their own target. The General Purpose Separator (GPS) has a resolution (m/ m) of approximately 1 and allows simultaneous extraction of three mass separated beams [Gorp, 212]. The High Resolution Separator (HRS) has a mass resolving power that exceeds 5, but it can only produce one radioactive beam. After having selected the required isotope, these radioactive ion beams are sent to the corresponding experimental setup Argon Production and Beam Preparation for the WITCH Experiment ISOLDE uses a CaO powder target for the production of argon beams. It was recently discovered that this type of target undergoes fast degradation due to sintering when exposed to high temperatures or high proton intensities. In order to prevent this deterioration, the effect of nanostructural properties on the target s performance has been examined

27 CHAPTER 2. EXPERIMENTAL SETUP 17 [Fernandes Ramos et al., 212]. The production process of the target was subsequently improved and higher yields were obtained in the WITCH runs of November 211 and November 212. To extract as pure an argon beam as possible, the transfer line between target and plasma ion source is water cooled. The less volatile elements diffusing out of the target will be adsorbed onto the wall of the transfer line, whereas noble gases are not. This way, unwanted reaction products are less likely to reach the plasma ion source, thus reducing isobaric contamination. In the plasma ion source, the argon atoms are brought to a charge state of 1+ via impact ionisation with high energy electrons in the plasma. This ion beam is then mass separated with the General Purpose Separator. The resulting beam consists mainly of argon and non-radioactive chlorine of mass 35. This beam is then transported to REXtrap for further manipulation. REXtrap consists of a large Penning trap (see Section for more information about Penning traps). The continuous radioactive ion beam coming from ISOLDE is accepted into the Penning trap and cooled down via collisions with neon buffer gas. The ions that are accumulated in the trap can be ejected towards the WITCH setup by changing the electrostatic potential that is applied in the Penning trap. This allows for a timespecific injection into the experiment. For future reference, it is important to note that the REXtrap setup operates at 3 kv. 2.2 WITCH A general overview of the setup is given in Figure 2.2. devoted to describing each element. The following subsections are Horizontal Beamline After the beam preparation in REXtrap, the ion bunches are sent through the horizontal beamline, which consists mainly of electrostatic elements for beam manipulation and focussing, like kickers, steerers and benders. The first kicker in the horizontal beamline acts as a beam gate for the WITCH setup. The voltage on this electrode pair determines if the ion bunches from REXtrap can reach the WITCH tower. Another important aspect of the horizontal beamline is the off-line ion source. Alkali ions such as 39 K + and 133 Cs + can be produced with a surface ionization source by heating an alkali-rich powder. The ions subsequently diffuse out of the ion source region and are trapped in a small Radio Frequency Quadrupole (RFQ). This RFQ consists of four parallel metal rods on which a radio frequency quadrupole field is applied. This ensures

28 CHAPTER 2. EXPERIMENTAL SETUP 18 Figure 2.2: Schematic drawing of the WITCH setup. Radioactive ions received from ISOLDE are cooled and bunched in REXTRAP, sent through the WITCH horizontal beamline (HBL) and vertical beamline (VBL), decelerated in the pulsed drift tube (PDT) and captured in the first penning trap (cooler trap, indicated in blue). After cooling and centering, the ions are transferred to a second trap (decay trap, indicated in green) where they are stored and left to decay. The recoil energy of the daughter ions from β decay is then probed by applying a voltage in the retardation spectrometer, which is located in the cryostat. Daughter ions with sufficient energy to pass the retardation barrier are accelerated and counted with the Micro Channel Plate (MCP) detector on top. The magnets indicated by the crossed, red rectangles. There are two superconducting magnets (6 T and.1 T) in the cryostat and a small resistive compensation magnet just above it. Taken from [Beck et al., 211]

29 CHAPTER 2. EXPERIMENTAL SETUP 19 trapping perpendicular to the rods. In addition, cylindrical electrodes surrounding these four rods are used to create a trapping potential parallel to the rods. Helium buffer gas is present in the RFQ to cool the ions and make sure they end up at the bottom of the potential well. When the ion cloud has been sufficiently cooled down, it can be ejected from the RFQ by switching the potentials on the electrodes. With this approach, ion bunches of stable isotopes can be produced for off-line testing purposes without using ISOLDE or REXtrap. In order to mimic the bunches that are coming from REXtrap, this ion source also operates at 3 kv Vertical Beamline After the ion bunches have traversed the horizontal beamline, they are steered into the vertical beamline. This beamline contains a pulsed drift tube (PDT) to take care of the potential difference between REXtrap and the WITCH tower. As mentioned before, the ion bunches coming from REXtrap or the off-line ion source have a potential energy of 3 kev, whereas the WITCH itself operates at ground potential. The pulsed drift tube is a cylindrical electrode which is kept at 21 kv when the ion bunch is moving from REXtrap (or the off-line ion source) to the vertical beamline. Hence the ion bunch obtains 9 kev kinetic energy and loses 9 kev potential energy when travelling to the PDT. When the bunch is inside the pulsed drift tube, the voltage is switched to -9 kv. Upon exiting the PDT, the ion bunch still has 9 kev kinetic energy. This kinetic energy is then reduced because of the electric field between the PDT at -9 kv and the Penning traps at V. Upon entering the first of the two Penning traps, the ions typically have a residual kinetic energy between ev and 25 ev. Note that it is not straightforward to guide these slowed ions into the magnetic field of the Penning trap. Indeed, just below the traps the stray magnetic field of the 6 T superconducting magnet is still quite strong. To optimize the injection of the ions into the trap, several drift electrodes and 3 steerer quadruplets were installed between the PDT and the traps Penning Traps After traversing the vertical beamline, the slowed ions are injected into the first Penning trap. In this section, the basic principles behind Penning traps are explained, as well as some useful properties concerning ion cloud manipulation. Next, the Penning traps of the WITCH experiment and the typical procedure for ion cloud preparation are introduced.

30 CHAPTER 2. EXPERIMENTAL SETUP 2 Figure 2.3: Schematic drawings of a hyberbolical (left) and cylindrical (right) Penning trap. Taken from [Gorp, 212]. Basic Principles The basic components of both an ideal and a cylindrical Penning trap are shown in Figure 2.3. The charged particles are confined along the radial direction by a strong static magnetic field, and along the axial direction by an electrostatic quadrupole field. The quadrupole field is created by applying a certain voltage on the ring electrode and the opposite voltage on the two endcaps shown in Figure 2.3. In the case of the ideal Penning trap, the hyperbolic shape of the electrodes ensures an ideal quadrupole electric field. In the cylindrical case, however, additional compensation electrodes are necessary to obtain a quadrupolar field around the centre of the trap. Even so, the farther away from the centre, the less accurate the quadrupole approximation becomes. The eigenmotions of a charged particle in this particular combination of electric and magnetic field are shown in Figure 2.4 (derivations can be found in [Bollen, 24]). Axially, the quadrupole electric field creates a harmonic potential and induces a harmonic oscillation around the trap centre. The angular frequency of this oscillation is given by qu ω z = md. 2 Here, q stands for the charge of the ion, U is the potential applied between the ring and endcap electrodes, m is the mass of the ion and d is related to the dimensions of the trap in the following manner: d = r/4 2 + z/2. 2 Radially, there are two eigenmotions: the magnetron motion (ω ) and the reduced cyclotron motion (ω + ). The respective frequencies are ω ± = 1 ( ω c ± ) ωc 2 2 2ωz 2, with ω c = ω + ω + = qb m, where ω c is the real cyclotron frequency. In a Penning trap, this frequency is slightly modified by the presence of the electric field. Hence the name reduced cyclotron frequency for ω +.

31 CHAPTER 2. EXPERIMENTAL SETUP 21 Figure 2.4: Eigenmotions of a charged particle in a Penning trap. The axial harmonic oscillation and the reduced cyclotron motion are stable. Reducing the total energy in these modes results in a decrease of the amplitude of the motion. The magnetron motion, on the other hand, is unstable. The radius of the magnetron motion becomes larger when reducing the total energy in this mode. This is because the electric field points radially outwards. The behaviour of a trapped ion is altered when there is more than one particle in the trap. The electrostatic repulsion between the ions changes their motion. Equations of motion are known for the single particle case and the many-particle plasma case, but the number of trapped ions in the WITCH experiment (which is typically ) lies somewhere in between those two regimes. This intermediate case is not yet fully understood. Hence, in order to gain insights in the behaviour of the ion cloud in the WITCH Penning traps, simulations that take into account the inter-ion Coulomb force are necessary. Chapter 3 explores this subject in more depth. Ion Cloud Manipulation The ion cloud inside a Penning trap can be manipulated in a myriad of ways. Here, only buffer gas cooling and the relevant applications of dipole or quadrupole excitations are discussed. Buffer gas cooling entails adding a buffer gas to the trap volume. This is typically a noble gas like helium or argon to prevent charge exchange with the ions in the trap. Through collisions with the buffer gas atoms, the ions lose kinetic energy. This process stops when the mixture is at thermal equilibrium. As mentioned above, during this process the amplitude of the axial oscillation will become smaller, just like the radius of the reduced cyclotron motion. The radius of the magnetron motion, however, will increase. This means that the ion cloud can gain in radius while being cooled. Hence pure buffer gas cooling is not recommended if a compact cloud is needed. To bypass this effect, an external excitation is necessary.

32 CHAPTER 2. EXPERIMENTAL SETUP 22 Figure 2.5: Segmentation of the ring electrodes required for dipolar (left) and quadrupolar (right) excitations. The arrows indicate the direction of the electric field created by the applied excitations. Taken from [Tandecki, 211]. In order to apply radio frequency excitations to the Penning trap volume, segmented ring electrodes are necessary. Figure 2.5 shows which type of segments are needed for dipolar and quadrupolar excitations. Three useful excitations are listed below, where ion species is defined as ions of a certain mass. Dipole excitation at ω Applying a dipole excitation at the magnetron frequency of a certain ion species results in an increase of the radial distance to the centre of the trap. On average, this effect grows linearly with the duration of the excitation and is proportional to its amplitude. Since the magnetron frequency is (to first order) independent of mass, all ions will get to a larger radius when this excitation is applied. Dipole excitation at ω + Applying a dipole excitation at the reduced cyclotron frequency of a certain ion species results in the decentering of that specific ion species. This is because the reduced cyclotron frequency is dependent on the mass of the ions. Quadrupole excitation at ω c Applying a quadrupole excitation at the cyclotron frequency of a certain ion species results in a coupling of the magnetron and reduced cyclotron motion of that ion species. This means that the magnetron motion is periodically converted into a reduced cyclotron motion and vice versa. It is similar to Rabi oscillations of an atomic two-level system [Bollen, 24]. One particularly useful application of this excitation is in buffer gas cooling. The amplitudes of both motions are reduced because of the cyclotron coupling between the two and the damping influence of the buffer gas. Eventually, the ions will end up cooled in the centre of the trap. Remember that the cyclotron frequency is mass dependent, hence this cooling and centring technique works only for the ions of that specific mass.

33 CHAPTER 2. EXPERIMENTAL SETUP 23 The WITCH Penning Traps The WITCH Penning traps consist of two cylindrical Penning traps separated by a small pumping diaphragm. A technical drawing can be found in Figure 2.6. The lower trap, which is called the cooler trap, contains He buffer gas to enable cooling of the ion cloud. Typical buffer gas pressures range from 1 4 to 1 5 mbar. The helium is prevented from diffusing upwards to the second trap (known as the decay trap) by a differential pumping diaphragm. This diaphragm is a tube of 5 cm with a radius of 2 mm. Given the small diameter of the tube, the estimated pressure in the decay trap is 26 times smaller than in the cooler trap [Gorp, 212]. This is sufficiently low for the trapped particles to be able to decay without scattering. The magnetic field for both traps is generated by a superconducting magnet which is located in the cryostat. The trap electrodes are placed in the bore tube of this superconducting magnet. Magnetic fields up to 9 T can be generated, with a field homogeneity of B/B < 1 5 [Gorp, 212]. The characteristic trap parameter U /d 2 equals V/m 2 for both traps when a voltage of 16 V is applied to the endcaps. The central ring electrode of both traps is divided into eight segments to enable different types of radio frequency excitations. A typical procedure for trapping radioactive ions is shown in Figure 2.7. An explanation of the different steps is given below. a) After the ion bunch is slowed down with the PDT, the ions are injected into the cooler trap. The voltage on the bottom endcap is kept low so the ions can enter the trap, whereas the upper endcap of the cooler trap is kept at typically 1 V to prevent the ions from exiting the trap. b) When the ion bunch is completely within the cooler trap, the bottom endcap is switched to the same voltage as the upper endcap. The ions are now trapped and cooled through collisions with the He buffer gas. Steps a) and b) can be repeated several times to allow multiple bunches into the cooler trap. c) After roughly a hundred milliseconds, the ions have cooled down to a few ev and the outer endcaps are lowered. The ions are now trapped in a shallow potential of around 1 V. At this time, excitations can be applied to centre the ions or to selectively remove a certain ion species. d) When the cloud is sufficiently cooled, it is transferred to the decay trap by switching to a Wiley-McLaren type of potential. This type of potential is optimized to keep the velocity and position distribution before and after the transfer the same. e) After the transfer of the ion cloud to the decay trap, the potential in this trap is switched to a quadrupole trapping potential. The ion cloud is now stored and acts as a scattering-free radioactive source. Recoil ions which have enough energy to overcome the trapping potential are able to escape from the decay trap. Half of the ions move towards the retardation spectrometer, whereas the other half is lost on the pumping diaphragm.

34 CHAPTER 2. EXPERIMENTAL SETUP 24 Figure 2.6: Geometry of the WITCH Penning traps. The cooler trap is separated from the decay trap by a differential pumping diaphragm of 2 mm radius. The total length of the traps is 42.8 cm. The buffer gas inlet for the cooler trap is also shown. The endcap electrodes of the traps are denoted by EE, the correction electrodes by CE, and the central ring electrode by RE.

