Gitai Feinberg. November Thesis submitted for the degree of "Doctor of Philosophy" Submitted to the Senate of the Hebrew University of Jerusalem

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1 Study of the 7 Li(p,n) Reaction Towards Measurements of Neutron-Capture Cross Sections in the Astrophysical s-process With the SARAF Accelerator and a Liquid-Lithium Target Thesis submitted for the degree of "Doctor of Philosophy" by Gitai Feinberg Submitted to the Senate of the Hebrew University of Jerusalem November

2 This work was carried out under the supervision of: Prof. Michael Paul 2

3 Abstract The mechanism for production of the majority of heavy elements in stars involves neutron-capture processes. Abundances of these elements are determined by the stellar rates of the slow (s-)process and rapid (r-)process and the half-life of relevant nuclides. The neutron capture cross section on stable and unstable nuclides in the stellar regimes of energy is consequently an essential parameter in nuclear astrophysics. For the "weak" s-process, occurring in the He-burning outer shells of asymptotic giant branch stars and responsible for the bulk of isotopes with atomic mass numbers 56 A 90, the stellar temperature is believed to be ~350 MK (kt 30 kev). After rapid thermalization, neutrons (produced by (α,n) reactions) reach a Maxwell-Boltzmann distribution. The goal of the nuclear-astrophysics experiment is to make a reliable laboratory measurement of the neutron Maxwellian-averaged capture cross section (MACS). Measurements and calculations have shown that the neutrons from the 7 Li(p,n) 7 Be reaction, for an incident proton energy ~30 kev above threshold (E th,p = 1880 kev) on a thick lithium target, are emitted in a cone of 60 angular opening with an energy dependence very similar to the Maxwellian flux E E / kt e and an effective value kt 25 kev. Information about the stellar MACS can be obtained by laboratory cross section measurements with this neutron spectrum and extrapolations can be done to the required stellar temperature. This parameter has not been measured yet for a number of nuclides at or near important branching points of the s-process due to the lack of an appropriate intense neutron source. For those new cross section measurements, an intense proton beam is required in order to generate a high neutron flux. A large effort is presently deployed to replace conventional Van de Graaff accelerators used for production of neutrons with largerintensity machines in the ma range, in particular radio-frequency (RF) linear accelerators as well as improving the heat removal capabilities of the neutron production targets. An intense neutron source of new design was built, based on the 7 Li(p,n) 7 Be reaction for the measurement of such cross sections. It is based on the high intensity proton/deuteron superconducting linear accelerator at the Soreq Applied Research Accelerator Facility (SARAF) and on a Liquid-Lithium Target LiLiT. This work 3

4 focuses on the development of the SARAF and LiLiT setups for nuclear astrophysics measurements and on first experiments using a high-power proton beam reaching neutron intensities in the range of to n/s. It includes beam dynamics simulations of SARAF proton beam, simulations of the (p,n) reaction, low intensity experiments using a Van de Graaff accelerator, low intensity experiments at SARAF using a solid LiF target and first experiments with LiLiT and a ~2 kw proton beam. The neutron energy spectrum and intensity are sensitive to both the proton average energy and energy spread. The evaluation of the proton beam characteristics expected at SARAF for both high and low beam intensities is therefore important. Keeping the required neutron spectrum along the irradiation period requires transporting a stable and well characterized high-intensity proton beam to the target position. In this work beam dynamics calculations for SARAF phase I proton beam were performed in order to optimize the operational conditions for stellar neutron production. Special care was given to issues and limitations related to the operation of a high intensity RF superconducting linear accelerator and for the transport of a high intensity proton beam. Simulations of low and high intensity proton beam including space charge effects were performed in order to investigate the energy spread limitations at the end of the SARAF linac and at the end of SARAF phase I beamline. Optimization of the beam line magnets was done in order to minimize the losses along the beamline, to control the collimation of the beam by cooled and non-cooled collimators and to focus the beam into a small spot on target with σ 2 mm. For quantitative understanding of the expected neutron spectrum and for verifying the (p,n) reaction simulations we have performed low-intensity experiments with a Van de Graaff accelerator at the Institute for Reference Materials and Measurements (IRMM, Geel, Belgium). The effects of an energy-broadened proton beam on the spectrum of neutrons emitted in the thick-target 7 Li(p,n) reaction at E p = 1912 kev and on the experimental cross section of the 197 Au(n,γ) 198 Au reaction were investigated experimentally for the first time. Measurements were made with the bunched and chopped proton beam at the IRMM Van de Graaff facility using the time-of-flight technique, both with a narrow-energy proton beam (distribution standard deviation of σ 1.5 kev) and with a broad-energy proton beam (σ 20 kev) obtained with a gold foil degrader. Neutron spectra measured with the narrow-energy proton beam are consistent with those previously reported. The angle-integrated spectrum obtained with the broad-energy proton beam is closer to a Maxwellian flux 4

5 distribution than for a narrow-energy beam. The measured neutron spectra agree well with Monte Carlo simulations that include experimentally measured cross sections of the 7 Li(p,n) reaction, two-body kinematics and proton energy loss in the target. Gold activation studies were performed for proton beams with both narrow-energy and broad-energy spread to check the impact of the ensuing spectra on this important reference standard for activation measurements. Characterization of the SARAF proton beam and neutron production were performed in a setup positioned similarly to the design location of LiLiT at the end of the SARAF beamline. The characterization of the proton beam was done by time-of-flight and Rutherford Back Scattering (RBS), information about the SARAF beam was collected and methods for controlling the proton beam were developed. We put special efforts in determination of the beam energy and energy spread close to target position; the dependency in the tune parameters was also investigated. We developed a precise measurement setup and quantitative analysis method based on RBS to determine the energy and energy spread of the proton beam at a position near the neutron production target. First production of stellar-energy neutrons and Au activation were performed at SARAF with a low-intensity proton beam and a Solid LiF Target (SoLiT). The target was developed based on the target design used for MACS measurements at the Van de Graaff facility of Forschungszentrum Karlsruhe (FZK). The activations and cross section calculations were performed based on the same concepts as the experiments done at IRMM. In a separate experiment, stellarenergy neutrons were produced for the first time with a high-intensity proton beam using SARAF and LiLiT. The MACS of the 94 Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr reactions were measured relative to Au reference targets and preliminary results are reported. During the activations, the SARAF high intensity proton beam (~1 ma) was focused into a small spot (σ 3 mm) on the LiLiT free surface lithium jet. The successful operation of this new setup leads us into a new era for MACS measurements. 5

6 Contributions This thesis includes experimental work done in collaboration between the Hebrew University (Israel) and Soreq NRC (Israel), Argonne National Laboratory (IL, USA) and JRC-IRMM (Belgium). It also includes the development of simulation codes for the beam dynamics of the SARAF proton beam, the 7 Li(p,n) reaction (SimLiT), transport simulations (Geant4) and proton beam characterization by RBS. Beam dynamics simulations were presented in chapter 3. The codes were developed and the simulations for the different experiments were performed by the author. The experiments described in chapter 4 were performed in collaboration between the Hebrew University and two laboratories Soreq NRC and JRC-IRMM, Belgium. The author contributed to the preparations and execution of the experiments including building the setup for the measurement, the development of the 7 Li(p,n) simulation code, performing the experiments and the analysis of the collected data. The operation of the Van de Graaff accelerator was done by the IRMM crew; Asher Shor and Yossi Eisen (Soreq NRC) contributed to the experiment. The development of the 7 Li(p,n) and transport (Geant4) simulation codes were made in collaboration with Moshe Friedman and Moshe Tessler (Hebrew University). The experiments described in chapter 5 were performed in collaboration between the Hebrew University and Soreq NRC. The author contributed to the design and manufacturing of the solid LiF target and the development of the target RBS system, the preparations and execution of the experiments and the operation of the SARAF accelerator. The author characterized the liquid lithium target and defined the specifications of the target for the operation and for the astrophysics experiments. The author contributed to the construction (including the water jet simulation) and operation of LiLiT, the preparations for the high intensity experiment and performed the Zr activation experiment. The operation of SARAF was performed by Leo Weissman (Soreq NRC). The operation of LiLiT during the experiment was done by Shlomi Halfon and Danny Kijel (Soreq NRC). Analysis of the Zr activation experiment was performed in collaboration with Moshe Tessler. The experimental work and simulations development were carried out under the supervision of Prof. Michael Paul. 6

7 Contents ABSTRACT... 3 CONTRIBUTIONS... 6 CONTENTS... 7 LIST OF ACRONYMS AND DEFINITIONS CHAPTER 1: INTRODUCTION CHAPTER 2: SCIENTIFIC BACKGROUND Nuclear astrophysics The 7 Li(p,n) 7 Be reaction for stellar neutron production High intensity neutron sources for MACS measurements SARAF high intensity RF linac Lithium targets for neutron production CHAPTER 3: BEAM DYNAMICS FOR THE SARAF-LILIT AND SOLIT SETUPS The lattice A. Lattice implementation B. Lattice representation The initial distribution PSM tuning A. Relative phase determination B. PSM tune for minimal energy spread proton beam Beam dynamics for Solid LiF Target (SoLiT) experiments A. Low current simulation B. High current simulation Beam dynamics for LiLiT experiments A. LiLiT experiments lattice B. High current simulation C. Beam rectangular collimation Beam dynamics for LiLiT experiments with large spot A. Large spot experiment B. Beam dynamics calculation for large spot C. Beam rectangular collimation

8 CHAPTER 4: EXPERIMENTAL INVESTIGATION OF A BROAD-ENERGY PROTON BEAM USING A VAN DE GRAAFF ACCELERATOR AND DEVELOPMENT OF SIMULATION TOOLS FOR THE 7 LI(P,N) 7 BE REACTION Experimental method A. Accelerator and targets B. Detector setup and TOF measurements C. Activation setup D. Scan curves Neutron spectra A. Neutron spectra analysis B. Experimental neutron spectra C. Simulated neutron spectra Activation measurements A. γ-ray spectra analysis B. 7 Be and 198 Au production C. 197 Au(n,γ) 198 Au cross section CHAPTER 5: NUCLEAR ASTROPHYSICS AT SARAF USING A LIQUID LITHIUM TARGET Introduction Determination of the optimized acceleration conditions for the proton beam A. Diagnostics systems B. The method used for determination of the acceleration conditions C. Characterization of the energy dependence on the phase of the last operating cavity by D-plate RBS and TOF measurements D. High current TOF measurement for phase determination Proton beam energy characterization with SoLiT RBS diagnostic system A. RBS experimental setup B. Extracting the beam parameters from the RBS spectrum C. Energy calibration D. Simulation of the RBS spectrum Neutron production using SoLiT The Liquid-Lithium Target (LiLiT) for nuclear astrophysics A. LiLiT specifications B. Experimental setup LiLiT loop C. Experimental setup - cross section measurements with LiLiT Methodology for cross section measurements with LiLiT A. Proton beam characterization B. Neutron beam characterization C. Methodology of MACS determination Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr cross section measurements with LiLiT A. nat Zr activation with LiLiT B. MACS of the 94 Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr reactions CHAPTER 6: DISCUSSION AND CONCLUSIONS

9 REFERENCES APPENDICES Appendix 1: LiLiT design parameters and operational characteristics Appendix 2: SARAF phase I PSM and beamline lattice Appendix 3: Beamline magnets specifications Appendix 4: Custom GDFA Program - SoLiTpiperrms Appendix 5: Custom GDFA Program - SoLiTrmax Appendix 6: Custom GDFA Program - SoLiTavgrXZ Appendix 7: Custom GDFA Program - SoLiTxrms Appendix 8: Custom GDFA Program - SoLiTxmax Appendix 9: Custom GDFA Program - SoLiTyrms Appendix 10: Custom GDFA Program - SoLiTymax Appendix 11: GPT Input File Appendix 12: RBS simulation code Appendix 13: Hydrodynamics similarity experiments

10 List of acronyms and definitions ANL Argonne National Laboratory (Argonne, IL, USA) CW Continuous Wave D-plate Diagnostics table ECR Electron Cyclotron Resonance EIS ECR Ion Source FZK Forschungszentrum Karlsruhe (Karlsruhe, Germany) HWR Half Wave Resonator IRMM Institute for Reference Materials and Measurements (Geel, Belgium) LEBT Low Energy Beam Transport line LiLiT Liquid Lithium Target MACS Maxwellian-Averaged Cross Section MEBT Medium Energy Beam Transport line RFQ Radio Frequency Quadrupole PSM Prototype Superconducting Module RBS Rutherford Back Scattering SARAF Soreq Applied Research Accelerator Facility SimLiT a tool for calculating the neutron spectrum from the 7 Li(p,n) reaction SoLiT Solid LiF Target TOF Time-Of-Flight 4-jaw an adjustable rectangular collimator 10

11 Chapter 1: Introduction The mechanism for production of the majority of heavy elements in stars involves neutron-capture processes. Abundances of these elements are determined by the stellar rates of the slow (s-)process and rapid (r-)process and the half-life of relevant nuclides. The Maxwellian-Averaged Cross Section (MACS) of neutron-capture reactions is an important quantity for the estimate of s-process production rate of heavy elements. The goal of the nuclear-astrophysics experiment is to make a reliable laboratory measurement of this parameter for stellar neutrons with kt 30 kev. This parameter has not been measured yet for a number of nuclides due to the lack of an appropriate intense neutron source. Measurements and calculations have shown that neutrons with an energy dependence very similar to the Maxwellian flux E e E / kt and an effective value kt 25 kev can be produced by the 7 Li(p,n) 7 Be reaction. For those new cross section measurements, an intense proton beam is required in order to generate the high neutron flux. A large effort is presently deployed to develop high intensity neutron sources based on high intensity machines in the ma range, in particular radio-frequency (RF) linear accelerators as well as improving the heat removal abilities of the neutron production targets. We report on the construction of an intense neutron source for the measurement of such cross sections. It is based on the high-intensity proton beam of the superconducting RF accelerator at the Soreq Applied Research Accelerator Facility (SARAF) and a high-power Liquid-Lithium Target (LiLiT). This work focuses on the development of the SARAF and LiLiT setups for nuclear astrophysics measurements and on first experiments using a highpower proton beam reaching neutron intensities in the range of to n/s. The combination of the intense SARAF proton beam and a liquid-lithium target, used both as neutron source and power dump, is expected to open new research era in nuclear astrophysics. The neutron energy spectrum and intensity are sensitive to both the proton average energy and energy spread. The evaluation of the proton beam characteristics expected 11

12 at SARAF for both high and low beam intensities is therefore important. Beam dynamics calculations for SARAF phase I proton beam were performed in order to optimize the operational conditions for stellar neutron production and investigate the limitations for SARAF proton beam, specifically the energy spread limitations, at the neutron production target position. A detailed updated calculation for the current design of the beam line and accelerator configuration was performed. Optimization of the beam line magnets was done in order to minimize the losses along the beamline, to control the collimation of the beam by cooled and non-cooled collimators and to focus the beam into a small spot on target with σ 2 mm. The beam dynamics code development and calculations for the astrophysics studies are described in details in chapter 3. Low-intensity experiments were performed with a Van de Graaff accelerator at the Institute for Reference Materials and Measurements (IRMM, Geel, Belgium). The effect of an energy-broadened proton beam on the spectrum of neutrons emitted in the thick-target 7 Li(p,n) reaction was investigated experimentally for the first time. The neutron spectrum was measured by the time-of-flight technique, both with a narrowenergy proton beam (distribution standard deviation of σ 1.5 kev) and with a broadenergy proton beam (σ 20 kev) obtained with a gold foil degrader. Having the proton bunch characteristics at target position, we can simulate the expected neutron spectrum based on the 7 Li(p,n) 7 Be cross section, the energy loss in the target and the reaction kinematics. A simulation tool SimLiT, was developed to estimate the angular neutron spectrum and intensity. The SimLiT code is capable to perform the calculation at various beam energies, energy spreads and Li target chemical compositions. Good agreement was obtained between the neutron spectra measured by time-of-flight and the SimLiT calculated spectra. The cross section of the 197 Au(n,γ) 198 Au reaction was measured for both narrow-energy and broad-energy spread proton beams to check the impact of the ensuing spectra on this important reference standard for activation measurements. The time-of-flight measurements, 7 Li(p,n) simulation code and Au activation studies are presented in chapter 4. In order to reduce the complexity of the experiments with a high intensity proton beam we performed first experiments at SARAF with a low intensity proton beam for neutron production via the 7 Li(p,n) reaction. Characterization of the SARAF proton beam and first Au activations were performed in a setup positioned similarly to the following positioning of LiLiT at the end of SARAF beamline. We put special efforts 12