35 CHAPTER 2. EXPERIMENTAL SETUP 25 Figure 2.7: Overview of a typical WITCH trapping cycle. The full line represents the applied voltage in the traps, the dotted line indicates the barrier between cooler trap (left) and decay trap (right). The blue/grey cloud stands for the buffer gas. The blue spheres represent radioactive ions, the red spheres are the recoiling daughter nuclei. f) After typically a few seconds, when the measurement cycle is over, the remaining ions are either shot out downwards (to the left in the figure) or ejected onto the walls of the decay trap using a dipole excitation at the magnetron frequency. This way, the traps are emptied. They are now ready to accept the next ion bunch for a new measurement cycle. A single measurement cycle with 35 Ar tends to take about 5 s Retardation Spectrometer The energy of the recoil ions that originate from the decay trap is analysed with a retardation spectrometer. This apparatus consists of a slowly decreasing magnetic field which is high at the two Penning traps (6 T) and low at the analysis plane (.1 T). An overview of the upper part of the WITCH tower is given in Figure 2.8. The analysis plane is situated at z = 1 cm. Recoil ions which move through the retardation spectrometer undergo magnetic adiabatic collimation: kinetic energy perpendicular to the magnetic field lines is transformed into longitudinal kinetic energy. This is based on to the principle of conservation of magnetic flux. The exact amount of conversion depends on B min /B max. In the WITCH case, with B min /B max = 6.T/.1T, only 1.67% of the initial radial kinetic energy is left when the ions reach the analysis plane, the remainder having been transformed into longitudinal

36 CHAPTER 2. EXPERIMENTAL SETUP 26 Figure 2.8: Schematic representation of the retardation spectrometer. The strength of the magnetic field and the electrostatic potential are shown in the graph on the z-axis. Taken from [Gorp, 212] energy. The longitudinal energy of the recoil ions can then be probed by creating a potential barrier at the analysis plane, i.e. by applying a certain retardation voltage to the main spectrometer electrode. The ions which get past this potential barrier are then post-accelerated to a few kev and focused onto a position sensitive MCP detector. An integrated energy spectrum can thus be obtained by counting the ions in function of the height of the potential barrier. A diagnostic spectrometer MCP was installed between the two post acceleration electrodes indicated in Figure 2.8. This detector is meant to monitor ions that are ejected from the traps. It is often used in off-line experiments for systematic studies of ion cloud behaviour. One of the main challenges of a retardation spectrometer is the unwanted accumulation of charged particles. These particles are moving around in the spectrometer volume and can create ionisation along their path when interacting with the residual gas. The secondary charges thus produced can create an avalanche effect of ionisation, which may end up on the MCP detector. As can be seen from the magnetic and electric field configuration in Figure 2.8, there are several places where positively or negatively charged particles can be trapped. For example, when applying a retardation voltage to the main electrode, a potential well is created for negatively charged particles between z = 5 cm and z = 15 cm. The depth of this potential depends on the retardation voltage. Ionisation which is created by the

37 CHAPTER 2. EXPERIMENTAL SETUP 27 particles in this trap and ends up on the detector creates a retardation voltage dependent background which interferes with the spectrum of recoil ions. In order to remove these particles, a wire was installed at the analysis plane (z = 1 cm). This wire collects any negatively charged particles that hit it. A second unwanted trap that was taken care of is situated near the einzel lens section (z = 22 cm). The high negative voltages in the reacceleration section and on the MCP, together with the stray fields of the 6 T and.1 T magnets, create a Penning-like trap for negatively charged particles. Moreover, the high voltages on the electrodes can induce ionisation due to field emission. A compensation magnet of -1 mt was installed near the einzel lens to reduce the magnetic field near it and effectively empty this unwanted Penning trap MCP detector A Micro Channel Plate detector was chosen because it is the only type of detector able to detect (post-accelerated) ions of a few kev with high efficiency and handle a high count rate. An MCP detector consists of one or more Micro Channel Plates. Such a plate contains between 1 5 and 1 6 coated channels which each act as an electron multiplier when a high voltage is applied over the detector (typically a few kv). The radius of these channels is typically a few microns, hence the name of the detector. The channels are tilted 8 with respect to the normal to avoid ions flying straight through the channels. When an ion hits the inner wall of one of the channels, an avalanche of electrons is created, as illustrated in Figure 2.9a. An anode is placed behind the MCP to collect the charges that are created in the channel. The specific type of MCP that was chosen for the WITCH experiment is the Roentdek DLD8 position sensitive MCP. This detector has an active radius of 83 mm and channels with a pore size of 23 µm. It contains two plates which are in chevron configuration (see Figure 2.9c). The anode in this detector consists of two sets of delay lines. A delay line anode consists of a wire convoluted to a coil. The electron avalanche coming from a micro channel hits the wire at a certain position and creates a signal. This signal travels to both ends of the coil. From the difference in travel time, the origin of the signal can be determined. This is illustrated in Figure 2.9b. Placing a second delay line anode perpendicular to the first one, a two-dimensional position can be reconstructed. For each event registered by the MCP detector, the following information is saved: Time The time at which the particle hits the channel, as well as when the signals from the delay lines arrive. Position The 2D position of the particle can be determined from the difference in arrival time of the corresponding ends of the two delay line anodes. Pulse height The pulse height of the signals created on the plate and in the delay lines.

38 CHAPTER 2. EXPERIMENTAL SETUP 28 (a) Micro channel. (b) MCP with delay line anode. (c) Chevron configuration. Figure 2.9: Drawings of an MCP detector. Incoming radiation creates an electron avalanche in one or more channels of the Micro Channel Plate (a). These charges are collected on a delay line anode (b). The position of the incoming particle is determined from the difference in travel time to both ends of the wire. The chevron stacking of two plates is illustrated in (c).

39 Chapter 3 Simulations with Simbuca This chapter focuses on the code used to simulate the behaviour of ion clouds in the WITCH Penning traps, i.e. Simbuca [Gorp et al., 211]. First, the role of Simbuca in the full simulation procedure is presented in Section 3.1. Then, the method used to obtain the angular correlation coefficient a from the experimental measurements is explained. Next, an introduction to the main features of Simbuca is given in Section 3.2. Lastly, Section 3.3 touches upon an interesting physical feature that was found in one of the offline measurements. By simulating these measurements, the origin of the observed effect becomes clear. 3.1 Introduction The goal of the WITCH experiment is to determine whether the Standard Model adequately describes nuclear beta decay. More concretely, the β-ν angular correlation coefficient a defined in Section will be determined for 35 Ar and its value will be compared to the Standard Model prediction of.94(16). However, the WITCH setup is designed to measure the number of recoil ions coming from the decay trap in function of the retardation voltage, implying that simulations are needed to extract a from this spectrum. When working with a radioactive source in a precision experiment, it is of utmost importance that the properties of the source are exactly known. The source of the WITCH experiment is an ion cloud in the decay trap. However, the behaviour of an ion cloud of typically 1 6 particles in a Penning trap is rather complex. It deviates markedly from the single particle picture, but is not yet in the plasma regime. There are no analytical solutions to its equation of motion because the Coulomb interaction couples all ions [Tandecki, 211]. Therefore, simulations are necessary to characterise the ion cloud. The simulation package that is up to this task is the Simbuca code. It was developed specifically for the WITCH experiment [Gorp et al., 211]. An overview of its features is presented in the next section. 29

40 CHAPTER 3. SIMULATIONS WITH SIMBUCA 3 Once the behaviour of the radioactive ions in the trap is simulated, the next step is to incorporate the creation of recoil ions and to trace their path through the spectrometer. The SimWITCH package is used for this [Friedag, 213]. It is a Monte-Carlo tracking routine that uses the output of Simbuca as initial positions and momenta for the radioactive ions. To emulate the recoil of the daughter nucleus after β decay, momentum is added in a random direction to one of the particles. The magnitude of the added momentum is sampled from a distribution according to a certain (chosen) value of a. The trajectory of this particle through the WITCH setup is then simulated using an ion tracking routine. Hence, for a certain value of a, the number of recoil ions that successfully reach the detector can be determined in function of the retardation voltage. This spectrum can be fitted to the experimental spectrum to determine the ideal value of a. It is clear that Simbuca and SimWITCH play an essential role in determining the value of a, so it is very important that their results are reliable. Hence, a thorough investigation of their correctness is warranted. This can be done by performing well-controlled measurements and comparing the results of these with simulations using both packages. 3.2 Simbuca Simbuca was developed by S. Van Gorp to simulate ions moving in a Penning trap. It is freely available under the GNU General Public License 1. Simbuca takes the Coulomb interaction between ions into account by adapting the output of the Cunbody-1-library [Gorp et al., 211]. This library calculates the gravitational interaction between matter on a Graphics Processing Unit (GPU). Using that library is possible because the form of the equations for the Coulomb and gravitational force is identical. Furthermore, by using the GPU, the calculation time is reduced considerably, making it possible to simulate larger clouds in a reasonable amount of time. The essential features of Simbuca are summarized in the following list: Trap configuration Either an ideal Penning trap can be used in the simulations, or the electric and magnetic fields of an existing trap can be provided through field maps. For the WITCH Penning traps in particular, the magnetic field map was obtained from the manufacturer of the magnet. The electric field map can be created with the program COMSOL 2. The geometry of the Penning trap electrodes is implemented in the program and by specifying the voltage on the electrodes, the field map can be calculated. Parameters of the ion cloud The number of initial ions can be specified, as well as the percentage of different isotopes that make up the cloud. Initial position, dimensions and energy of the cloud can be set. 1 Simbuca can be downloaded from its Sourceforge site simbuca/ 2 For more information, see

41 CHAPTER 3. SIMULATIONS WITH SIMBUCA 31 Integrating the equations of motion There are three integrators implemented in Simbuca: a first order Gear method, a fourth order RungeKutta method and a fifth order DormandPrince method. For each integrator, the time step can be fixed to a given value, or it can be set to adaptive. Operations There are several operations implemented in Simbuca: dipole/quadrupole/octupole excitation, rotating wall excitation or no excitation. Each time, the use of buffer gas is optional. Coulomb interaction It is possible to use a scaled Coulomb force. Here, more weight is put to the charge of one ion to simulate more ions. For example, a cloud of one million particles can be simulated using a thousand particles with a Coulomb scale factor of 1. Moreover it is possible to disable the Coulomb interaction between ions, while still keeping the interaction with external fields. 3.3 Axial Motion In this section, a measurement to determine the axial motion in the decay trap is introduced. This measurement was performed in an off-line experiment and shows some interesting non-trivial physical effects. Simulations are shown to be valuable in explaining the observed behaviour of the ions. As a bonus, this type of measurement is specifically suited as a consistency test for Simbuca: it is especially sensitive to the physical correctness and numerical stability of the simulation Optimal Transfer Time Figure 3.1 shows what happens to the ion cloud for different transfer times from cooler to decay trap. We define the transfer time as the time that the transfer potential is active in the traps: from switching from cooling to transfer potential, until switching from transfer to decay potential. The blue curve stands for the axial potential well of the cooler trap, the black curve depicts the decay trap. The Wiley-McLaren transfer potential is shown in red. The cooled ion cloud is represented by the orange circle in the cooler trap. After sufficient buffer gas cooling, it is situated at the bottom of the potential well. When the voltages on the trap electrodes are switched from the cooler trap potential to the transfer potential, the ion cloud starts to move towards the decay trap. When the transfer time has passed, the transfer potential is switched to the decay trap potential. The optimal situation would be that the transfer potential is switched to the trapping potential when the ion cloud is exactly in the centre of the decay trap. In this way, no potential energy is gained by the ion cloud upon switching. This case is represented by

42 CHAPTER 3. SIMULATIONS WITH SIMBUCA 32 Figure 3.1: Schematic drawing of the transfer of an ion cloud from the cooler trap to the decay trap. When the transfer time is just right, the ion cloud ends up in the middle of the decay trap, as show in purple. When the transfer time is too short or too long, the ion cloud will oscillate up and down in the decay trap after transfer, as shown in green. the purple circle in the decay trap in Figure 3.1. However, when the transfer time is too short, the ion cloud has not reached the centre of the decay trap yet when the trapping potential is applied. This results in an increase of potential energy, after which the cloud will start oscillating up and down in the trap, as illustrated in Figure 3.1 with the green circles. If the transfer time is too long, the ion cloud is reflected by the transfer potential and moves back towards the cooler trap. Upon applying the trapping potential, the ions receive a similar energy boost and will start oscillating axially Measuring the Axial Motion In order to get a handle on the axial position of the ion cloud, the ejection potential shown in red in Figure 3.2 was designed. The blue curve represents the trapping potential of the decay trap. When the cloud is below the decay trap centre, and thus on the left side of the centre of the blue potential well in Figure 3.2, it will gain potential energy when the trapping potential is switched to the ejection potential. The total amount of energy

43 CHAPTER 3. SIMULATIONS WITH SIMBUCA 33 Figure 3.2: Schematic drawing of the ejection procedure to determine the axial position of the ion cloud. Ions below the center can escape (orange), whereas ions above the center are trapped (green). is higher than the potential barrier applied at the end of the decay trap, hence the ion cloud is effectively ejected from the decay trap. This is illustrated with the orange circles in Figure 3.2. When the ion cloud is on the other side of the centre, its potential energy will be reduced upon switching. The cloud now lacks sufficient energy to overcome the potential barrier at the end of the decay trap. This situation is indicated with the green circles in Figure 3.2. The potential barrier at the end of the decay trap has a height of.5v to ensure that ions coming from the centre of the trap are blocked, hence increasing the contrast between the extremal axial positions. The experimental procedure is sketched in Figure 3.3. First the ion cloud is prepared in the cooler trap as shown in steps (a) (c). Then, the cloud is transferred to the decay trap with a Wiley-McLaren potential (d) for a certain transfer time t tr. The ion cloud is then trapped in the decay trap (e) for a certain time t DT. Subsequently, the ions are subjected to the ejection potential described in the previous paragraph (f). The number of ions ejected from the decay trap is monitored with the spectrometer MCP. If this whole procedure is repeated for a range of values for t tr and t DT, a plot like the one shown in Figure 3.4 can be produced. Because of the pattern in this plot, this type of measurement is called a wingplot measurement. The experimental conditions for which Figure 3.4 was obtained are summarized below. Voltage over MCP plates: 21 V Magnetic field: 3 T