13 in determination of the beam energy and energy spread close to target position, the dependency in the tune parameters and accelerator operation was also investigated. We developed a precise measurement setup and quantitative analysis method based on Rutherford back scattering to determine the energy and energy spread of the proton beam at a position near the neutron production target. First production of stellar neutrons and Au activations were performed at SARAF with a low intensity proton beam and a Solid LiF Target (SoLiT), similar to solid targets used for astrophysics elsewhere. By the experience we acquired with a low intensity proton beam we developed the experimental methods and optimized the planned high intensity experiments at SARAF. For the first time stellar-energy neutrons were produced with a high intensity proton beam using SARAF and LiLiT. The MACS of the 94 Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr reactions were measured relative to Au reference targets and preliminary results are reported. During the activations, the SARAF high intensity proton beam (~1 ma, ~2 kw) was focused into a small spot (σ 3 mm) on the LiLiT free-surface lithium jet. The measurements performed at SARAF are presented in chapter 5. LiLiT specifications are listed in details in appendix 1. 13

14 Chapter 2: Scientific Background 1. Nuclear astrophysics Charged-particle fusion reactions account for the abundances of nearly all the isotopes of elements through the Fe group (6 < Z < 30). Almost all isotopes of Z > 30 elements are created from captures of free neutrons by Fe-peak target nuclei [BUR57, ROL88, SNE03]. For neutron capture reactions there are no electric charge barriers; as nuclei accrete neutrons, they become unstable and will undergo β - -decay transformation of neutrons into protons, thereby moving to higher Z (Fig. 1). The main sources for neutrons in stars which create the conditions for heavy elements production are believed to be the 13 C(α,n) 16 O and 22 Ne(α,n) 25 Mg reactions [KÄP98]. The produced neutrons are quickly thermalized through elastic scattering. The neutron velocity and energy distribution can be described by the Maxwell-Boltzmann distribution: 3 2m 2 2 n 2kT dn n v e dv / 2 ( kt) kt mv 2 E e E kt de where dn is the number of neutrons with velocity between v and v + dv (or energy between E and E + de), n 0 is the number of neutrons per unit volume, T is the temperature of the stellar interior and m is the neutron mass. The neutron fluxes in the He-fusion outer shells of asymptotic giant branch stars are sufficiently low (neutron density N n cm -3 ) that nearly all possible β-decays have time to occur between successive neutron captures. This relatively slow process is called the s-process and it can account for about half of the isotopes of the n-capture elements [KÄP98, BUS01]. Another process occurs in explosive sites where the neutron density can reach cm -3. Fast successive captures of neutrons may then happen before the isotope undergoes a β-decay creating a neutron-rich nucleus. Creation of n-capture isotopes in this rapid mode is called the r-process. The distribution of s-process elements can be fitted with two components of the s-process. The first component is called the "weak component" at temperatures corresponding to 14

15 Fig. 1: The s-process path (taken from [REI10]). kt 30 kev and is responsible for the bulk of isotopes with atomic mass numbers 56 < A < 90, the second component, called the "main component" at kt 5-10 kev, produces the heavier isotopes [HEI07]. The neutron capture cross section averaged over the energy-dependent stellar neutron flux the Maxwellian-Averaged Cross Section (MACS), on stable and unstable nuclides in the stellar energy regimes, is consequently an essential parameter in nuclear astrophysics which governs the evolution of heavy-nuclide synthesis. The goal of the nuclear astrophysical experiments is to make a reliable measurement of the MACS in the relevant range of neutron energies. 2. The 7 Li(p,n) 7 Be reaction for stellar neutron production The 7 Li(p,n) 7 Be reaction plays an important role in the production of neutrons in the kev-energy range. Beer and Käppeler [BEE80] showed that for a proton energy of 1912 kev (about 30 kev above the reaction threshold of 1880 kev), neutrons emitted from a thick target and integrated over kinematically allowed angles (<63 ), have an energy distribution similar to that of a flux of Maxwellian neutrons at a temperature kt 25 kev, except for the region close to and above the neutron-energy cutoff at E n 15

16 = 106 kev. The neutrons produced by this reaction with Van de Graaff accelerators have been widely used to activate nuclides involved in the s-process by providing a direct measure of the MACS at kt 25 kev. The experimental cross section of the 197 Au(n,γ) 198 Au reaction for the integral neutron spectrum was carefully measured by Ratynski and Käppeler [RAT88]. This cross section value is extensively used as a standard to monitor the neutron flux in MACS measurements on various targets [HEI05, HEI08, LED11]. 3. High intensity neutron sources for MACS measurements Following pioneering works on radioactive nuclides, such as 135 Cs(n,γ) [PAT04] and 60 Fe(n,γ) [UBE09], there exists a strong interest in expanding the activation measurements with samples of unstable nuclides, either at branching points of the s- process, off the valley of stability or for stable nuclides for which measurements are experimentally difficult (i.e., small cross sections, small isotopically enriched samples, decay radiation hard to detect, see, for example, Ref. [REI09b]). Higher proton-beam intensities (in the milliampere range) are then required, which are incompatible either with traditional Van de Graaff accelerators or with the poor thermal properties of conventional lithium targets. The use of RF accelerators with high-intensity proton beams for this purpose is also planned in other laboratories (e.g., FRANZ [RAT10, WIE10] and BINP [BAY09]). However, the properties of a high-intensity ion beam from a RF accelerator are different from those of Van de Graaff accelerators in two main aspects: a much poorer energy definition and a larger transverse distribution, limited by space-charge effects. These will, in turn, affect the shape of the neutron energy and angular distributions and the yield of neutrons emitted in the 7 Li(p,n) reaction within the solid angle subtended by a target and will require establishing a new methodology. 16

17 4. SARAF high intensity RF linac The Soreq Applied Research Accelerator Facility (SARAF) [MAR09a, MAR09b, WEI10, BER12] is based on a continuous wave (CW), proton/deuteron RF superconducting linear accelerator with currents up to 2 ma, built in two phases [NAG06, NAG08] (Fig. 2). SARAF phase I commissioning finished in 2009 and since then proton beam of up to 4 MeV and pulsed deuteron beam of up to 5 MeV are available. Phase I Phase II Fig. 2: SARAF scheme. Phase I of SARAF consists of a 20 kev/u Electron Cyclotron Resonance (ECR) ion source, a low-energy beam transport section, a 4-rod Radio Frequency Quadrupole (RFQ, 1.5 MeV/u), a medium energy beam transport section, a prototype superconducting module (PSM) housing 6 half-wave resonators and 3 superconducting solenoids. The beam line downstream the accelerator, as presented in Fig. 3, transports the high intensity beam to the target position. A rectangular collimator with 4 movable cooled plates (4-jaw) is positioned at the end of the beamline as can be seen in Fig. 3, this collimator is important for beam shaping and will be discussed in chapters 3 and 5. Target 4-jaw PSM Beamline RFQ Ion source Fig. 3: 3D model of SARAF phase I 25 m long setup. 17

18 5. Lithium targets for neutron production Two laboratories had a major contribution in developing our experimental method - Forschungszentrum Karlsruhe (FZK) in Germany and Argonne National Laboratory (ANL) in the USA. Astrophysics MACS measurements were performed at FZK since the 80's. Based on the 7 Li(p,n) 7 Be reaction, a solid-lithium or LiF target was irradiated by a Van de Graaff with a proton beam ( 100 μa) to create stellar-like neutrons with kt = 25 kev [BEE80, RAT88]. Calibration measurements were done with Au targets that served as a reference for following cross section measurements [BAO00, MAR09c]. The use of a solid target poses limitations on the heat removal abilities which limit the proton beam intensity and therefore limit the available neutron flux. Those limitations enable MACS measurement for most of the stable s-process nuclei but for some of the nuclei, higher neutron fluxes are required. Two liquid-lithium setups were built at ANL Nuclear Engineering Division in the recent years both for the RIA (FRIB) accelerator. The first setup included a free liquid-lithium jet for production of radioactive ions via fragmentation [REE04, NOL05] (Fig. 4). A stripper prototype for the uranium beam was also built as a thin liquid-lithium sheet (~10 μm) and proved to be feasible at velocity of ~60 m/s [MOM09]. It has been tested with an electron beam and recently also with a 260 W proton beam [REE13]. Based on the FZK and ANL experience, we developed at SARAF solid LiF and liquid-lithium targets of our own design. The solid target and the liquid-lithium target are described in chapter 5. Fig. 4: ANL fragmentation target design (taken from [REE05]). 18

19 Chapter 3: Beam Dynamics for the SARAF-LiLiT and SoLiT Setups We have performed detailed beam dynamics simulations for SARAF phase I linac and beamline. A schematic 3D drawing of the SARAF phase I linac and beamline is presented in Fig. 5. The simulations described here included the Medium Energy Beam Transport line (MEBT), the Prototype Superconducting Module (PSM) - cryogenic module consisting of six β = 0.09 Half-Wave Resonators (HWRs) made of bulk Nb and three superconducting solenoids for transversal focusing, the beamline which will be discussed in details in the following sections and the target chamber. In this thesis the ECR Ion Source (EIS), Low Energy Beam Transport line (LEBT) and the Radio Frequency Quadrupole (RFQ) were not simulated but an initial distribution of 1.5 MeV protons at the RFQ exit was used. This RFQ exit distribution was simulated [BAZ10] and will be discussed in section 2. Target Beamline D-plate PSM MEBT 2 RFQ LEBT EIS Fig. 5: 3D scheme of SARAF phase I linac and beamline. The simulations were aimed mainly to provide information about the following: Feasibility check for SoLiT and LiLiT experiments, i.e., the possibility to produce a beam with the required energy, energy spread and transversal parameters at the target position. 19

20 Provide a guiding tune for the PSM and beamline magnets. Estimate the energy resolution of the proton beam. Estimate the expected beam-loss and predict high losses locations. Reaching the required energy spread was in question since up to this work such astrophysics studies were performed in a Van de Graaff accelerator where the beam energy spread is small. This is not the case for RF accelerators that are characterized with a relatively large energy spread. The calculations were performed for both a solid LiF target - SoLiT and for LiLiT taking into account the differences of the lattice and proton beam characteristics. The General Particle Tracer (GPT) code [GPT07] used here for the beam dynamics calculations is a well-established simulation platform for the study of charged particle transport in electromagnetic fields. The code is entirely three-dimensional (3D), it is time based and uses 5 th order Runge Kutta integration. Realistic fields were used for the cavities and parameterizations for the magnets. For the space-charge effect a 3D multigrid based GPT routine [PÖP02] was used after verifying its validity for our case. This routine is based on an algorithm with semi linear dependency of the CPU time in the number of particle. Special care was given to make a precise and detailed description of the current beamline lattice. Our GPT model for the accelerator was tested and verified against another beam dynamics code (TRACK from ANL) and experimental measurements [ROD08]. 1. The lattice A. Lattice implementation The general scheme of SARAF MEBT, PSM and beamline including the main beamline magnets (quadrupoles and dipoles) are shown in Fig. 6, the lattice is specified in details in appendix 2. It is based on manufacturer specifications (PSM, quadrupoles, bending magnets) and on measurements of the beamline components and vacuum tubes. The beamline magnets specifications are specified in appendix 3. The effective and actual lengths of the beamline magnets are also presented in Fig. 6. The bore radius of all components (except the cavities) for SoLiT lattice from the 20

21 RFQ exit PSM MEBT 1 st doublet 45 dipole 45 dipole quadrupole 2 nd doublet target position Quad Quad target Quad HWR Quad Quad ,146,692 - actual lengths 231,118 - effective lengths Fig. 6: Up - 3D scheme of SARAF phase I MEBT, PSM and beamline, down - a schematic positioning of the beamline magnets, effective and quadrupole actual lengths are shown (in mm). Fig. 7: SoLiT lattice bore radius along the MEBT, PSM, beamline and SoLiT chamber. RFQ exit to the last collimator in the experimental chamber, positioned m downstream the RFQ, are shown in Fig. 7 with a 3D representation of the relevant part of SARAF. 21

22 B. Lattice representation The elements position and orientation are determined relative to the GPT coordinate system. It is possible to define tilted coordinate systems at different positions in space, run the simulation and produce realistic results but the visual representation of the particles using the GPT standard routines may be only produced relative to the GPT standard coordinate system - "wcs" (world coordinate system) where z is the longitudinal axis at the center of the PSM beam pipe, x is the horizontal axis and y is the vertical axis. In order to visualize SARAF phase I "S"-shape beamline, understand the beam dynamics behavior and minimize the losses, new routines for the actual SARAF phase I lattice were written. The RMS radius of the bunch can give important information about the quality of the transversal tune. This parameter was calculated specifically for the geometry of SARAF phase I beamline. The new GPT routine "SoLiTpiperrms" calculates the bunch RMS radius - R rms R i i 2 while the contribution of each macroparticle to the bunch RMS radius is calculated based on the position of the particle at the time of the integration step. The calculation is done along the accelerator and beamline with the reference of the geometric center of the beam pipe (see Fig. 8). Error analysis (typical measurement error is 1 mm) was not performed, however, misalignments and measurements errors can be compensated in part during beam tuning by the steerers. The calculation is done for 5 different sections, see Fig. 8 and Fig. 6 (all lengths are in mm): 1) Section 1 before the first bending magnet (yellow, z < 8592): relative to the center of the beamline which is the "wcs" z axis (x = y = 0): R 2 i X 2) Section 2 inside the first bending magnet (blue, limit: x = -z ): relative to the bend arc at the X-Z plane which is the geometric place of all the points with a distance of 1350 mm from the point (Z, X) = (8592, 1350): R 2 i 2 i Y 2 i Z 8592 X 1350 Y 1350 i i i 3) Section 3 between the bending magnets (green, limit: x = -z+11360): relative to the center of the beamline: L R i 2 L 2 2 Y 2 i 2 L 2 Y 2 i, L X i Z i

23 ) Section 4 inside the second bending magnet (pink, limit: z = 11210): relative to the bend arc at the X-Z plane which is the geometric place of all the points with a distance of 1350 mm from the point (Z, X) = (11210, 150): R 2 i Z X 150 Y 1350 i i i 5) Section 5 after the second bending magnet (purple, z > 11210): relative to the center of the beamline which is parallel to the "wcs" z axis at a distance of mm: R 2 i 2 2 X.8 Y i 1499 i The GPT new routine "SoLiTpiperrms" is presented in appendix 4. The transversal parameters for RMS and maximal values for X, Y and R are calculated by the new GPT routines "SoLiTrmax" (App. 5), "SoLiTavgrXZ" (App. 6), "SoLiTxrms" (App. 7), "SoLiTxmax" (App. 8), "SoLiTyrms" (App. 9) and "SoLiTymax" (App. 10). 2 (8592,1350) SoLiT beamline - bending magnets XZ plane: (Z,X) X (Z 0,X 0 ) X=-Z Y Z L 2 L L X Z ( ,1104.5) X=Z-9151 (9546.3,395.3) (Z 0,Z ) (10651,1499.8) 1350 X=-Z (11210,1499.8) (11210,150) (8592,0) 559 (9151,0) Fig. 8: The X-Z plane geometric representation of the 45 bending magnets and the beam pipe between them starting 8592 mm after the RFQ exit. The linac and beamline are divided into 5 sections for the calculation of the beam transversal parameters, the calculation is done with the reference of the geometric center of the beam pipe. Lengths presented are in mm. 23

24 2. The initial distribution This work does not address the transport of particles through the LEBT and RFQ which are independent of the properties of the eventual accelerated beam. We take as input for the subsequent calculations, an initial distribution of 5000 particles transported by simulation through the RFQ (Fig. 9 and Fig. 10) with energy of 1.5 MeV/u [BAZ10]. The particles coordinates are given with the reference of the end of the RFQ end flange. The transverse emittance values are and π mm mrad for the X-X' and Y-Y' planes and the longitudinal emittance is ev sec Energy (kev) GPT Position (mm) Fig. 9: The protons longitudinal initial distribution at the RFQ exit. BetaX (%) GPT X (mm) BetaY (%) GPT Y (mm) Fig. 10: The protons transversal initial distribution at the RFQ exit for X (horizontal, left) and Y (vertical, right) planes. The Y axis represents the velocity of the particles in % of c. 24