44 CHAPTER 3. SIMULATIONS WITH SIMBUCA 34 Figure 3.3: Schematic overview of the measurement procedure. The potential in (f) is the same as the red one in Figure 3.2. Buffer gas pressure measured at the cross piece: mbar Depth of the quadrupole in the cooler trap: 15 V Depth of the quadrupole in the decay trap: 15 V Number of accumulations from the off-line ion source: 2 Cooling time: 2 ms Transfer potential: Wiley-McLaren potential of 14 V The transfer time ranges from 31 µs to 33 µs (in steps of.5 µs) and the trapping time is scanned from ms to 1.4 ms in steps of 5 µs. Notice that the pattern has a very small oscillatory period in the horizontal and vertical direction, compared to the total cooling and trapping time. As such, it is very sensitive to the oscillatory frequency of the ion cloud. Hence, if we were to simulate this measurement, the result would be very sensitive to both the physical correctness of the code, and the numerical stability for long simulations. The Pattern Explained? The pattern that is obtained in Figure 3.4 is related to the axial motion of the ion cloud in the trap. As explained in the previous section, ions that are below the centre of the decay trap when the ejection potential is applied, are ejected from the trap. These ions thus create a signal in the spectrometer MCP. The ions that are above the centre upon ejection, are stopped by the potential barrier and hence don t create a signal. This way,

45 CHAPTER 3. SIMULATIONS WITH SIMBUCA 35 Figure 3.4: The results of the transfer time vs. trapping time measurement. The colour scale indicates the integrated signal on the spectrometer MCP (arbitrary units). information about the axial position of the ion cloud can be extracted. When looking at one column in Figure 3.4, the axial position of the ion cloud can be tracked in time for a specific transfer time. It is clear from Figure 3.4 that the ion cloud oscillates axially in the decay trap for all transfer times, except for the ideal transfer time just below 32 µs. Indeed, for that transfer time, the cloud ends up exactly at the minimum of the trapping potential and will not oscillate. When looking at neighbouring transfer times, this blue-white oscillation seems to have shifted. This can be explained when combining two observations. Firstly, the decay trap is not a perfect Penning trap. The electric field does not have a perfect quadrupole shape because of the cylindrical electrodes. This deviation from the ideal case is clearly visible in Figure 3.5. It shows the (simulated) axial frequency in function of the amplitude of the oscillation. The colours indicate the radial position of the particle. These results were obtained by simulating one particle in the decay trap and fitting a sine to its z-component for different initial positions. In an ideal trap, the frequency would remain constant in function of amplitude and radius. Secondly, one has to consider the effect of non-optimal transfer times. When the transfer time is too short, the ion cloud will not have reached the centre of the decay trap when the voltages are switched to the quadrupole trapping potential. This means that the ion cloud was placed (axially) off-centre in the decay trap. Hence, it will start oscillating around the centre with a certain amplitude and frequency. The closer to the optimal transfer time, the smaller the amplitude of the oscillation, and the larger the frequency (according to Figure 3.5). The same holds for the transfer times that are too long. Combining the relation between transfer time and amplitude with the relation between amplitude and frequency, one can understand that the small difference in transfer time results in a small difference of frequency between neighbouring columns in Figure 3.4. This leads to a larger and larger phase shift between the two oscillations as time passes.

46 CHAPTER 3. SIMULATIONS WITH SIMBUCA 36 Figure 3.5: Axial amplitude versus axial frequency. The colour indicates the radius: 3 mm > red > yellow > green > blue > mm. These results were obtained through simulations.

47 CHAPTER 3. SIMULATIONS WITH SIMBUCA 37 Note that we assumed that the oscillating ion cloud remains coherent, i.e. that it is a single ion packet that oscillates back and forth. This is not evident a priori. Indeed, the Penning trap is not ideal, so dispersive effects are expected for oscillations at different amplitudes. This would have the tendency to smear and eventually homogenize the vertical direction of Figure 3.4. Secondly, the ions also interact amongst themselves through the Coulomb repulsion. As previously explained, the regime with the number of particles that are used in the experiment is still quite badly understood. In order to explain the coherence, either the dispersion must be sufficiently small to not manifest itself significantly after the trapping time of 1 ms, or the Coulomb interaction must help to keep the dispersion at bay. In the following section, it will be shown that it is the Coulomb interaction that plays the crucial role Qualitative Investigation In this section, simulations are used to show how the qualitative structure of Figure 3.4 emerges from the combined effects of dispersion and Coulomb repulsion. The influence of dispersion is studied by varying the initial energy of the ion cloud. The higher the energy, the larger the spread in axial amplitudes after the transfer. The effect of Coulomb repulsion is investigated in two ways: a vast range of effective ion numbers is used in the simulations, and the Coulomb interaction between the ions is switched off during one simulation. The simulation procedure is presented below and followed by a discussion of the results which are shown in Appendix A. Simulation Procedure The initial ion cloud configurations are generated as follows: an ion cloud is initialised in the centre of the trap with a radius of 1 mm and an initial Maxwell Boltzmann energy distribution 3 of 1 ev. This cloud is then cooled with a buffer gas of 1 4 mbar (as suggested by [Gorp, 212]) and the positions and momenta of the particles are saved after every 1 ms of cooling. For each saved cloud, the total energy is calculated for each particle, using the momenta to determine the kinetic energy and the positions to determine the potential energy derived from the field map. The distribution of these energies is then fitted with a Maxwell Boltzmann energy distribution. The resulting MB energies are used to track the state of the ion cloud during cooling. In order to investigate the effect of the energy in the cooler trap on the pattern of measurements, the cooling process was stopped at a wide range of Maxwell Boltzmann energies: 16 mev, 1 mev, 65 mev, 325 mev, 18 mev and 1 mev. The corresponding cooled ion clouds are then used as initial configuration for the subsequent simulation. This procedure is repeated for a broad range of effective ion numbers. The precise combinations of ion number and scaling factor are shown in Table A.1 in the appendix, on page 81. For the high effective number of ions, simulations were repeated once with 25 3 A Maxwell-Boltzmann (MB) distribution of energy E is a MB distribution where the point of maximum probability corresponds to that energy E.

48 CHAPTER 3. SIMULATIONS WITH SIMBUCA 38 real ions and once with 1 real ions (with the scaling factors adjusted accordingly). This was done to cross check if the scaled Coulomb force gives similar results for the same effective number of ions. Steps (d), (e) and (f) of the measurement procedure are then simulated for each energy distribution and for all ion numbers using the voltages on the electrodes to generate the corresponding field maps. The height of the simulated signal is then determined from the number of ions that escape from the trap over the potential barrier of.5 ev. The results of these simulations can be found in Appendix A. Discussion of the Results As mentioned in the previous paragraph, the winglike structure is a result of the approximated quadrupole potential of the decay trap. This creates a dependence of axial frequency on (axial) amplitude. Hence, if there is a little spread in the axial amplitudes of the ions, one would expect dispersion of the whole ion cloud after a while. However, this is not what is seen in the first column of Figure 3.6. The black and white lines don t become grey after 1 ms (middle row) or even 2 ms (bottom row) of trapping. When switching off the Coulomb interaction between the ions, the second column of Figure 3.6 is obtained. Here, it is clear that the ion cloud has a certain spatial spread which results in a spread in frequency and thus in dispersion of the ion cloud. The black and white lines are still visible in the top row, but become less and less pronounced as time goes by. It thus seems that the repulsive Coulomb interaction ensures a synchronisation of ion movement. This effect has been observed before in the case of charged particles oscillating between two electrostatic mirrors [Pedersen et al., 21] and also in a Fourier transform ion cyclotron resonance cell [Nikolaev et al., 27]. The name given to this effect is phase locking. As can be seen from the simulation results in Appendix A, the initial energy of the ion cloud and the number of ions determine when phase locking occurs. For the range of energies investigated, it seems that the Coulomb interaction only starts to dominate the dispersion effects when 25 ions or more are in the trap. Even so, the phase locking is gone when the energy of the ion cloud crosses a certain threshold. For 25 ions, this threshold seems to be at 18 mev. Moreover, the phase locking becomes stronger when more ions are present in the traps. The winglike pattern is seen for higher and higher energies when the number of ions is increased. For 2 5 ions, the threshold energy is above 1 ev. The simulations for the same effective amount of ions produce similar wingplots. The position of the black and white structure seems almost identical for all pairs of simulations, except for 2 5 ions. Indeed, the plots for 18 mev and 325 mev show deviations

49 CHAPTER 3. SIMULATIONS WITH SIMBUCA 39 Ion cloud energy: 1meV 25 ions With ion ion interaction Ion cloud energy: 1meV 25 ions Without ion ion interaction Ion cloud energy: 1meV 25 ions With ion ion interaction Ion cloud energy: 1meV 25 ions Without ion ion interaction Ion cloud energy: 1meV 25 ions With ion ion interaction Ion cloud energy: 1meV 25 ions Without ion ion interaction Figure 3.6: Wingplots for 25 ions and 1 mev. The first column shows the simulation with Coulomb interaction between the ions, the second column shows the same plot without ion-ion interaction. The top row contains trapping times from ms to 1 ms, the trapping time in the middle row ranges from 9 ms to 1 ms. The bottom row shows the simulations for trapping times between 19 ms and 2 ms.

50 CHAPTER 3. SIMULATIONS WITH SIMBUCA MB energy: 325meV 1*25ions MB energy: 325meV 1*25ions Figure 3.7: Wingplots for 1*25 ions. The left and right plots are started from two independently sampled initial configurations with Maxwell Boltzmann energy of 325 mev. between simulating 25*1 and 1*25 ions. The effect is most visible on the left side of the wingplots. This might indicate that the scaled Coulomb force calculation is not 1% reliable for scaling factors in and above the range of 1. As a word of warning, note that all simulations that are shown with the same initial energy and the same number of ions are started from identical initial configurations of the ion cloud, which was generated as explained above. Hence, it is possible that sampling another initial configuration with the same energy and redoing the simulations with those starting points can explain some of the observed differences between 25*1 and 1*25 ions. However, due to time constraints 4 we could not fully verify this for all plots. However, we did test this for the case of 25*1 ions with initial energy of 325 mev, as shown in Figure 3.7. Although there is some variation between the plots (the right plot seems to be shifted to the left somewhat), it is certainly not of the same magnitude as the difference with the 1*25 ions plot at 325 mev in Figure A.1. Currently ongoing investigations have also found deviations when simulating the cooling of 25*1 versus 1*25 ions [Porobic, 213], reinforcing the suspicion that Coulomb scaling factors of 1 are too crude Reproduction of the Measurement In order to see if Simbuca can reproduce the measured wingplot in Figure 3.4, the entire measurement procedure was simulated. Unfortunately, there are two unknown parameters: the number of ions and the buffer gas pressure in the cooler trap. From previous measurements with the off-line ion source, it seems likely that the number of ions in the 4 Each wingplot consists of 41 individual simulations. Depending on the number of simulated ions and the scaling factor for the Coulomb force, the CPU/GPU time needed to simulate one wingplot varies from about a day (e.g. for 1*25 ions) to almost a month (for the case of 25*1 ions).

51 CHAPTER 3. SIMULATIONS WITH SIMBUCA 41 cooler trap during this measurement is a few 1 4 to 1 5. Hence the wingplots are simulated for 25 and 25 ions with 25 real ions and a Coulomb scaling factor of 1, respectively 1. The buffer gas pressure at the cross piece was measured, but this can only give an estimate of the pressure in the cooler trap: it probably ranges between mbar and mbar. As such, the wingplot is simulated for both of these values. The following simulation procedure was used. An ion cloud of 1*25, respectively 1*25, is initialized in the cooler trap with a MB energy of 1 ev and a radius of 1 mm. Next, buffer gas cooling is applied for 2 ms with buffer gas pressure mbar or mbar. Then the transfer is simulated, as well as the trapping in and ejection from the decay trap. The results of these simulations are shown in Figure 3.8. It seems that the influence of the buffer gas pressure on the wingplot is negligible, the top and bottom rows are almost identical. There is a difference however between de plots for 1*25 and 1*25. The whole structure seems to have shifted a bit upwards when going from 1*25 to 1*25 ions. When comparing these results to the measurement in Figure 3.4, there are some discrepancies. The slope of the curves in the measurement is steeper than the slope in the simulations. Moreover, the optimal transfer time seems to have shifted towards lower values in the simulations. The optimal simulated transfer time is µs, whereas the measured optimal transfer time is around 31.9 µs. These two discrepancies can be due to instability in the code, but there is also another plausible explanation: the switching of potentials happens infinitely fast in the simulations, whereas in real life, the switching happens during a finite time. The finite switching times can influence the effective speed at which the ion cloud is transferring from cooler to decay trap. It seems that the transfer happens faster in the simulations. The different slope of the curves in the plot indicate that the relation between transfer time and axial amplitude is altered. Again, due to the finite switching times, the energy that is gained or lost upon switching can be different than for the ideal case. Another possibility is that the potentials which are applied in the simulation are not exactly equal to the real potentials, as the slope of the wingplot is extremely sensitive to such deviations. Nevertheless, qualitatively, measurement and simulation are in very good agreement Conclusion We found that caution is advised when trying to simulate along the order of 1 6 or more effective particles with large Coulomb scaling factors of order 1 4, as the scaled Coulomb force calculations then give inconsistent results.

52 CHAPTER 3. SIMULATIONS WITH SIMBUCA Buffer gas: 25nbar 1*25ions Buffer gas: 25nbar 1*25ions Buffer gas: 2nbar 1*25ions Buffer gas: 2nbar 1*25ions Figure 3.8: Wingplots for 1*25 ions (left) and 1*25 ions (right). The top row contains the results for mbar buffer gas pressure, the bottom row belongs to mbar buffer gas pressure.

53 CHAPTER 3. SIMULATIONS WITH SIMBUCA 43 Furthermore, we found no exact match between the experimental and simulated wingplots. This can possibly explained by finite switching times in the experiment that are not yet taken into account in the simulation, or slight deviations between simulated and real trap potentials. Hence no definitive conclusion about the physical correctness and numerical stability of Simbuca can be made with the data at hand. Nonetheless, it is pleasant to see that the qualitative pattern is replicated. Doing so, we also found evidence of an interesting phenomenon called phase locking. This effect only manifests itself when the Coulomb interaction between the ions is taken into account. It seems that the parameters that determine the occurrence of this effect are the number of ions and the energy of the ion cloud.