25 3. PSM tuning For the base PSM tune, the current was determined to be 100 μa. For the initial distribution given at the RFQ exit (average energy of 1507 kev and energy spread of 8.1 kev (1 σ)), the average energy remains constant through the MEBT and the energy spread for low current beam increases somewhat to 8.2 kev. Tuning the PSM included the determination of the amplitudes and phases of the 6 HWRs and the PSM solenoids. The cavities' amplitudes are limited by the HWR peak field (25 MV/m) corresponding to a maximal total accelerating voltage of 840 kv. The tune was performed aiming for a required average proton energy of 1912 kev at the PSM exit and at the target position, beam transversal dimensions were kept small inside the PSM and focused properly to match the consecutive beamline magnet. A. Relative phase determination SARAF cavities absolute phases are determined with reference to the accelerator master oscillator. GPT also uses absolute phases for the cavities with reference to the start time of the simulation (time = 0). Since the absolute phase is determined by the cavity only and have no dependency on the beam bunches, we characterize the cavity by its "relative phase" with reference to the "zero phase" (0 ) which corresponds in maximal energy gain for the bunch. For a specific tune the 0 for each cavity is calculated iteratively by maximizing the bunch energy at the cavity exit using a GPT optimization routine, the cavities relative phases are determined respectively. B. PSM tune for minimal energy spread proton beam The longitudinal behavior in the PSM is shown in details in Fig. 11. Because of the long distance between the RFQ exit and the first cavity we use cavity 1 as a buncher to reduce the bunch length. Cavity 2 is not active in order to increase the bunching and most of the required energy is gained by cavities 3 and 4 working close to the standard accelerating relative phase of φ rel =-30. Tuning of cavity 6 was done iteratively (amplitude and phase) after tuning the proton energy after cavity 4 to be ~33 kev below the final value. Both the amplitude and the phase of cavity 6 were determined to get the required energy of 1912 kev and to tilt the longitudinal phase ellipse horizontally minimizing the energy spread at the cavity exit to a value of 4.4 kev (Fig. 11 inset 6). The behavior of the longitudinal phase ellipse is shown in Fig. 25

26 11 insets 1-6; the insets full scale was kept to be 2.5 cm for the position and 150 kev for the energy. The setting of the cavities (amplitudes and relative phases) is presented in Table 1. The power consumption of the cavity couplers limits the proton current the cavities are able to accelerate. The amplitudes of cavities 3 and 4 which provide most of the acceleration are relatively low therefore this tune is lowering the demands of the couplers and is increasing the current limit well above the current required for future planned experiments Energy (MeV) GPT Position (m) Energy (MeV) Position (m) GPT Energy (MeV) GPT Position (m) Energy (MeV) GPT Position (m) Energy spread (kev) GPT Position (m) Fig. 11: The energy spread (RMS) along the PSM and the longitudinal ellipses. Energy (MeV) Energy (MeV) GPT GPT Position (m) Position (m) Relative HWR Amplitude phase 1 22% % % % -46 Table 1: The setting of the cavities. The amplitude is given as % of the maximum voltage. 26

27 LiLiT lattice option Energy (MeV) Energy (MeV) The dependency of the energy and energy spread with cavity 6 phase was checked at 1.90 the PSM exit and presented in Fig. 12. Maximal energy is gained by operating cavity Energy (MeV) 6 at an 1.88 absolute phase of φ abs = For minimization of the energy spread while reaching 1.86 an energy of 1912 kev, the 1.86 cavity was 1.86 tuned for 1.86 an absolute phase of 70 (Fig. 12) therefore cavity 6 operates at a relative phase of φ rel =-46 (Table 1) Energy (MeV) Energy (MeV) Energy (MeV) Relative cavity 6 phase (deg) Relative cavity 6 phase (deg) GPT Cavity 6 GPT phase Cavity (deg) 6 phase (deg) Cavity 6 phase GPT (deg) GPT Cavity 6 GPT phase Cavity (deg) 6 phase (deg) Cavity 6 phase (deg) GPT Energy (MeV) φ rel= Energy (MeV) Energy (MeV) φ abs=70 φ abs = φ 15 rel= φ abs =70 φ abs = GPT GPT Absolute Cavity Cavity 6 Cavity phase cavity 6 phase (deg) 6 phase (deg) (deg) GPT GPT GPT Absolute Cavity 6 Cavity phase cavity Phase 6 (deg) 6 phase phase (deg) (deg) GPT Energy (MeV) Energy Energy spread (MeV) (kev) Fig. 12: Average energy (left) and RMS energy spread (right) at the PSM exit vs. cavity 6 phase. 4. Beam dynamics for Solid LiF Target (SoLiT) experiments A. Low current simulation We present here beam dynamics results for low-intensity experiments with the Solid LiF Target (SoLiT); see chapter 5 for details. The GPT code, given in appendix 11, includes an up-to-date lattice of the linac, beamline and the target chamber design (Fig. 13, see chapter 5 for details) and provides a tune for 5000 protons with the desired average energy of 1912 kev with negligible beam-loss along bellows SoLiT lattice Fig. 13: SoLiT chamber scheme and longitudinal lengths in mm. the linac and beamline. The target chamber is defined in the input file as the element after the end of the beamline. The overall distance between the end of the beamline and the LiF target is ~52 cm. The behavior of the beam radius (RMS and 5000 macroparticles envelope compared to the bore radius) is presented in Fig. 14. The simulation specification and results are summarized in Table 2. The PSM solenoids bellow SoLiT chamber collimator (dia. = 14 mm) beam LiLiT lattice option 1 Diagnostics chamber A SoLiT cup collimator (dia. = 6 mm) X SoLiT LiF cup

28 and beamline magnets were tuned to minimize the losses and focus the beam on target through the 2 collimators designed for the SoLiT chamber and for the target a 14 mm dia. cooled collimator in the SoLiT chamber and a 6 mm dia. collimator positioned just before the LiF target (Fig. 13) out of 5000 macro-particles reached the SoLiT chamber, while 4568 SoLiT, low current Lattice SoLiT beamline Number of macroparticles 5000 Final energy 1912 kev Current 100 μa 4-jaw cuts NO R RMS (target position) 1.8 mm Energy spread (σ, PSM exit) 4.4 kev Energy spread (σ, target position) 4.5 kev Table 2: Specifications for simulating the SoLiT low current experiment and results. macro-particles reached the LiF layer. All the macroparticles passed the cooled collimator (dia. = 14 mm) and 432 macroparticles were lost at the SoLiT cup collimator (dia. = 6 mm). The simulation results for the transversal beam parameters at target position (15.83 m) are: R RMS = 1.8 mm, X RMS = 0.8 mm and Y RMS = 1.7 mm. Fig. 14: Beam RMS radius (blue) and 5000 protons envelope (red) as function of the position along the accelerator, I = 100 μa. The bore radius (black) represents the SoLiT beamline lattice. 28

29 Energy (MeV) GPT Position (m) 25 Energy (MeV) GPT Position (m) Energy (MeV) GPT Position (m) Energy (MeV) GPT Position (m) Energy spread (kev) Energy (MeV) φ rel= Position (m) GPT Fig. 15: The energy spread (RMS) along the MEBT, PSM and beamline for low intensity beam. The longitudinal phase ellipses are shown at different positions. The energy full scale is kept constant (full range of 150 kev) in all insets, the position full scale of insets 1 and 2 is 2.5 cm and 20 cm for insets 3 and 4. The behavior of the longitudinal ellipse from the RFQ exit and until the end of the beamline 1.92is presented in Fig The resulting values of the energy distribution are: <E> = MeV, de = 4.4 kev (1 1.90σ) at the 1.90 PSM exit and kev at target position. This slight increase is the result of 1.88 the space-charge 1.88 effect 1.88 for current of 100 μa. The dependency of the average energy and energy spread on cavity-6 phase is presented in Fig. 16 for 2 positions PSM exit and target position. The dependency is Relative cavity 6 phase (deg) Relative cavity 6 phase (deg) GPT Cavity 6 GPT phase (deg) Cavity 6 phase Cavity (deg) 6 phase GPT (deg) GPT Cavity 6 GPT phase (deg) Cavity 6 phase Cavity (deg) 6 phase (deg) GPT Energy (MeV) Energy (MeV) Energy (MeV) At PSM exit At target position φ rel= φ= φ= Cavity GPT Cavity 6 phase 6 phase (deg) GPT (deg) Cavity GPT Absolute Cavity 6 phase 6 phase (deg) (deg) GPT Cavity cavity 6 phase (deg) GPT Absolute Cavity cavity 6 6 phase (deg) (deg) GPT Energy (MeV) Energy (MeV) Energy (MeV) Energy (MeV) Energy (MeV) Energy Energy spread (MeV) (kev) At PSM exit At target position Fig. 16: Average energy (left) and RMS energy spread (right) vs. cavity 6 phase at PSM exit and at target position, I=100 μa Energy (MeV)

30 quite similar while operating close to the tune (φ abs = 70 ), the small differences are caused by low losses and space charge effects along the beamline. Major differences are seen for phases out of tune because of major losses along the beamline. The energy spread minimal value for a tuned beam is achieved for φ abs ~ 70. B. High current simulation The same PSM tune was used for accelerating a 2 ma proton beam to 1912 kev. The significant increase in space charge required a new tune for the beamline magnets. The simulation specification and parameters are summarized in Table 3. For a high intensity beam, the ability to control and focus the beam on target is important and losses or deviation from the desired spot size should be minimized. In order to have better focusing on target, the beamline quadrupole and second doublet magnetic fields were changed. In order to optimize the tune, the beam transversal parameters at the second doublet were examined - the beam is wider at the Y axis at the second doublet first quadrupole than at the X axis and narrower at the Y axis at the second doublet second quadrupole. Analyzing the losses origin, we find that the collimated particles were lost at the cup collimator at the Y axis tails, therefore in order to have better focusing at the Y axis, the beam needs to get wider Lattice SoLiT, high current SoLiT beamline Number of macroparticles 5000 Final energy Current 4-jaw cuts R RMS (target position) Energy spread (σ, PSM exit) Energy spread (σ, target position) 1912 kev 2 ma NO 1.8 mm 4.8 kev 6.7 kev Table 3: Specifications for simulating the SoLiThigh current experiment and beam parameters. Fig. 17: Beam RMS radius (blue) and 5000 protons envelope (red) as function of the position along the accelerator, I = 2 ma. The bore radius (black) represents the SoLiT beamline lattice. 30

31 on Y at the second doublet. Increasing the beamline single quadrupole field enlarged the beam on the Y axis which enabled stronger focusing by the following doublet and lower Y RMS value at the waist. Tuning the waist at target position gave R RMS = 1.8 mm, X RMS = 1.0 mm and Y RMS = 1.5 mm at Z = m (Fig. 17). Losses of 293 macroparticles were observed on the 6 mm dia. collimator of SoLiT target. The behavior of the energy spread in the PSM is shown in Fig. 18 together with the longitudinal phase space at 6 different locations: before and after cavity 1 insets 1 and 2 respectively, before and after cavity 4 insets 3 and 4 respectively and before and after cavity 6 insets 5 and 6 respectively. For proton current of 2 ma, the space Energy (MeV) GPT 30 Energy (MeV) Position (m) Position (m) GPT Energy (MeV) GPT Position (m) Energy (MeV) GPT Position (m) Energy spread (kev) GPT Position (m) Fig. 18: RMS energy spread along the PSM. Insets 1-6 show the longitudinal phase space. Energy (MeV) GPT Position (m) Energy (MeV) GPT Position (m) 31

32 charge effect has significant effects on the energy spread, the decrease in the energy spread between positions 1.3 m and 1.8 m can be explained looking on the longitudinal phase space in inset 2 the slow particles are at the head of the bunch and been accelerated by the space charge effect, the fast particles are at the end of the bunch therefore Energy spread (kev) GPT Position (m) Fig. 19: RMS energy spread along the accelerator. The increase along the beam line is due to the space charge repulsion. being decelerated. The net effect is a decrease in the energy spread due to space charge. As can be seen in Fig. 19, the energy spread is increasing along the beamline from 4.8 kev to 6.7 kev because of the space charge effect. In Fig. 20 we see the development of the longitudinal ellipse along the beamline. The X axis scale is 25 Energy (MeV) GPT Position (m) 30 Energy (MeV) GPT Position (m) Energy (MeV) GPT Position (m) Energy (MeV) GPT Position (m) Energy spread (kev) GPT Position (m) Fig. 20: RMS energy spread along the linac and beam line. Insets 1-4 show the longitudinal phase space at different positions. The bunch length at target position is 20 cm (inset 4). 32

33 mm for insets 1 and 2 and 200 mm for insets 3 and 4, the energy axis scale is 150 kev for insets 1-4. For λ = cm (176 MHz) and β = 6.4% (E = 1912 kev) we get βλ 11 cm. At position of 16 m, the bunch full length is 20 cm (inset 4), the bunches are not separated any more therefore the space charge effect is reduced. The simulation includes only one bunch and not taking into account this effect therefore may predict higher energy spread at the end of the beamline for high currents. The PSM tune was based on the low current simulation where the energy spread was constant along the beamline, therefore a minimum at the end of the PSM resulted in a minimum at target position. Since for 2 ma there is a growth in the energy spread along the beamline due to space charge repulsion, it is possible to lower the energy spread by changing the longitudinal ellipse orientation after cavity 6 in order to cause the space charge repulsion to reduce the energy spread. We change the longitudinal focusing of cavity 6 to produce a bunch at the end of the PSM with opposite velocity distribution the slow protons at the head of the bunch and the fast protons at the end of the bunch. Optimizing the PSM tune resulted in lower relative phase (-57 ) for cavity 6 in order to have better focusing, with a higher amplitude (8.9%) for keeping the energy the same 1912 kev. It can be seen in Fig. 21 that the energy spread is decreasing at the PSM exit since the fast particles at the end of the bunch are decelerating because of the coulomb repulsion and the slow particles at the head of the bunch are accelerating because of this effect. The energy spread at target position gets a lower final value of 5.9 kev. Energy spread (kev) Position (m) GPT Fig. 21: RMS energy spread along the linac and beam line. Stronger longitudinal focusing together with the space charge effect causes reduction in the energy spread after exiting cavity 6. 33

34 SoLiT lattice 5. Beam dynamics for LiLiT experiments A. LiLiT experiments lattice bellow The differences between the 10lattice for SoLiT and LiLiT experiments include 329 cancelation of the SoLiT chamber collimator and SoLiT cup collimator and enlargement of the last drift. 50 The 115 lattice for LiLiT experiments is shown in Fig and the longitudinal dimensions are presented in Table 4. The distance between the end of the beamline and the lithium jet is larger by ~19 cm than for SoLiT LiF layer. LiLiT lattice option 1 beam bellow End of beamline End of beamline Diagnostics chamber SoLiT chamber Diagnostics Bergoz chamber LiLiT lattice ampermeter option 2 A X LiLiT valve LiLiT chamber Fig. 22: The lattice for LiLiT experiments. LiLiT lattice diagnostics chamber Bergoz current transducer LiLiT valve LiLiT chamber Total 270 mm 40 mm 75 mm 329 mm 714 mm Table 4: Longitudinal lengths for LiLiT lattice. End of SoLiT bellow B. High beamlinecurrent chamber simulation chamber 329 Foils Foils Diagnostics chamber + chamber KF->CF adapter Diagnostics Bergoz LiLiT ampermeter A X chamber valve The tune for LiLiT experiments was done based on the beam dynamics simulations performed for SoLiT experiments The operational characteristics defined for LiLiT 270 [FEI08a] were the references for this tune (Table 40 5). The simulation specification and results are summarized in Table 6. Simulating a high current beam required increasing the magnetic field of the third solenoid in the PSM and some of the beamline quadrupoles in order to keep the beam loss at low level along the beamline. The simulation results are presented in Fig. 24. Fig. 24a and Fig. 24b show the mean energy and energy spread, respectively, of the bunched beam as function of the bunch longitudinal average position along the accelerator. In Fig. 24c and Fig. 24d the RMS radius is presented along the accelerator and at target position. Fig. 24e and Fig. 24f show the transversal behavior for X and Y respectively. The envelope and the RMS value are presented as a function of the longitudinal position. In order to reach the transversal beam parameters, the beam was focused along both X and Y axis in order to have a waist after the target position (45 cm after the target for X and 35 cm for Y). 75 LiLiT chamber

35 LiLiT user requirement specification (App. 1) Energy 1912 kev Current at PSM exit 3.5 ma σ x = σ y 2.2 mm R RMS cut x = 1.8σ x cut y = 1.5σ y proton beam width proton beam height Current at lithium jet 3.1 mm 3.96 mm 3.3 mm 7.9 mm 6.6 mm 2.8 ma Table 5: LiLiT user requirement specifications. LiLiT, high current Lattice LiLiT beamlines Number of macroparticles 5000 Final energy 1912 kev Current 3.5 ma 4-jaw cuts NO YES R RMS (target position) 3.1 mm 2.8 mm Energy spread (σ, PSM exit) 5.7 kev Energy spread (σ, target position) 8.6 kev 8.5 kev Table 6: Specifications for simulating the LiLiT high current experiment and results. The beam parameters at target position fitted almost absolutely the required values X RMS = 2.1 mm, Y RMS = 2.2 mm and R RMS = 3.1 mm. Special care was given for transversal tuning to obtain very low losses 4991 macroparticles reached the target. 9 macroparticles were lost along the beamline at 3 different positions (Fig. 23), for a 3.5 ma simulation, beamloss of < 0.1% at a specific position is reasonable in terms of heat removal abilities Rmax (mm) GPT Position (m) Fig. 23: The maximum radius for 5000 protons along the accelerator. Losses of 9 macroparticles occur at 3 different locations (red circles). 35