54 Chapter 4 Data Analysis This chapter pertains to the analysis of the data that was taken during the experimental run in November 212. This run is the first set of measurements with radioactive argon that gathered enough statistics to be physically relevant. During previous runs with 35 Ar, either technical issues at the WITCH setup or problems with the CaO target limited the quantity and quality of data that was taken. Considering the large amount of data and the fact that time is restricted to the span of a master s thesis, only the data of highest quality is analysed in this chapter. Even so, the analysis of a high precision experiment typically takes longer than a few months. Indeed, even the smallest of effects need to be fully understood before drawing conclusions. Furthermore, there is no pre-existing, fixed methodology for extracting the recoil spectrum from the measurements, as this is the first data set in the history of the experiment with sufficiently high statistics. Hence, part of the goal of this thesis was to develop a novel strategy for analysing this type of WITCH data and extracting as much information as possible. The results hereof are described in this chapter. A general overview of the data handled in this chapter is given in Section 4.1. Section 4.2 gives a detailed account of the selection procedure that was used to remove as much background effects as possible. Section 4.3 pertains to the fitting of the selected data. The different aspects of the fitting procedure are presented and the fit results are carefully scrutinized. Finally, effects that require more investigation are summarized in the outlook at the end of this chapter. 4.1 General Overview This section provides a general overview of the data that was accumulated in November 212. The information that is saved per event is summarized in Section These events are part of a measurement cycle. The time structure of a measurement cycle is 44

55 CHAPTER 4. DATA ANALYSIS 45 discussed in Section Measurement cycles are grouped into runs, according to the retardation voltages that are applied. An overview of the runs that are selected for this thesis is given in Section Events All information of particles that hit the main MCP detector is registered with the FASTER data acquisition system. This electronics module was developed by the engineering department of LPC Caen. It was installed at the WITCH setup in October 212, replacing the old CAMAC system which performed unsatisfactorily (one of the reasons the previous runs were not successful). Two types of events are registered with the FASTER data acquisition system. The first type of event is a particle triggering a channel of the MCP. As mentioned in Section 2.9, there are several pieces of information saved for this type of event. The time at which the particle hits the MCP plate is recorded, as well as the corresponding pulse height of the signal that is created. Furthermore, the arrival times of the four pulses travelling through the two delay line anodes is registered, together with the respective pulse heights. For each pulse height signal, a saturation flag is implemented, which indicates if the height of the signal is larger than a certain threshold. In our experiment, the threshold was set at 1 V. From this information, the time, position and pulse height of an event can be determined. The second type of event is an external trigger event. This signal does not originate in the MCP detector, but is sent from REXtrap when an ion bunch is injected into the WITCH beamline. It indicates the start of a measurement cycle and is used to synchronize the time structure of the WITCH setup with the argon bunches coming from REXtrap. More about this in the following section Cycles The events that are registered between one proton pulse on the CaO target and the next, are part of a measurement cycle. Such a cycle has a duration of 6 s or more, depending on the time interval between the proton pulses that are sent to ISOLDE (it is certainly a multiple of 1.2 s). The entire measurement procedure described in Figure 2.7 is carried out within the 6 s time window. After the initial loading of the trap, step a) and b) are repeated twice, so the trap is filled three times. The time structure of the cycle is presented in Figure 4.1. Here, the start of the cycle is given by the first of the three trigger pulses coming from REXtrap, hence the beginning of the cycle is defined as the moment of injection of the first ion bunch into the WITCH system. As can be seen in Figure 4.1, ion bunches from REXtrap are injected into the WITCH setup at ms, 3 ms and 6 ms. These ion bunches are accumulated and cooled in the cooler trap. Due to a human error, the endcaps are lowered too early, at 2 ms and

56 CHAPTER 4. DATA ANALYSIS 46 Figure 4.1: The time structure of a measurement cycle. Graph (a) shows the triggers from REXtrap, i.e. when the ion bunches are injected into the WITCH setup. Plots (b) and (c) show when the voltages on the lower endcap and the upper endcap respectively are lowered: means low voltage, 1 mean high voltage. Line (d) represents the gate that was applied on one of the steerer quadruplets in the vertical beamline. A value of means that the steerer is working normally, a value of 1 indicates that one of the four elements of the steerer is grounded. Plot (e) shows when the ions are radially ejected from the decay trap with a dipole excitation. Figures (f) and (g) indicate when the ions are accumulated in the cooler trap and when the ions are in the decay trap respectively. Finally, a typical retardation voltage pattern is shown in the top row (h) for comparison.

57 CHAPTER 4. DATA ANALYSIS 47 5 ms, instead of at 3 ms and 6 ms. Luckily, the consequences of this error are not grave, except for a somewhat reduced efficiency. Indeed, the highest energy fraction of the freshly injected ions in the cooler trap can get lost when the endcaps are switched because these ions are not cold enough to be trapped in a 15 V potential. The gate on the steerer is also switched 1 ms too early for the last two injections. When the steerer is functioning normally (i.e. gate signal is ), all ions can pass the steerer. When one of the steerer elements is switched from 8 V to ground level (i.e. gate signal 1), however, the background ions are deflected from their path towards the cooler trap, hence reducing background coming from below the traps. The result of the error in switching patterns is simply a change in the background level at 2 ms and 5 ms. Since these time bins are still in the preparation phase of the experiment, this premature switching does not have an effect on the actual measurement. After 8 ms, the ion cloud is transferred to the decay trap. At this point, a retardation voltage sequence such as that shown on top of Figure 4.1 is started. Between 8 ms and 3.2 s, the argon ions are kept in the decay trap and the number of recoil ions is measured in function of the retardation voltage. The voltages of a typical retardation sequence are summarized in Figure 4.2. The width of a retardation bin is.2 s. Two different retardation voltages are probed during each measurement cycle. The 5 V and 6 V parts are included for normalisation purposes. After 3.2 s, the decay trap is emptied. The ions are driven towards larger radii by a dipole excitation of 1 ms at the magnetron frequency (18 Hz) and at the same time pushed downwards by an electric potential. So either the ions are neutralised at the ring electrode or at the pumping diaphragm. These neutral ions can then get pumped away. At this point, the retardation pattern between.8 s and 3.2 s is repeated from 3.2 s until 5.6 s. This is done in order to characterise the behaviour of background. Since a lot of ionisation was present in the system during the November runs, it was decided to measure an argon-free cycle after each measurement cycle in order to investigate the behaviour of the background. The argon ions were blocked from the WITCH tower by applying a non-optimal voltage on the first kicker in the horizontal beamline. Apart from that, the whole measurement procedure was repeated exactly as before. These cycles are referred to as background cycles. Figure 4.3 shows a typical measurement cycle (left) and background cycle (right) Runs The measurement cycles and background cycles can be grouped into a run for each set of retardation voltages. A run takes about half an hour of measurement time and thus contains around 3 cycles. The runs that were selected for this thesis are the ones with highest statistics. More precisely, runs 96 to 19 were chosen, with the exception of run 15. These runs cover a broad range of retardation voltages, going from 2 V up to 7 V. The particulars of these runs are summarized in Table 4.1.

58 CHAPTER 4. DATA ANALYSIS 48 Figure 4.2: A typical retardation sequence. The 5 V (red) and 6 V (blue) bins are included for normalisation purposes. There are two different retardation voltages probed in each measurement cycle, one during the yellow bins, the other during the green bins. The values of these retardation voltages is varied to obtain a recoil energy spectrum. Figure 4.3: A typical measurement cycle (left) and background cycle (right).

59 CHAPTER 4. DATA ANALYSIS 49 Run M1 (V) M2 (V) #MC # clean MC Table 4.1: The two retardation voltages M1 and M2 are given for each run, together with the number of measurement cycles (MC). In the last column, the number of clean measurement cycles according to the selection procedure of Section 4.2 is shown. 4.2 Data Selection As the WITCH experiment is a precision experiment, it is imperative to remove as many background effects as possible. This section pertains to the efforts that are done to clean the data set. The strategy that is used to filter out bad cycles is explained in Section The possibility of noise reduction is investigated in Section Two approaches are examined: the consequences of limiting the pulse height on one hand, and noise reduction by position restriction on the other hand Background Cycles The most prominent effect that is visible in the measurement cycles and background cycles is sudden shifts of the background level. These jumps in the count rate are most probably due to the release of ionisation that is building up somewhere in the setup. As mentioned in Section 2.2.4, charged particles can ionise residual gas atoms when moving through the setup. These secondary charges can then be accelerated towards an electrode, creating more charged particles, and hence resulting in an avalanche of ionisation. If these charged particles are trapped in magnetic field lines or a potential well, ionisation will build up in this part of the setup. Upon switching a voltage, these charged particles can be released from their trap and end up on the MCP detector. Another possible scenario, is that the (unwanted) trap for ionisation is gradually filling until a certain density of charges is reached. After this point, charged particles can spill out of the trap and create a continuous stream of particles to the MCP detector. Such an overfull trap results in a shift in count rate of long duration.

60 CHAPTER 4. DATA ANALYSIS 5 Figure 4.4: A bad measurement cycle (left) and a bad background cycle (right). In order to avoid trapping of charged particles in the spectrometer region, a wire was implemented, as explained in Section In addition, a compensation magnet was installed after the post acceleration section to avoid charge build-up near the einzel lens. Nevertheless, there are other places in the WITCH setup where charges can be accumulated. The stray magnetic field of the 6 T magnet, for example, can create a trap together with the high voltages in the pulsed drift tube section. Two examples of shifts in the background level are shown in Figure 4.4. The left plot demonstrates a jump in the background of short duration between 4.5 s and 5 s. The cycle on the right side displays a background shift of a more extensive nature after 2 s. Both cycles indicate that these changes in background level can occur at any moment. However, shifts in the background level of a measurement cycle are not always distinctly visible. Indeed, a pure measurement cycle contains quite some jumps in count rate on its own due to the switching of the retardation voltage. Therefore it is important to find reliable selection criteria for removing these corrupted cycles from the data set. There is a caveat, however. If background subtraction is desirable, simply throwing away cycles with jumps might jeopardize the accuracy of this procedure. This is illustrated in Figure 4.5. The top two plots show the amount of counts in the time bin between 2. s and 2.2 s in function of cycle number for run 96. The left figure contains the background counts, the rightmost figure shows the counts in the measurement cycle. It is clear that the background level shifts quite a lot over the course of one run. Therefore, for each measurement cycle with a certain background level, there should be an associated background cycle with the same background level. This requirement is not met when only the bad cycles are removed. In order to incorporate background subtraction, the following selection procedure was developed. All measurement cycles which have a distinct shift in background level that do not appear in other measurement cycles are removed from the data set. If a measurement cycle seems clean, the background level just before and just after the measurement cycle is checked in the two neighbouring background cycles. If these levels have the same value and at least one of the neighbouring background cycles does not contain any jumps in the count rate, the measurement cycle is accepted. The associated background cycle is either

61 CHAPTER 4. DATA ANALYSIS 51 Figure 4.5: The amount of counts in the time bin between 2.s and 2.2s is given in function of cycle number for run 96. The top left figure shows the counts in the background cycles, the top right figure displays the counts in the measurement cycle, whereas the bottom figure shows the number of count after background subtraction according to the selection procedure discussed in Section

62 CHAPTER 4. DATA ANALYSIS 52 an average of the two neighbouring cycles if no jumps are present in both cycles, or the one background cycle that is clean. The number of clean measurement cycles obtained for each run is given in Table 4.1. The result of this procedure is illustrated in the bottom plot of Figure 4.5. The number of counts in the 2. s 2.2 s time bin is shown for all accepted measurement cycles with their associated background cycle(s) subtracted Noise Reduction The goal of this section is to make the signal from the recoil ions as clear as possible. As such, one wants to remove all counts that are not coming from 35 Cl +. However, it is not easy to distinguish between events coming from a recoil ion and events that have a different origin. For example, some beta particles from argon decays can end up on the detector, not to mention ionised particles, implanted argon, etc... Two approaches for noise reduction are investigated. First, the applicability of background reduction with pulse height limitation is discussed. Next, the possibility of position restrictions is examined. The figures for this section are grouped in Appendix B. Pulse Height Distributions The top row of the figures in Appendix B show the sum of all measurement cycles (left), background cycles (middle) and the difference thereof (right) for run 96. The pulse height and position distribution of the corresponding counts in the retardation bin indicated in red in the top row are shown in the middle and bottom row, respectively. Each figure shows the pulse height distribution and position distribution for a different.2 s time bin. In the pulse height distributions for the measurement cycles and the background cycles, a peak is present at the end of the distribution. This peak is a sign of saturation. When a signal is created that has an amplitude that is larger than the set threshold, the top of the signal will be cut off and only the lower part of the signal will be integrated. So all signals above the threshold end up in the peak at 6 kunits. Moreover, all signals which have a pulse height below a certain value are not registered in order to reduce counts due to electronic noise. This value is called the discriminator threshold. When subtracting the background from the measurement cycles, the peak at 6 kunits is completely gone, indicating that all high pulse heights come from background events. The endpoint energy of the recoil ions is 452 ev, so no recoil ions are visible when the retardation spectrometer is at 6 V. As can be seen from Figure 4.2, 6 V is applied before.8 s, between 1 s 1.2 s, 2.2 s 2.4 s, 3. s 3.2 s and three more times after the ejection of ions from the trap. This means that there are no recoil ions present in Figures B.1, B.3, B.9 and B.13. Since the ions are ejected from the decay trap at 3.2 s, no ions are present either in Figures B.14 and B.15.