36 Energy (MeV) GPT Position (m) Figure 24a: The average proton energy as function of position of the center of the bunch as it progresses along the accelerator starting at the RFQ exit. The target is placed at a position of ~16.0 m. RMS radius (mm) GPT Position (m) Figure 24c: The RMS radius as function of position of the center of the bunch as it progresses along the accelerator starting at the RFQ exit. The target is placed at a position of ~16.0 m. 30 Energy spread (kev) GPT Position (m) Figure 24b: The energy spread (1 STD) as function of position of the center of the bunch as it progresses along the accelerator starting at the RFQ exit. The target is placed at a position of ~16.0 m. RMS radius (mm) GPT Position (m) Figure 24d: The RMS radius as function of position of the center of the bunch at LiLiT chamber position. The RMS radius is 3.1 mm at the lithium jet position (red circle). 35 X (mm) X envelope 5000 protons X RMS Y (mm) protons Y envelope Y RMS GPT Position (m) Figure 24e: The X RMS and envelope as function of position of the center of the bunch as it progresses along the accelerator starting at the RFQ exit. The target is placed at a position of ~16.0 m Position (m) GPT Figure 24f: The Y RMS and envelope as function of position of the center of the bunch as it progresses along the accelerator starting at the RFQ exit. The target is placed at a position of ~16.0 m. Fig. 24: Simulation results - LiLiT, high current (Table 6). 36

37 C. Beam rectangular collimation As specified, the beam should be cut at 1.8 σ x (92.8%) and 1.5 σ y (86.6%) assuming Gaussian distribution for the X and Y axis. Both cuts results in 20% losses therefore reduction of the current from 3.5 ma to 2.8 ma. At the 4-jaw collimator position the transversal beam parameters are X RMS = 6.5 mm and Y RMS = 4.5 mm. Cutting the beam to get a 23.4X13.5 mm beam spot results in 17% losses (4157 macroparticles passed the 4-jaw). The distribution of the proton beam at target position while the 4- jaw is open is presented in Fig. 25 (left). All the 4991 macroparticles are focused inside the jet width of 18 mm. In Fig. 25 (right) the results of similar simulation with 4-jaw closed as specified are presented, the beam tails are smaller at target position and the entire beam (4157 macroparticles) hit the jet with a total width of 11 mm Y (mm) 0 Y (mm) X (mm) GPT X (mm) Fig. 25: The X-Y beam distribution at target position (16.0 m). Left - the 4-jaw is open, 4991 macroparticles reach the target. Right - the 4-jaw cuts the beam, 4157 mocroparticles reach the target. GPT 37

38 6. Beam dynamics for LiLiT experiments with large spot A. Large spot experiment LiLiT experiments demand a focused beam with σ ~ 2 mm (see chapter 5 and [HAL13a] for details). For preliminary experiments and heat removal tests it is preferable to irradiate the lithium with a large beam spot. The limitation of enlarging the beam spot comes from the poor heat removal ability of the lithium jet stainless steel sides (SS ears, see Fig. 26 and Fig. 55). Irradiating the SS ears by the proton beam can cause over heating and excessive evaporation of lithium from the SS ears, therefore for those experiments, the collimation of the beam is very important and may be achieved by closing the 4-jaws and cutting the proton beam X distribution tails. The jet width is 18 mm and the limit for the power deposited by the beam outside the jet width is ~10 W, however, the 4-jaw collimation is also limited by heat removal ability of 1 kw for every jaw. Lithium jet 18 mm SS ears Fig. 26: LiLiT lithium jet. Beam dynamics calculation were performed to evaluate the possibility to double the beam spot diameter (σ ~ 4 mm) while protecting the SS ears by leaving safety margins at the sides between the beam and the SS ears. B. Beam dynamics calculation for large spot Beam dynamics calculations were performed for LiLiT experiments with large spot without 4-jaw collimation and with collimation. The simulation specifications and parameters are summarized in Table 7. The simulation results are presented in Fig

39 protons No 4-jaw collimation 20 No 4-jaw collimation 5000 protons 30 R envelope 15 Radius (mm) RMS radius Radius (mm) 10 5 R envelope RMS radius GPT Position (m) Figure 26a: The RMS and maximum radius as function of position of the center of the bunch as it progresses along the accelerator starting at the RFQ exit. The target is placed at a position of ~16.0 m. GPT Position (m) Figure 26b: The RMS and maximum radius as function of position of the center of the bunch at LiLiT chamber position. The RMS radius is 6.1 mm at the lithium jet position (red circle) protons X envelope No 4-jaw collimation protons Y envelope No 4-jaw collimation X (mm) X RMS Y (mm) Y RMS Position (m) GPT Figure 26c: The X RMS and envelope as function of position of the center of the bunch as it progresses along the accelerator starting at the RFQ exit. The target is placed at a position of ~16.0 m Position (m) GPT Figure 26d: The Y RMS and envelope as function of position of the center of the bunch as it progresses along the accelerator starting at the RFQ exit. The target is placed at a position of ~16.0 m. Radius (mm) protons R envelope RMS radius 4-jaw collimation Radius (mm) After the 4-jaw collimation R envelope 5000 protons GPT Position (m) Figure 26e: The RMS and maximum radius as function of position. The 4-jaw collimator cuts the beam at a position of 14.5 m. The target is placed at a position of ~16.0 m. GPT RMS radius Position (m) Figure 26f: The RMS and maximum radius as function of position at LiLiT chamber position after the 4-jaw cut. The RMS radius is reduced to 4.6 mm at the lithium jet position (red circle). Fig. 27: Simulation results - LiLiT, large spot (Table 7). 39

40 Keeping the 4-jaw aperture open, 4991 out of 5000 macroparticles reached the target. The beam transversal dimensions at target position were: X RMS = 4.6 mm, Y RMS = 4.0 mm and R RMS = 6.1 mm. When closing the 4-jaw to form a rectangular collimator with dimensions of 16.6X21.6 mm (blocking all particles with X > 8.3 mm or Y > 10.8 mm), only 3615 passed the 4-jaw and reached the target reducing the current to 2.5 ma. The beam transversal dimensions at target position fitted the required specifications and will be presented in the following section. C. Beam rectangular collimation Lattice LiLiT, large spot LiLiT beamlines Number of macroparticles 5000 Final energy Current at PSM exit Energy spread (σ, PSM exit) 1912 kev 3.5 ma 5.7 kev 4-jaw collimation 4-jaw open 4-jaw closed Energy spread (σ, target position) 8.6 kev 8.4 kev Current at target 3.5 ma 2.5 ma R RMS at target position 6.1 mm 4.6 mm X RMS at target position 4.6 mm 3.1 mm Y RMS at target position 4.0 mm 3.4 mm X max at target position 15 mm 8 mm Table 7: Specifications for simulating the LiLiT large spot experiment and results. The 4-jaw collimation is done mostly on the X axis particles with X > 8.3 mm or Y > 10.8 mm are blocked. Fig. 28 shows the collimation of the beam while it is passing through. The beam is focusing before the target and reaches the target position with the required dimensions as can be seen at simulation time of 885 ns. The transversal distribution at target position (time = 885 ns, position at "CS_shifted" = m) is presented in Fig. 29 with visualization of the lithium jet nozzle. The X- Time = 787 ns Time = 794 ns Time = 799 ns Time=885 ns Y (mm) 0 Y (mm) 0 Y (mm) 0 Y (mm) GPT X (mm) GPT X (mm) GPT X (mm) GPT X (mm) Fig. 28: The X-Y beam distribution, collimation of the particles by the 4-jaw for X > 8.3 mm or Y > 10.8 mm. From left to right - at the 4-jaw entrance (time=787 ns), while the front part of the bunch is inside the 4-jaw (time=794 ns), at the 4-jaw exit (time=799 ns), at target position (time=885 ns). 40

41 axis is on scale and the width of the jet is represented by the blue lines. The particles distribution without 4-jaw collimation is presented in Fig. 29 (up), significant fraction of the beam deviate from the jet borders by up to 6 mm. Collimating the beam by the 4-jaw (Fig. 29, down), eliminate the beam tails at the X and Y axis keeping safety margins of 1 mm from the SS ears Y (mm) GPT X (mm) Y (mm) GPT X (mm) Fig. 29: Visual representation of the lithium nozzle and beam transversal distribution at target position. The blue dashed lines represent the jet width (18 mm). Up no 4-jaw collimation, significant fraction of the beam hit the SS ears. Down the beam is collimated by the 4-jaw, all the macroparticles hit the lithium jet, no losses on the SS ears. 41