63 CHAPTER 4. DATA ANALYSIS 53 The shape of the pulse height distribution on the right hand side of the figures is different for 6 V and 5 V. For 6 V, the distribution has a sharp rise at the discriminator threshold followed by an exponential decrease. Comparing this to a neighbouring 5 V distribution, one can see that the pulse height distribution is more voluminous and deviates from exponential behaviour. The difference of both distributions (taking radioactive decay into account) gives the pulse height distribution of the recoil ions. When focusing on the last column of each figure, one can conclude that the recoil ions don t have a pulse height above 5 kunits. This means that a large amount of background can be removed from the data set by putting a constraint of 5 kunits on the pulse height of an event. Position Distributions Similar investigations can be done for the bottom row of the figures in Appendix B. Here, the position distribution of the events on the MCP detector is shown for the time bin indicated in red in the top row. The x and y position is given in nanoseconds, corresponding to the difference in travel time through the opposite ends of the delay line anode. A first thing that stands out is that the position distribution of the background depends on the retardation voltage. For 6 V, the background seems more concentrated around a ring in the centre of the MCP, whereas for 5 V, the background is a bit less focused. This trend is also visible in the 12 V and 26 V parts. The position distribution of the background at 26 V (1.6 s 2. s and 2.6 s 2.8 s) resembles the distribution at 6 V, whilst the 12 V parts look more like the 5 V distribution. Upon checking the difference of the measurement and background position distribution, the influence of the retardation voltage on the background seems to have disappeared. This means that background subtraction gives reliable results. A second observation worth mentioning is that the ion signal covers a large part of the detector. The difference between the first 5 V part and the following 6 V distribution is a rough estimate of the ion spot size on the MCP detector for 5 V retardation voltage. The ion spots for the other retardation voltages seem to be centred at the same position. Moreover, the width of the ion spot seems roughly the same for different retardation bins of similar intensities. For example, the bottom right plot in Figure B.7 is almost identical to the ones in Figures B.1 and B.12. The fact that the ion spot covers almost all of the detector surface implies that it is impossible to cut away background with a restriction on position.

64 CHAPTER 4. DATA ANALYSIS Fitting This section focusses on the fitting procedure that was developed during the span of this thesis to analyse the time spectra of runs 96 to 19 (without run 15). First, a detailed overview is given of all effects that were identified in the time spectra in Section At the end of that section, an overview is given of the fitting procedure that was developed taking these effects into account. Next, the fit results are presented in Section A preliminary recoil energy spectrum is presented and its features are discussed Modelling the Data In order to extract a recoil spectrum in function of retardation voltage, an accurate model of the data is crucial. The components of the model that resulted from this thesis are discussed below. In order to highlight the shape of a typical time spectrum, the clean cycles of all runs are summed together to reduce the effect of noise. These summed spectra are shown in Figure 4.6. Behaviour of the Background The plot of the summed background cycles in Figure 4.6 shows that the background level is dependent on the retardation voltage. This is in agreement with the shifts in position distribution that were noted in Section The focussing of charged particles changes due to a different potential in the analysis plane, resulting in slightly different amounts of background ions or electrons that end up on the detector. The same kind of retardation dependent jumps that are seen in the background cycle, are also present in the measurement cycle. The dip between 4.6 s and 4.8 s is the most prominent, which corresponds to a retardation voltage of 6 V. When taking the difference between measurement and background, these dips have disappeared. Since the counts gathered in our spectrum are the results of a Poisson process, the error on the number of counts in a time bin is given by the square root of the bin content. However, when subtracting two Poisson distributions, the result is no longer characterised by a Poisson distribution. Instead, this difference behaves according to a Skellam distribution. Since the data analysis program ROOT [Brun and Rademakers, 1997] does not incorporate fit routines based on a Skellam distribution, it is not possible to use the background subtracted spectrum for fitting purposes. Instead, we fit the background and the measurement simultaneously. In order to develop a model for the background, the behaviour shown in Figure 4.6 has to be understood. Keeping the time structure of Figure 4.1 in mind, the build up curves of about 1 ms that start at ms, 3 ms and 6 ms in Figure 4.6 seem to be correlated to the switching of the pulsed drift tube. Indeed, the shape of the background resembles the

65 CHAPTER 4. DATA ANALYSIS 55 Summed Measurement Cycles Time (s) Summed Background Cycles Time (s) Sum of Background Subtracted Measurement Cycles Time (s) Figure 4.6: The time spectra obtained when summing the clean measurement cycles (top) and background cycles (middle) of runs (with the exception of run 15). The difference is shown in the bottom figure. The peaks that are clipped in the top graph have heights of 18, 19 and 12 kcounts, respectively. The time bin size is 8 ms. (Note that the large bin size flattens out the magnetron oscillation effect explained in Section )

66 CHAPTER 4. DATA ANALYSIS 56 charging curve of the pulsed drift tube. At 2 ms and 5 ms, there is a sudden decrease in the background level. According to Figure 4.1, this can be caused by two things: the lowering of the endcaps, or the switching of the steerer. Since a similar decrease in the count rate is present at 5.8 s, the steerer seems a more likely candidate. If that is effectively the case, then the gate on the steerer has the opposite effect of what was intended. The grounding of one of the steerer electrodes was meant to defocus the background ions passing through, but according to the background cycle, the background level is higher when the steerer is defocusing. Moreover, in the measurement cycles, additional peaks are seen at 2ms and 5ms, indicating that an unwanted trap is emptied at these moments due to the switching of these electrodes. This supports the theory that the defocusing of the steerer is not working as intended. The large peak that is visible at 5.6 s occurs when the spectrometer voltage is switched to V. The large amount of counts suddenly registered at the detector indicates that a trap of charged particles is emptied. The origin of this trap seems to lie between the analysis plane and the magnetic or electric field of the decay trap. However, since the important information about ions is contained in the.8 s 3.2 s region, only the background of this region had to be modelled. The background level was assumed to be constant for similar retardation voltages in this time region. Hence, for each retardation bin, an average background is determined from all the other retardation bins with the same voltage. Implantation Another aspect that has to be taken into account is the implantation of 35 Ar into the MCP detector. As can be seen from the top time spectrum in Figure 4.6, a large number of counts is registered at ms, 3 ms and 6 ms. These are the times at which the trap is loaded, indicating that some ions are not captured in the Penning traps. Instead, they seem to be shot through the traps and the retardation section, and get implanted in the MCP. Note that this is strange behaviour, as the particles exciting the pulsed drift tube should certainly not have energies exceeding the 6 ev retardation barrier. Still, some high energy ions seem to come through. This is possibly due to excessive spread on the ion packet in the pulsed drift tube, whereby some particles can already escape before the PDT is fully switched. Further inquiry to this effect is certainly warranted, as implantation is and should be avoided if at all possible. The worst-case implantation depth in the detector would be due to ions with an energy of the order of 3 kev (in the hypothetical worst case where the pulsed drift tube would have no effect at all). The implantation depth resulting from this scenario is simulated with SRIM 1 to be on the order of a few tens of nanometers Zákoucký [213]. When these 1 SRIM: A simulation package to calculate the stopping and range of ions in matter. srim.org

67 CHAPTER 4. DATA ANALYSIS 57 ions decay, the daughter nuclei do not move more than 1 nm due to their low energy and are not likely to create a signal in the MCP. The beta particles, however, have a higher energy (typically a few MeV) and are capable of triggering a channel. Given that the implanted radioactive ions can still create a signal in the detector upon β decay, there will be an exponential background present in the time spectrum due to these implanted ions. Notwithstanding the fact that the half-life of this decay process is equal to the nuclear half-life, the observed decay component does not have to correspond to this value. Seeing that argon is a noble gas, the implanted ions can diffuse out of the MCP plate and escape detection, manifesting itself in a shorter half-life than expected from nuclear decay. Hence this decay component is best modelled with two free fit parameters: the implantation half-life T imp and the implantation amplitude A imp. The implanted decay component is visible in the figures in Appendix B. The position distribution in the bottom right corner of Figure B.1 shows where the implanted ions end up on the detector. When glancing through Figures B.2 B.15, this spot always seems to be present in the bottom right figure, albeit less intense with time. The decay of the implanted ions is clearly visible when the retardation voltage is at 6 V (Figures B.3, B.9, B.13), because then their signal is not overshadowed by that of the recoil ions. Even after the ions are ejected from the decay trap, the decay of the implanted ions is still visible, as is shown in Figures B.14 and B.15. This means that in order to get a handle on the half-life of this background component, it is useful to fit the part between.6 s and.8 s, and between 3.2 s and 5.6 s as well, even though there are no recoil ions present. Hence, also the flat background component of these parts has to be taken into account. Since the background between.6 s and.7 s is still reacting to the charging of the pulsed drift tube, it seems wise to leave out this part and start the fit only at.7 s. The model for the non-radioactivity related background is a constant that depends on retardation voltage, but since the situation is slightly different before and after the transfer of the ions to the decay trap (at 8 ms), the flat background between.7 s and.8 s is fitted independently from the other 6 V parts. Neutralisation As mentioned in the previous section, it seems useful to fit the second half of the measurement cycle to obtain better constraints on the half-life of the implanted argon ions. Ergo, it is important that all effects that play a role between 3.2 s and 5.6 s are taken into account. As can be seen from the background subtracted measurement in Figure 4.6 (bottom), something is influencing the count rate just after the ejection of the ions from the decay trap. The position distributions in Figures B.13, B.14 and B.15 in Appendix B indicate that this effect is not localised in a specific spot on the MCP. The position distribution in the bottom right plot looks more or less the same before and after the ejection. The ions are ejected at 3.2 s with a dipole excitation of 18 Hz with an amplitude of 1 V and a duration of 1 ms. At the same time, the trapping potential is switched to enable downward ejection. The dipole excitation at the magnetron frequency drives the ions

68 CHAPTER 4. DATA ANALYSIS 58 to larger radii and eventually onto the electrode walls of the trap. Simultaneously, the downward ejection potential pushes the ions towards the top of the pumping diaphragm. Either way, the ions can be neutralised due to charge exchange with the walls of the trap. Since the energies at which the ions are ejected are rather low (1 15 ev) and we are dealing with a noble gas, it is unlikely that the atoms are sticking to the lattice of the electrode or diaphragm for a significant time. The atoms desorb from the electrode and diffuse back into the trap volume. When such a neutral argon atom disintegrates via β + decay, it is very unlikely that the daughter nucleus ends up in a positively charged state. Hence, the sudden growth in count rate is presumably not caused by recoil ions from neutral argon. Another observation that reinforces this assumption is that the bump in count rate is not influenced by the retardation voltage. At 3.4 s, the spectrometer is switched from 5 V to 6 V, yet there is no jump in the count rate visible. However, the decay of neutralised argon atoms also produces positively charged β + particles. Assuming that part of these beta particles can find their way to the MCP detector, this small peak in the count rate is not surprising. In fact, a model can be drawn up. Assuming that adsorbed particles can decay or desorb, and that desorbed particles can decay or be pumped away, the following differential equation is obtained for the amount of desorbed argon: dn desorb dt = λ desorb N e t(λ+λ desorb) λ N desorb λ pump N desorb, with N the initial amount of adsorbed argon, λ desorb the desorption rate, λ pump the pumping rate and λ the nuclear decay constant of argon. Using the fact that no desorbed particles are present at t =, the solution to this equation is λ desorb ( N desorb (t) = N e t(λ+λ desorb ) e ) t(λ+λpump). λ pump λ desorb The evolution of N desorb in function of time is given in Figure 4.7 for a range of values for λ desorb and λ pump. The shape of those neutralisation curves matches the bump in the measurement quite well. As such, this model was implemented in the fitting procedure, taking λ equal to its value ln(2)/1.775 s 1 and using N, λ desorb and λ pump as fit parameters. Typical values for the rates are 1 4 s 1 for λ desorb and 6 2 s 1 for λ pump, as obtained from the fits mentioned at the end of this section. Betas and the Magnetron Oscillation When inspecting the 6 V part between 1 s and 1.2 s in the measurement cycle of Figure 4.6, the count rate is higher than the implantation background at.7 s. Since no recoil ion signal is possible when the spectrometer is at 6 V, this implies that there is yet another background component in play. Comparing the different 6 V parts at 1 s 1.2 s, 2.2 s 2.4 s and 3. s 3.2 s, one gets the impression that this additional background component behaves exponentially. This means that it has to be connected to the decay of argon; and

69 CHAPTER 4. DATA ANALYSIS 59 N d / N λ desorb = 1 and λ pump = 6 λ desorb = 4 and λ pump = 6 λ desorb = 1 and λ pump = 2 λ desorb = 4 and λ pump = 2 λ desorb = 2.5 and λ pump = Time (s) Figure 4.7: The evolution of the number of desorbed ions for different values of λ desorb and λ pump. since this exponential trend is not continued after the ions are ejected from the trap at 3.2 s, it must be related to trapped ions. The figures in Appendix B seem to suggest that this background component is spread out over the whole detector surface. A suitable candidate for this background component are the beta particles that originate from decaying ions in the trap. A beta particle typically has an energy of a few MeV and thus will not be influenced much by the electric fields in the spectrometer. The magnetic field, however, might be able to guide the betas to the top of the setup. Since the cyclotron radius of a positron is quite large compared to that of an ion, the spot size of the betas on the detector is expected to be a lot broader. Moreover, not all betas will end up on the detector, only the ones with the right initial momentum can be observed. In order to incorporate this beta background into the fit function, an exponential component has to be added with half-life T β and amplitude A β. This component should be present as long as the ions are present in the decay trap, i.e. from.8 s until 3.2 s. Another effect supporting the assumption of a beta background is the oscillation in count rate that is observed when the ions are in the decay trap. As shown in Figure 4.8, the signal is modulated with an oscillation of 172 Hz (or 5.81 ms), which is approximately equal to the magnetron frequency of argon in a 6 T, 15 V Penning trap. This sinusoidal effect does not react to changes in the retardation voltage: the amplitude does not change at 1 s when the spectrometer is switched from 5 V to 6 V, implying that the oscillation is not caused by recoil ions. However, the frequency suggests it is related to the motion of the ion cloud in the decay trap. Hence, the only reasonable explanation is that part of the betas coming from the decay trap are able to reach the detector. The fact that a magnetron oscillation is visible in the count rate implies that the ion cloud is not perfectly centred in the decay trap, but is coherently circling around the centre. Hence the axial symmetry is broken in the trap or during transfer. One of the explanations is that there might be a small misalignment of electric and magnetic fields.

70 CHAPTER 4. DATA ANALYSIS 6 Figure 4.8: Part of the measurement cycle. A bin size of.1 ms is used to resolve the magnetron oscillation. This effect was noticed before in the November run of 211. The misalignment issue was investigated and it was concluded that the trap electrodes had moved in their holder during the bake out procedure. This procedure heats the entire system to a few hundreds of degrees centigrade to remove contamination. Due to a difference in thermal expansion coefficients for electrodes and trap holder, the trap electrodes shifted slightly in position. In order to fix this problem, the trap electrodes were mounted in a new holder of a different material. However, it seems that this misalignment is still present in the system, albeit in a lesser form. There are two options when dealing with an oscillation in the count rate. The first option is to average out the oscillation by taking 1 to 2 periods together in one bin. Since the period of oscillation equals 5.81 ms, averaging over 2 periods requires (more than) 1 ms per bin, resulting in only 2 data points per retardation bin. Moreover, as will be discussed below, not all parts of the.2 s retardation bin are valid, so grouping data becomes difficult. Given these disadvantages, averaging out does not seem to be the way to go. The second option entails the implementation of the oscillation into the fit function. In order to get an accurate fit of the oscillation, about 1 data points (or more) have to be present within 1 period of oscillation. Hence, the bin size has to be reduced to.5 ms. Of course, when incorporating the oscillation into the fit function, a model is needed to describe the oscillation. Given that the oscillation is the result of the magnetron motion of the ions, the model of an underdamped harmonic oscillator seems adequate. This model consists of a sine with frequency f and phase φ multiplied by a decreasing exponential with half-life T sine and amplitude A sine. So in order to implement this oscillation into the fit function, four parameters have to be added.

71 CHAPTER 4. DATA ANALYSIS 61 Recoil Ions The most important component of the measurement data is the signal of the recoil ions. First of all, let us focus on the transfer of the ion cloud from cooler trap to decay trap. Figure 4.9 shows a close up of the summed measurement cycles around the time of transfer. At.8 s, a spike is visible, indicating that a small part of the ions are shot over the decay trap and sent through the rest of the spectrometer. In order to improve the fit, this part should not be taken into account. Moreover, in the part right after the transfer peak, some counts seem to be missing, implying that more time bins should be removed from the fit. The explanation of this behaviour can be found in the following section. Secondly, the recoil ions should be fitted whenever they are capable of reaching the detector. This means that a model has to be found that describes the presence of recoil ions in the time spectrum. Recoil ions should be visible when the spectrometer is at 5 V or at one of the measurement voltages M1 or M2. Since the recoil ions measured for all three retardation voltages originate from the same radioactive source, the half-life associated to these component should be the same. Switching the retardation voltage has no influence on the decay trap, after all. Of course, the amplitude should be different for each retardation voltage. So in order to model the recoil ion signal, an exponential has to be added to the fit function with half-life T ion and amplitudes A 5V, A M1 and A M2 to be used when the respective retardation voltage is applied. Thirdly, the recoil ions end up in a quite large spot on the detector. From the figures in Appendix B, it becomes clear that the ions seem to hit the MCP in roughly the same place for different retardation voltages. Moreover, although it cannot be deduced from the figures in the appendix, the effect of the magnetron motion is not visible in the recoil ion signal: the ion spot is not moving around on the detector surface in function of the magnetron phase. Charging of the Retardation Spectrometer One last important effect has to be discussed: the charging time of the retardation spectrometer. Measurements have been performed to investigate the charging characteristics of the retardation electrodes. The results are that the spectrometer reaches > 99% of the applied value 1 ms after the switch is triggered [Breitenfeldt, 212]. This effect is visible in Figure 4.9. After the transfer peak, the count rate is rising for a few milliseconds as the retardation voltage is reduced from 6 V to 5 V. In order to take the charging time into account in the fitting procedure, a 1 ms window is removed from the time spectrum after each retardation switch. Summary of the Fit Function All the effects mentioned in the previous paragraphs are incorporated into the fit. The input data spans from.7 s until 5.59 s and uses input from both the measurement cycles and the background cycles. Each run has to be fitted separately in order to obtain the

72 CHAPTER 4. DATA ANALYSIS 62 Figure 4.9: Part of the measurement cycle with bin size of.1 ms. The overshoot peak after transfer is clearly visible at.8 s. The charging delay of the spectrometer is also seen after the transfer peak. Furthermore, the magnetron oscillation is clearly noticeable in the subsequent part. amplitudes in function of retardation voltage. An example of this fit function is shown in figure 4.1 for run 14. The upper part shows the global fit in the measurement cycles, the bottom plot is zoomed in to show the magnetron oscillation. The fit function is described by 2 parameters, which are summarised in the list below. Fitting this many parameters can lead to convergence problems. Therefore, the fit is performed in two passes. First the global features of the spectrum are fitted, leaving out the damped oscillator model describing the magnetron oscillation. Next, the result of this global fit is used as initial guess for the parameters of the detailed fit. This two-pass scheme improves the convergence to the correct result. Flat background This retardation voltage dependent flat background is fitted in the summed measurement cycles and in the summed background cycles. Component BG imp is used between.7 s and.8 s. Components BG 5V, BG 6V, BG M1 and BG M2 are used when the retardation voltage is set to 5 V, 6 V, and the first and second measuring voltage M1 and M2, respectively. The time intervals in which these parameters are active is summarised in the Table below:

73 CHAPTER 4. DATA ANALYSIS 63 BG 5V BG 6V BG M1 BG M2.81 s 1. s 1.1 s 1.2 s 1.21 s 1.6 s 1.61 s 2. s 2.1 s 2.2 s 2.21 s 2.4 s 2.41 s 2.6 s 2.61 s 2.8 s 2.81 s 3. s 3.1 s 3.2 s 3.61 s 4. s 4.1 s 4.4 s 3.21 s 3.4 s 3.41 s 3.6 s 4.81 s 5. s 5.1 s 5.2 s 4.41 s 4.6 s 4.61 s 4.8 s 5.21 s 5.4 s 5.41 s 5.6 s Exponential implantation background with half-life T imp and amplitude A imp This exponentially decaying background component is fitted in the summed measurement cycles when counts from decaying implanted argon ions are visible, i.e. in the time interval.7 s 5.59 s. Neutralisation curve with parameters λ pump, λ desorb and N The function mentioned in Section is fitted (with t replaced by t 3.2 s) in the summed measurement cycles after the ions are ejected from the decay trap and the neutralised argon ions are present in the system: 3.21 s 5.59 s. Exponential β background with half-life T β and amplitude A β This exponentially decaying background component is fitted in the summed measurement cycles when ions are present in the decay trap:.81 s 3.2 s. Damped harmonic oscillation of β background with half-life T sine, amplitude A sine, frequency f and phase φ This underdamped harmonic oscillator is fitted in the summed measurement cycles when ions are present in the decay trap:.81 s 3.2 s. Exponential ion signal with half-life T ion and retardation voltage dependent amplitudes A 5V, A M1 and A M2 This exponentially decaying ion signal is fitted in the summed measurement cycles when ions are present in the decay trap and the retardation voltage is not 6 V. The amplitudes A 5V, A M1 and A M2 are used in the time intervals: A 5V A M1 A M2.81 s 1. s 1.21 s 1.6 s 1.61 s 2. s 2.1 s 2.2 s 2.41 s 2.6 s 2.61 s 2.8 s 2.81 s 3. s Fit Results Using the fit procedure described in Section 4.3.1, the cleaned measurement cycles of each run can be analysed. This section discusses the stability of the fit and the physical consistency of its results.

74 CHAPTER 4. DATA ANALYSIS Time (s) Time (s) Figure 4.1: The clean measurement cycles of run 14 fitted with the fit function described in Section 4.3. The upper graph shows the global fit, whereas the lower plot is zoomed in to show the magnetron oscillation.

75 CHAPTER 4. DATA ANALYSIS 65 Figure 4.11: cycles. Logarithmic plot of the sum of all background subtracted measurement Stability of the Fit When looking at the logarithmic plot of all background subtracted measurement cycles in Figure 4.11, there is still one effect visible that has not yet been discussed: the 5 V part between.8 s and 1 s seems too flat to be consistent with the sum of three exponentials. One would expect that the slope of the peak at.8 s and 1 s is the steepest, compared to the other 5V parts 2 at 2 s 2.2 s and 2.8 s 3 s. This is however not the case. The same is seen in each run separately. The reason for this is still under investigation. In order to see how far this flatness actually continues (maybe the subsequent 6 V part is also too flat), the fitting routine has been repeated several times, leaving out larger and larger parts after the transfer. The results of the fits for run 13 are shown in Figure 4.12 to indicate when the fit stabilizes. When removing more and more bins after.8 s, the half-life of the ions T ion and the halflife of the betas T β start to fluctuate, as shown in Figure 4.12 (top). These half-lives do not seem to level out to a certain value (even though it may look like they stabilize after 16 ms for the plotted run, this is not the case for all runs). The reason for this is twofold. First of all, the amount of statistics for each trap component reduces significantly when removing parts just after the transfer. This is seen in the evolution of the errorbars in all three plots in Figure When cutting away only a part of the first 5 V bin, the errorbars remain small. If everything between.8 s and 2 s is cut away, the errorbars are 2 Indeed, the first part will have more contribution from the fastest decaying exponentials compared to the later parts, where only the slow decaying exponentials survive. Hence, the slope will evolve from ln(2)/t < for small t to ln(2)/t > for large t, where T < and T > are the smallest, respectively largest half-lives of the exponentials.

76 CHAPTER 4. DATA ANALYSIS 66 Run T imp T β T ion 1.3 T 1/2 (s) Starting point of the fit (ms) 3 25 Run 13 34V 12V 5V 2 Amplitudes Starting point of the fit (ms) Run 13 34V 12V A/A 5V Starting point of the fit (ms) Figure 4.12: Half-lives (top), ion amplitudes (middle) and normalised amplitudes (bottom) in function of the starting point of the fit for run 13. Do note that the.7 s.8 s bin is always kept in the fit to constrain the implantation half-life.

77 CHAPTER 4. DATA ANALYSIS 67 Figure 4.13: Correlation matrices for the fit of run 13 with the first 5V and 6V bins included (left) and excluded (right). The correspondence between the parameter numbers and the parameter labels is given in Table 4.2. significantly larger. The only parameter that does not exhibit this type of behaviour is the implantation half-life, its errorbar is not influenced by the removal because it is mainly determined by the.7 s.8 s time bin and the part after ejection. Secondly, there are correlations between the fit parameters. Figure 4.13 shows two correlation matrices for the fit of run 13, the one on the left is for a fit without any removal of bins after the transfer, the one on the right corresponds to a fit without the first 5 V and 6 V bins. It is clear that the 3 decay components are correlated (parameters 1 8). When no bins are removed, the implantation background and the β background are strongly correlated (parameters 1 4). When removing the first 5 V and 6 V bins, the beta background and the ion component are much more linked. This can be explained when realising that at least three points are needed to characterise an exponential decay curve. When the first 6 V bin is removed, only two 6 V bins remain to constrain the half-life of the beta background. Of course, the beta component is also fitted underneath the ion signals, but due to the three exponential components in the fit, this does not give much restriction on the beta exponential. Moreover, for each exponential component, the half-life and the amplitude are anti-correlated. Furthermore, the implantation component is strongly correlated with the parameters (14 16) of the neutralisation model, and hence the beta component is correlated with the neutralisation as well. In addition, it seems that the magnetron oscillation is completely uncorrelated to the other parameters in the fit, except the beta component. As can be seen in the two upper graphs in Figure 4.12, the amplitudes of the ion parts are anti-correlated to the ion half-life T ion. When the ion half-life goes down, the amplitudes become larger. This is indeed indicated in the correlation matrix for parameters 4 8. When normalising the measurement amplitudes A M1 and A M2 to the 5 V amplitude A 5V, at least this effect is removed. The normalised amplitudes for run 13 are shown in the bottom of Figure A small drift is seen in both normalised amplitudes when

78 CHAPTER 4. DATA ANALYSIS 68 Number Parameter Number Parameter 1 A imp 11 BG 6V 2 T imp 12 BG M1 3 A β 13 BG M2 4 T β 14 N 5 A 5V 15 λ desorb 6 T ion 16 λ pump 7 A M1 17 A β 8 A M2 18 T β 9 BG imp 19 f 1 BG 5V 2 φ Table 4.2: The correspondence between the parameter numbers in Figure 4.13 and the fit parameter labels. parts of the first 5 V bin are removed. The data points for 12 V (red) seem to have stabilised after the removal of the full 5 V bin at 1 s. However, when inspecting the trend for 34 V (blue), the drift persists up to 1.2 s. This indicates that something is happening during both the first 5 V bin and the first 6 V bin. This effect seems to disappear after 1.2 s. In the other runs, similar behaviour is seen. From this we can conclude that the first 5 V and 6 V bins have to be removed from the fit function. In order to give an idea of the goodness of fit when removing the first 5 V and 6 V bins, the reduced χ 2 -values are shown in Figure The reduced χ 2 -value for each run is slightly larger than one, indicating that either the fit has not fully captured the data, or that the error on the number of counts per bin is somewhat underestimated. Another conclusion that can be drawn from this discussion is that the value of the normalised amplitudes is quite robust. Even when the values of the half-lives fluctuate, the normalised amplitudes do not change significantly. Half-lives The determination of the implantation, beta and ion half-lives is quite difficult using only runs As mentioned in Section 4.3.2, there are large correlations between the half-lives of the three decay components. Moreover, the parts which have the most restrictive power for the ion and beta half-lives, i.e. the first 5 V and 6 V regions after the transfer, have to be removed from the fit because of an effect that is not yet understood. In addition, Figure 4.12 tells us that the ion and beta half-lives fluctuate in function of starting point of the fit. For some runs, the values of the half-lives even swap places, as shown in Figure This implies that the ion and beta half-lives can not be determined accurately from the fits. The implantation half-life, however, is a different story. Since the.7 s.8 s and 3.2 s 5.59 s bins were implemented to constrain the implanted activity, the value of the implantation half-life does not fluctuate significantly per run, with the exception of Figure 4.15, of course. Hence, the determination of the implantation

79 CHAPTER 4. DATA ANALYSIS 69 Figure 4.14: Goodness of fit for the various runs, indicated with a reduced χ 2 -value. The first 5 V and 6 V retardation sections were not included in the fit. A value of one is ideal. 1.8 Run T imp T β T ion 1.2 T 1/2 (s) Starting point of the fit (ms) Figure 4.15: Strange behaviour of the half-lives in function of the starting point of the fit for run 1. Do note that the.7 s.8 s bin is always kept in the fit to constrain the implantation half-life.

80 CHAPTER 4. DATA ANALYSIS Values of the implantation half life per run T imp (s) Run Number Figure 4.16: The implantation half-lives per run. half-life using this fitting procedure seems quite reliable. The obtained half-lives are shown per run in Figure Taking the weighted average of these points gives T imp = (1.282 ±.11) s (4.1) In order to accurately determine the other two half-lives, dedicated half-life measurements are necessary. During the run in November, an attempt was made to measure the implantation half-life and the lifetime of the ions in the decay trap. Since no background component due to beta particles was expected at that time, the implantation measurement consisted of putting the spectrometer at 6 V. For the ion half-life measurement, the spectrometer was put at 5 V after the transfer. In hindsight, these measurement can be used to determine the beta half-life and the ion half-life. However, the implantation background is still present underneath both measurements, making it difficult to extract the half-lives from these measurements alone. Luckily, an accidental implantation measurement was found in which the pulsed drifted tube was switched at the wrong moment, resulting in ions of 3 kev being implanted in the MCP detector. The half-lives that were extracted from these runs by [Finlay, 213] are T ion = 1.194(15) s, T β =.67(3) s and T imp = 1.311(31) s. The value of the implantation half-life is in agreement with what we found in equation (4.1). It is clear that these half-lives lie far below the nuclear half-life of s. In the case of the implantation half-life, this discrepancy can be explained by diffusion (as mentioned in section 4.4.1). Argon ions that are implanted on the detector surface, can diffuse out of the detector. These particles can then be pumped away and escape detection, resulting in a shorter implantation half-life than expected from nuclear decay. There is one caveat to this conclusion: what if the effect that causes the flatness of the first 5 V bin already plays a role at.7 s? Then the implantation half-lives determined from these fits are not reliable. Therefore it is imperative that this effect is better understood.

81 CHAPTER 4. DATA ANALYSIS 71 For the ion half-life and the beta half-life, the situation is a bit more complicated. It is clear that there have to be loss mechanisms at play in the decay trap, otherwise both half-lives would equal the nuclear half-life. Unfortunately, the physical mechanisms behind these losses are not known. One striking observation is that the ions and the betas have a completely different half-life, although both species come from the same source, i.e. the ion cloud in the decay trap. Somehow the loss mechanisms for the ions and the betas are different, or at least act differently. Besides, one has to take the magnetron oscillation into account. Only the count rate due to betas is influenced by the magnetron motion in the trap. This implies that there is an asymmetry in the transmission of beta particles through the WITCH tower. Positrons coming from one side of the trap (radially speaking) are able to reach the detector, whereas beta particles from the opposite side are not. This asymmetry can be caused by the mechanical asymmetries that are present in the spectrometer. For example, the wire breaks the axial symmetry, as well as the residual field of the spectrometer MCP. The half-life that was fitted to the decay component of the oscillation lies around.6 s.7 s for most runs. This is lower than the ion half-life, but in agreement with the beta half life found from the dedicated half-life measurement. Because of the large difference between nuclear half-life and the ion half-life, it is clear that ions are lost in the decay trap. Hence we are faced with the question, what happens to these ions? It is possible that they neutralise via charge exchange with the trap walls or with residual gas present in the decay trap. In that case, they can undergo the same fate as the desorbed atoms from Section Either the argon atom is pumped away, or it moves around until it decays. As with the desorbed argon, it is possible that the beta particle created in this decay ends up on the detector. This means that there might be another background component which we haven t taken into account yet. This additional source of beta particles besides that which is already due to the decaying ions in the trap could potentially account for a difference in half-live between T ion and T β. Although in that case, it would make more sense for T β to be larger than T ion, which is not what is observed. Amplitudes The normalised amplitudes that are obtained with the fit function of Section are shown in Figure As determined in the previous sections, the first 5 V and 6 V bins are removed from the fit. A weighted average is determined for the retardation voltages that occur twice: 2 V, 12 V, 26 V, 3 V and 34 V. In order to extract the β-ν angular correlation coefficient a from this graph, it has to be compared with simulated versions thereof. Extended simulations with Simbuca are required to determine the position and velocity distribution in the decay trap. These distributions then serve as input parameters for SimWITCH, which tracks the recoil ions from the decay tray, through the spectrometer and towards the MCP. Such simulations are already ongoing at the time of writing.

82 CHAPTER 4. DATA ANALYSIS A/A 5V Retardation voltage (V) Figure 4.17: Preliminary spectrum of normalised amplitude versus retardation voltage. Nonetheless, from the shape of Figure 4.17, a preliminary analysis can already be made. Given that the Standard Model prediction for a equal is to.94(16), one expects more parallel emission of beta and neutrino, and thus more recoil ions at the high energy side of the spectrum. Looking at Figure 4.17, one sees that the low energy recoils seem to dominate. The slope of the preliminary retardation spectrum is too steep near low retardation voltages. This indicates that there is still a retardation voltage dependent effect we haven t identified yet. One of the features that still have to be incorporated into the data analysis procedure is the efficiency map of the MCP detector surface. The position dependent efficiency was calibrated with an alpha source before and after the run in November, but there are still some issues with regard to the measurement results. In the calibration measurements, there are hotspots on the detector surface which were not seen at all during the measurements with radioactive argon. Moreover, these hotspots seem to have changed position when comparing the calibration before and after the run. So the efficiency of the MCP is not fully understood yet and is still under investigation [Knecht, 213]. In order to estimate the effect of the MCP efficiency, one can resort to comparisons of ion spot shapes in function of retardation voltage. If the ion spot on the detector has a different shape or centre for different retardation voltages, a position sensitive efficiency could create a retardation voltage dependent effect. In order to check if the spot shapes are identical, the values of the implantation half-life and the beta half-life are essential. Using the values obtained from the extensive fit function of Section 4.3.1, one can distil the ion spot shape for all retardation voltages applied in the runs from the position information present in a cycle. The following procedure was applied to obtain the position distributions in Figure 4.18:

83 CHAPTER 4. DATA ANALYSIS 73 a) The position distribution of the clean background cycles is subtracted from the clean measurement cycles for each run. b) The.7 s.8 s part of the data is used to determine the position distribution of the implanted activity. c) The implanted position distribution is subtracted from each.2 s retardation bin (actually.19 s: from.1 s to.2 s) using an appropriate scaling factor. This factor is determined by the integral of the fitted implantation decay curve over the retardation bin in question, divided by the integral of the decay curve over the.7 s.8 s normalisation bin. This implantation decay curve is taken from the aforementioned fit and is different for each run. d) The resulting 6 V parts and the measurement parts M1 and M2 are summed separately. Although Section suggests that there is a small unknown effect underneath the 6 V retardation bin at 1. s 1.2 s, it is still included in the position distribution for 6 V in order to have more statistics on the beta distribution. e) The beta half-life is estimated from the fit and used to subtract the 6V distribution from the two other position distributions. Again, the scaling factor is determined by the integral of the fitted beta decay curve over the retardation bins in question, divided by the integral over the 6V bins. f) The resulting position distributions are all rescaled to the same maximum value in order to allow comparisons of the shape. Figure 4.18 shows some interesting features. First of all, the centre of the ion spot moves slowly to the right with increasing retardation voltage. Secondly, the shape of the ion spot changes with retardation voltage. For low voltages, the ion spot is quite broad. For high voltages the spot is very narrow. These remarks indicate that the position sensitive efficiency has to be taken into account. In order to estimate the effect of the efficiency, preliminary monte carlo simulations were done by [Knecht, 213] starting from these position distributions. At first sight, it seems that the effect of the efficiency results in differences of about 5%. However, the efficiency map is not fully understood, so further investigation is needed. Moreover, if this effect is truly of that order, it is not enough to explain the distorted shape of the recoil spectrum. 4.4 Outlook Over the course of this chapter, the progress made in the analysis of the data taken in November 212 has been presented. Step by step, (some of) the complexities of the WITCH experiment were unravelled. A preliminary recoil spectrum was obtained, but there are clearly some issues with its shape. It seems that there is still a retardation voltage dependent background effect present in the spectrum. Further analysis is needed to figure out what lies at its origin. Moreover, there are some outstanding questions which have to be investigated. Below, several effects that merit further research are summarised.

84 CHAPTER 4. DATA ANALYSIS 74 Figure 4.18: Ion spot shapes for 2 V, 1 V, 2 V and 3 V.

85 CHAPTER 4. DATA ANALYSIS 75 Unwanted Implantation During the injection in the cooler trap, radioactive ions seem able to reach the MCP where they are implanted. This can be due to the pulsed drift tube not operating as planned on all ions (e.g. if the ion bunch is too spread out in the longitudinal direction). Further investigation as to the exact origin of this implantation is merited, as fixing it would get rid of an extra background effect. Flatness around the first 5 V bin The time spectrum in the first 5 V retardation bin seems inexplicably flat. Moreover, the subsequent 6 V bin also seems unreliable. The effect that causes this is still unknown. Obviously, it needs to be explained. Efficiency As shown in the previous section, the shape of the ion spot is dependent on the retardation voltage, giving rise to systematic effects due a position dependent efficiency of the MCP. One of the issues that still has to be solved is characterizing and calibrating this efficiency. At the time of writing, this is already under investigation. Neutral 35 Ar As was already hinted in the previous section, the large rate of ion loss could mean that quite some argon ions neutralise in the decay trap. As described in Section 4.3.1, neutral argon is still capable of producing a signal in the MCP upon beta decay. This raises the question: is the signal due to (the decay products of) neutral argon retardation voltage dependent? In order to find an answer to this question, simulations can be helpful. For example, it would be useful to know at which place in the spectrometer the decay of an argon atom is still visible. This sort of investigation can be done with the particle tracking software SimWITCH. Simulations Since the magnetron oscillation is visible in the count rate, the axial symmetry is broken in the setup (for example by the wire or the residual field of the spectrometer MCP). However, the SimWITCH package uses an axially symmetric code to track particles through the setup. To gain more insight into the spot size, the magnetron oscillation and the behaviour of decay products of neutral argon outside the traps, SimWITCH should be extended to enable full 3D calculations.

86 Chapter 5 Conclusion and Outlook 5.1 Conclusions In Chapter 3, we introduced the Simbuca simulation framework and used it to simulate the behaviour of trapped ions. We found that caution is advised when trying to simulate along the order of 1 6 or more effective particles with large Coulomb scaling factors of order 1 4, as the scaled Coulomb force calculations then give inconsistent results. We also compared off-line measurements with simulated results for a process that is highly sensitive to the physical correctness and numerical stability of the simulation code. Although we found no exact match between the experimental and simulated results, this is not conclusive evidence for an error in the simulation. Indeed, this discrepancy can possibly be explained by finite switching times in the experiment that are not yet taken into account in the simulation, or slight differences between the simulated and the real trap potentials. Nonetheless, even though an exact match was not found, the qualitative pattern of the data is perfectly reproduced. Doing so, we found evidence of an interesting phenomenon called phase locking. This effect only manifests itself when the Coulomb interaction between the ions is taken into account. It seems that the parameters that determine the occurrence of this effect are the number of ions and the energy of the ion cloud. In Chapter 4 we presented the progress made in the analysis of the data from the November 212 run. Several effects were observed of which the origin could be determined. These include, of course, the actual recoil ions that we want to analyse. However, also a number of other, unwanted background effects were identified. Some of these effects were unforeseen, which is not really surprising, as this is the very first time that data with sufficient statistics is available. For instance, a large fraction of the beta particles that are emitted during the decay of the trapped ions were found to end up on the detector as well. 76

87 CHAPTER 5. CONCLUSION AND OUTLOOK 77 The retardation voltage and switching of the pulsed drift tube also had a measurable influence on the static background level, which had to be taken into account. Furthermore, the switching of the steerer, which was added to the measurement cycle in an attempt to decrease the background level that entered the trap, is found to quite possibly have the opposite effect. Additional background due to neutralised argon atoms was noted. When the trap is cleared, the argon ions neutralise on the walls of the setup. Due to their noble gas configuration, they can rather easily separate from the walls and diffuse back into the trap. Here, they can still decay and send β + particles towards the detector. Furthermore, during the filling of the cooler trap, high energy ions apparently make their way through the trap and retardation section and get implanted in the detector. Upon decay, they create unwanted background signals by triggering channels in the MCP. An explanation for the high energy ions is an improper working of the pulsed drift tube, possibly due to incoming ion bunches from REXtrap that are too spread out longitudinally. We also observed persistent magnetron oscillations, showing that the ion cloud is not perfectly centred in the decay trap, but is coherently circling around the centre. A fitting procedure that handles the recoil ions and takes into account all listed background effects was developed and used for an exploratory initial investigation. Some peculiarities arise from the data. Firstly, the half-lives for the betas and the ions coming from the decay trap are consistently smaller than the nuclear half-live of Ar-35. Moreover, the beta and ion half-life are not equal, although they arise from the same radioactive source, i.e. the ion cloud in the decay trap. Hence, there must be loss mechanisms at play in the decay trap which are different for betas and ions. One possibility is that neutralisation occurs there as well. Secondly, the obtained preliminary energy distribution of the recoiling nuclei deviates too strongly from the Standard Model prediction to be considered credible. This seems to indicate that there is a retardation voltage dependent effect that was not accounted for yet. 5.2 Open Questions and Future Work We found evidence for implantation of high energy radioactive ions into the detector when ion bunches are injected into the cooler trap from REXtrap. An improper deceleration of the (potentially longitudinally stretched) ion cloud in the pulsed drift tube is possibly to blame for these high energy ions. This certainly needs to be investigated and mitigated if possible. Furthermore, we showed that the time spectrum measurements in the first 5 V retardation bin are too flat to be consistent. It is likely that the subsequent 6 V retardation bin is also affected. However, the reason for this flatness still lacks an explanation.

88 CHAPTER 5. CONCLUSION AND OUTLOOK 78 The shape of the recoil ion spot on the detector seems to depend on the retardation voltage. Hence the efficiency map of the MCP needs to be characterized and calibrated in order to avoid systematic bias in the final energy distribution of the recoil ions. Fitted half-lives are consistently lower than the nuclear half-live. This points towards a continuous loss of ions in the decay trap. The origin of this ion loss needs to be pinpointed and either avoided or taken into account in the analysis of the data. One possible explanation is that there is neutralisation happening here as well. Because these neutral atoms can still create beta particles upon decay, it needs to be examined if this results in a signal in the MCP that is retardation voltage dependent. For example, it would be useful to know at which place in the spectrometer the decay of an argon atom is still visible. This sort of investigation can be done with the particle tracking software SimWITCH. Finally, the preliminary energy distribution of the recoil atoms that was extracted from the analysed data has a shape that deviates too strongly from the Standard Model prediction. Is this problem solved if the previous points are attended to? Or are there other retardation voltage dependent effects that are not yet taken into account? 5.3 Future Improvements Finally, this section lists some suggestions for future improvements of the experiment. The last two sections touch upon some improvements that have not yet been discussed in the main text Software Changes Simbuca is able to simulate the measurements discussed in Section 3.3 to obtain a qualitatively correct result. However, slight deviations with the measured data are observed. Implementing more realistic finite-time switching of the trap voltages in Simbuca might bring this to exact agreement. The observed magnetron oscillations in Chapter 4 show that axial symmetry is broken in the setup. The tracking software SimWITCH currently assumes axial symmetry and should thus be extended to enable full 3D calculations Background Reduction In the analysis of the results, we argued that the switching of the steerer at the entrance of the Penning traps did not seem to have its intended effect. There was still quite some background signal detected coming from below the traps when the steerer should have been defocussing.

89 CHAPTER 5. CONCLUSION AND OUTLOOK 79 A suggestion for future improvement would be to introduce an actual mechanical shutter into the system at the position of the steerer. This shutter would then physically close off the entrance of the traps during a measurement, thereby diminishing background ionization from below the Penning traps and blocking ionisation from stray and accidental traps that are created by the fields of the PDT and the Penning trap magnets Beta Reduction The analysis showed two sources of beta background. On the one hand, the betas emitted at the decay of the trapped ions could end up on the detector. On the other hand, betas from neutralised argon that diffuses around in the decay trap can reach the detector as well. A mass separator between the post acceleration stage and the MCP would allow one to discriminate between betas arriving at the MCP and the actual recoil ions that we want to measure. However, due to the vertical setup of the WITCH experiment, this mass separator would have to come on top of the WITCH tower, where space limitations can become a concern. Furthermore, the stray fields from the mass separator will have to be shielded to avoid interference with the fields in the Penning traps. Another possibility is to install a time-of-flight detection system after the post acceleration section. This would make kev ions clearly distinguishable from MeV betas. Again, there are spacial limitations, but at least problems with stray magnetic fields can be avoided. As an aside, placing a β detector below the decay trap would allow one to do coincidence measurements between the recoil ions that are directed upwards and associated β particles that are directed downwards. This would potentially cut out all background effects. However, this idea has already been proposed and was met with some prohibitive technical difficulties at the time. Nonetheless, as is apparent from the analysis of Chapter 4, unintended background is a much more significant problem than anticipated. This may warrant a reboot of the coincidence measurement proposal.

90 Appendix A Simulation Results This appendix contains the results of the simulations mentioned in Chapter 3. The results of the wingplot simulations are shown in Figures A.1 A.1. These results were obtained by simulating an ion cloud of 25, 1 or 25 ions, with a Coulomb scaling factor as mentioned in Table A.1. This cloud was cooled until a certain Maxwell Boltzmann energy distribution (characterised by the energy of maximal probability) and then subjected to the potentials applied in the wingplot measurement. The used MB energy distributions are for 1.6 ev, 1 ev, 65 mev, 325 mev, 18 mev and 1meV. For each scaling factor and number of ions, the results for the 6 different energy distributions are grouped into one figure. 8

91 APPENDIX A. SIMULATION RESULTS 81 Number of ions Coulomb scaling factor Effective number of ions Table A.1: The number of ions and Coulomb scaling factors that were used in the simulations. The last column shows the effective number of ions for each combination of ion number and scaling factor.

92 APPENDIX A. SIMULATION RESULTS MB energy: 16meV 1*25ions MB energy: 1meV 1*25ions MB energy: 65meV 1*25ions MB energy: 325meV 1*25ions MB energy: 18meV 1*25ions MB energy: 1meV 1*25ions Figure A.1: Wingplots for 1*25 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

93 APPENDIX A. SIMULATION RESULTS 83 MB energy: 16meV 1*1ions MB energy: 65meV 1*1ions MB energy: 18meV 1*1ions MB energy: 1meV 1*1ions MB energy: 325meV 1*1ions MB energy: 1meV 1*1ions Figure A.2: Wingplots for 1*1 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

94 APPENDIX A. SIMULATION RESULTS MB energy: 16meV 1*25ions MB energy: 1meV 1*25ions MB energy: 65meV 1*25ions MB energy: 325meV 1*25ions MB energy: 18meV 1*25ions MB energy: 1meV 1*25ions Figure A.3: Wingplots for 1*25 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

95 APPENDIX A. SIMULATION RESULTS MB energy: 16meV 1*25ions MB energy: 1meV 1*25ions MB energy: 65meV 1*25ions MB energy: 325meV 1*25ions MB energy: 18meV 1*25ions MB energy: 1meV 1*25ions Figure A.4: Wingplots for 1*25 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

96 APPENDIX A. SIMULATION RESULTS 86 MB energy: 16meV 25*1ions MB energy: 65meV 25*1ions MB energy: 18meV 25*1ions MB energy: 1meV 25*1ions MB energy: 325meV 25*1ions MB energy: 1meV 25*1ions Figure A.5: Wingplots for 25*1 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

97 APPENDIX A. SIMULATION RESULTS MB energy: 16meV 1*25ions MB energy: 1meV 1*25ions MB energy: 65meV 1*25ions MB energy: 325meV 1*25ions MB energy: 18meV 1*25ions MB energy: 1meV 1*25ions Figure A.6: Wingplots for 1*25 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

98 APPENDIX A. SIMULATION RESULTS 88 MB energy: 16meV 25*1ions MB energy: 65meV 25*1ions MB energy: 18meV 25*1ions MB energy: 1meV 25*1ions MB energy: 325meV 25*1ions MB energy: 1meV 25*1ions Figure A.7: Wingplots for 25*1 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

99 APPENDIX A. SIMULATION RESULTS MB energy: 16meV 1*25ions MB energy: 1meV 1*25ions MB energy: 65meV 1*25ions MB energy: 325meV 1*25ions MB energy: 18meV 1*25ions MB energy: 1meV 1*25ions Figure A.8: Wingplots for 1*25 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

100 APPENDIX A. SIMULATION RESULTS 9 MB energy: 16meV 25*1ions MB energy: 65meV 25*1ions MB energy: 18meV 25*1ions MB energy: 1meV 25*1ions MB energy: 325meV 25*1ions MB energy: 1meV 25*1ions Figure A.9: Wingplots for 25*1 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

101 APPENDIX A. SIMULATION RESULTS MB energy: 16meV 1*25ions MB energy: 1meV 1*25ions MB energy: 65meV 1*25ions MB energy: 325meV 1*25ions MB energy: 18meV 1*25ions MB energy: 1meV 1*25ions Figure A.1: Wingplots for 1*25 ions. The initial Maxwell Boltzmann energy is: 1.6 ev (top left), 1. ev (top right), 65 mev (middle left), 325 mev (middle right), 18 mev (bottom left), 1 mev (bottom right).

102 Appendix B Position and Pulse Height Distributions This appendix contains the position distributions and pulse height distributions for run 96 in function of retardation voltage time bin. The upper row of each figure shows the number of counts in function of time. The relevant retardation bin is indicated in red. The middle row contains the pulse height distributions of the events in the time bin indicated in red. The corresponding position distributions on the MCP detector are shown in the bottom row. The left column pertains to the summed measurement cycles, the middle column shows the distributions for the summed background cycles and the subtraction of both is shown on the right. 92

103 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.1: The position and pulse height distributions for the time bin between 6 ms and 8 ms. At this moment, the retardation voltage is at 6 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

104 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.2: The position and pulse height distributions for the time bin between 8 ms and 1 ms. At this moment, the retardation voltage is at 5 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

105 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.3: The position and pulse height distributions for the time bin between 1 ms and 12 ms. At this moment, the retardation voltage is at 6 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

106 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.4: The position and pulse height distributions for the time bin between 12 ms and 14 ms. At this moment, the retardation voltage is at 12 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

107 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.5: The position and pulse height distributions for the time bin between 14 ms and 16 ms. At this moment, the retardation voltage is at 12 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

108 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.6: The position and pulse height distributions for the time bin between 16 ms and 18 ms. At this moment, the retardation voltage is at 26 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

109 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.7: The position and pulse height distributions for the time bin between 18 ms and 2 ms. At this moment, the retardation voltage is at 26 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

110 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.8: The position and pulse height distributions for the time bin between 2 ms and 22 ms. At this moment, the retardation voltage is at 5 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

111 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.9: The position and pulse height distributions for the time bin between 22 ms and 24 ms. At this moment, the retardation voltage is at 6 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

112 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.1: The position and pulse height distributions for the time bin between 24 ms and 26 ms. At this moment, the retardation voltage is at 12 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

113 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.11: The position and pulse height distributions for the time bin between 26 ms and 28 ms. At this moment, the retardation voltage is at 26 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

114 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.12: The position and pulse height distributions for the time bin between 28 ms and 3 ms. At this moment, the retardation voltage is at 5 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

115 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.13: The position and pulse height distributions for the time bin between 3 ms and 32 ms. At this moment, the retardation voltage is at 6 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

116 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.14: The position and pulse height distributions for the time bin between 32 ms and 34 ms. At this moment, the retardation voltage is at 5 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

117 APPENDIX B. POSITION AND PULSE HEIGHT DISTRIBUTIONS Time (s) Time (s) Time (s) Pulse Height (a.u.) Pulse Height (a.u.) Pulse Height (a.u.) y (ns) y (ns) y (ns) x (ns) x (ns) x (ns) Figure B.15: The position and pulse height distributions for the time bin between 34 ms and 36 ms. At this moment, the retardation voltage is at 6 V. The top row shows the number of count in function of time and the relevant time bin is indicated in red. The pulse height distributions of the events in this time bin are shown in the middle row. The corresponding position distribution is displayed in the bottom row. The left column shows the events in the measurement cycles. The middle column pertains to the events in the background cycle. The column on the right displays the difference between measurement and background cycles.

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120 BIBLIOGRAPHY 11 Jackson, J. D., Treiman, S. B., and Wyld, H. W. (1957). Possible tests of time reversal invariance in beta decay. Phys. Rev., 16: Johnson, C. H., Pleasonton, F., and Carlson, T. A. (1963). Precision measurement of the recoil energy spectrum from the decay of he 6. Phys. Rev., 132: Knecht, A. (213). Efficiency calibration of the position sensitive mcp detector. Private communication. Nikolaev, E. N., Heeren, R. M. A., Popov, A. M., Pozdneev, A. V., and Chingin, K. S. (27). Realistic modeling of ion cloud motion in a fourier transform ion cyclotron resonance cell by use of a particle-in-cell approach. Rapid Communications in Mass Spectrometry, 21(22): Paul, S. (29). The puzzle of neutron lifetime. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 611(23): ce:title Particle Physics with Slow Neutrons /ce:title. Pedersen, H. B., Strasser, D., Ring, S., Heber, O., Rappaport, M. L., Rudich, Y., Sagi, I., and Zajfman, D. (21). Ion motion synchronization in an ion-trap resonator. Phys. Rev. Lett., 87:551. Porobic, T. (213). The reliability of the scaled coulomb force in simbuca. Private communication. Scielzo, N. D., Freedman, S. J., Fujikawa, B. K., and Vetter, P. A. (24). Measurement of the β-ν correlation using magneto-optically trapped 21 Na. Phys. Rev. Lett., 93:1251. Serebrov, A. P. and Fomin, A. K. (21). Neutron lifetime from a new evaluation of ultracold neutron storage experiments. Phys. Rev. C, 82:3551. Severijns, N. and Naviliat-Cuncic, O. (213). Structure and symmetries of the weak interaction in nuclear beta decay. Physica Scripta, 213(T152):1418. Severijns, N., Tandecki, M., Phalet, T., and Towner, I. S. (28). Ft values of the t = 1/2 mirror β transitions. Phys. Rev. C, 78:5551. Sudarshan, E. C. G. and Marshak, R. E. (1958). Chirality invariance and the universal fermi interaction. Phys. Rev., 19: Tandecki, M. (211). Progress at the WITCH Experiment towards Weak Interaction Studies. PhD thesis, Katholieke Universiteit Leuven. Vetter, P. A., Abo-Shaeer, J. R., Freedman, S. J., and Maruyama, R. (28). Measurement of the β-ν correlation of 21 Na using shakeoff electrons. Phys. Rev. C, 77:3552. Weinberg, S. (29). V-A was the key. J.Phys.Conf.Ser., 196:122. Wilson, F. L. (1968). Fermi s theory of beta decay. American Journal of Physics, 36:115. Wu, C. S., Ambler, E., Hayward, R. W., Hoppes, D. D., and Hudson, R. P. (1957). Experimental test of parity conservation in beta decay. Phys. Rev., 15:

121 BIBLIOGRAPHY 111 Zákoucký, D. (213). SRIM simulations to characterise the implantation of ions into the WITCH detector. Private communication.

122 Departement Natuurkunde en Sterrenkunde Celestijnenlaan 2d - bus Heverlee, BELGIË tel

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