42 Chapter 4: Experimental Investigation of a Broad-energy Proton Beam Using a Van de Graaff Accelerator and Development of Simulation Tools For The 7 Li(p,n) 7 Be reaction Using the Van de Graaff accelerator of the Institute of Reference Materials and Measurements (IRMM, Geel, Belgium) [SAG10, FEI10], we studied experimentally the energy and angular distributions of neutrons emitted by the 7 Li(p,n) reaction and investigate the effects of a broadened-energy proton beam compared to the case of a typical beam with well-defined energy. The broadened-energy distribution was obtained by straggling of the incident protons in a gold foil placed immediately in front of a LiF target. The experiments are used to validate extensive simulation codes for the calculation of energy and angular distributions of the emitted neutrons. Neutrons were detected by 6 Li-glass detectors, and their energy was measured with the time-of-flight (TOF) technique, using a 625-kHz pulsed proton beam. The angular range of interest was covered in steps of 5. The energy spectra for these emission angles were weighted and were summed to obtain the integral energy distribution. For nearly monoenergetic protons (σ 1 kev), the high-energy end of the neutron spectrum has a sharp cutoff. In the broad-energy case, this cutoff is more diffuse, which results in a closer match with the E E / kt e dependence of the Maxwellian stellar flux. This behavior is expected from simulations of the 7 Li(p,n) reaction [REI09a, FRI11, FRI13]. The experimental cross section of neutron capture on gold was measured for the Van de Graaff narrow-energy proton beam and for the energybroadened proton beam and was compared to the standard value established in ref. [RAT88]. The main aim was to determine the change in the spectrum-averaged cross section due to the difference in the neutron spectrum in these two beams. Sec. 1 describes the experimental setup for neutron detection and activation measurements. Results and analysis of the neutron energy and angular distributions are presented in 42

43 Sec. 2 and are compared to the results of the simulation. Sec. 3 describes the neutron activation of gold. The results of this experiment were presented in [FEI12a, FEI12b]. An experimental work, similar to the present one, was performed in parallel by Lederer et al. [LED12]. 1. Experimental method A. Accelerator and targets The experiments were performed in the low-scatter target hall of the 7-MV Van de Graaff laboratory at IRMM [SAG10]. Proton beams with energies of MeV and currents of less than 1 μa were used in the experiments. The mean proton energy is defined by a 90 analyzing magnet with a calibrated NMR probe. The calibration and energy spread (σ(e) ~ 1.5 kev) were checked by using the resonance energy of the 27 Al(p,γ) 28 Si reaction at kev [BRI94] as well as the threshold energy of kev of the 7 Li(p,n) 7 Be reaction [TIL02] (Sec. 1 D). To monitor and to correct possible fluctuations in beam energy, regular checks were performed during the course of the experiments by stepping the beam energy through the threshold of the 7 Li(p,n) 7 Be reaction and by recording the neutron yield by using a 6 Li-glass scintillator as a monitor normalized to the charge on the suppressed target. To enable TOF measurements, the accelerator was operated in pulsed mode with a frequency of 625 khz. The bunched and chopped proton beam had a pulse width of ns FWHM. The target assembly and detector setup are illustrated in Fig. 30 and Fig. 31. The proton beam (~3-mm diameter) passed through a collimator of 5-mm diameter, ensuring that any transmitted beam impinges on the target. LiF targets of 6-mm diameter were prepared by evaporation on a 1-mm thick Cu disk, 40.7 mm in diameter. The LiF layer thickness was determined by weighing to be in the range of 1 to 2 mg/cm 2, thick enough to reduce the proton energy to well below the reaction threshold for the above incident energies, which allowed, however, most of the beam power to be dissipated in the Cu target backing. During irradiations, the target assembly was cooled by a forced air flow on the external side of the Cu target backing. For all measurements, materials that may cause neutron scatter were minimized. In order to mimic the energy spread expected for a proton beam from a rf accelerator, a gold foil nominally 2-μm thick was used as an energy degrader (Fig. 31). The foil was glued on a copper ring placing it 1 mm upstream of the LiF layer to 43

44 Fig. 30: (a) Schematic of the experimental setup, which shows the goniometer with 6 Li-glass detectors at the beam height of 108 cm above the floor. See Fig. 31 for details of part A (target assembly). (b) Schematic of the 6 Li-glass detector [SCI]: aluminum can (0.6-mm thick, blue), Si rubber (1 mm, light green), Teflon layer (0.25 mm, red), 6 Li-glass 25.4 mm, light blue), photomultiplier tube (borosilicate, 2.5 mm, green), μ-metal (1.5 mm, brown), and tape (between the Al can and the 6 Li-glass). All quantities are in millimeters; dimensions in figure are not to scale. minimize transverse beam growth by the scattering in the gold foil. The degrader foil [AME] was selected for its calibrated thickness and thickness homogeneity; x-ray fluorescence measurements indicated, however, thickness variations of up to 2%. In order to have better knowledge of the energy loss and spread for the proton beam in our experiments, we determined average energy loss and spread through the Au foil for α particles from a spectroscopic mixed source ( 239 Pu, 241 Am and 244 Cm) and scaled the measured values to those expected for protons by using the simulation code TRIM and stopping powers from SRIM-2008 [ZIE08]. The α particles incident on the Au foil were collimated to a cylindrical beam perpendicular to the foil and 3 mm in diameter, geometrically similar to the exposure with the proton beam and averaging, in a similar way, possible thickness inhomogeneities at corresponding length scales. The average energy loss and the energy spread (standard deviation σ) of keV Fig. 31: (a) Scale drawing of the target assembly. (b) Scale drawing of the gold activation setup (to scale except for the gold foil thickness). All dimensions are in millimeters. 44

45 α s ( 241 Am) through the Au foil, due to both straggling and thickness inhomogeneity, were determined, respectively, as 940 ± 2 kev (difference between line centroids measured with and without foil) and 61 ± 3 kev (difference in the quadrature of the line widths measured with and without foil). These values confirm the nominal thickness of 2 μm for the Au foil but indicate a ~6% thickness inhomogeneity when averaged over an area equivalent to that of the particle beam, which amounts to an estimated ~80% of the total energy spread. By using the ratio of energy loss and energy straggling for α s and protons calculated with the code TRIM and by taking into account the energy width (1.5 kev) of the Van de Graaff proton beam, we determined that 2096-keV protons emerge with 1913 ± 6-keV mean energy and an energy spread of σ = 21 ± 2 kev. The quoted uncertainties are derived from the statistical errors in the α counting, a 3% uncertainty attributed to α and protonstopping powers [ZIE08, PAU10] (although the uncertainty in their scaling is expected to be smaller) and a conservative estimate (~8%) of the uncertainty in the calculated straggling. A similar range of values for the energy spread (16 22 kev) is independently estimated from a comparison of the experimental TOF spectrum of neutrons emitted by the 7 Li(p,n) reaction (by using the Au degrader foil for the proton beam) and simulations performed with the codes SimLiT and GEANT4 (Sec. 2 C). In the following, we use the term broad-energy proton beam for protons that impinge on the LiF target after a gold degrader foil in case of an incident energy of kev before the degrader. We use the term narrow-energy proton beam for a proton beam of 1912 kev directly from the Van de Graaff accelerator. B. Detector setup and TOF measurements Neutron spectra were measured by the TOF technique by using two 6 Li-glass detectors and photomultipliers purchased from Scionix Ltd. [SCI]. It was deemed necessary to use relatively thick detectors to keep beam time within practical limits. One movable 6 Li-glass detector (5.08-cm diameter x 2.54-cm thick, see Fig. 30 and Table 8 for a detailed structure of the detector) was positioned at a distance of 51 cm (from the LiF target to the detector face) at emission angles of 0, 5,..., 65 for the measurements of the narrow-energy proton beam and up to 80 for the measurements of the broad-energy proton beam. A second 6 Li-glass detector of the same dimensions was used as a neutron monitor. It was placed at a fixed position 85 cm from the source and at an angle of 12 from the goniometer symmetry axis and 10 upward out of 45

46 plane. A special goniometer was constructed to provide accurate and reproducible angular positioning with a minimal scatter of neutrons (Fig. 30(a)). The goniometer consisted of an aluminum plate positioned on the accelerator target hall floor with holes for the placement of detector stands at angles from 0 to 80 at 5 intervals. Rigid holders, which placed the detectors at the height of the beam, were attached to aluminum rods that fit into positioning holes at the goniometer base. An accuracy of ±0.3 was obtained after proper alignment of the goniometer. Fig. 30(b) shows the internal structure of the 6 Li-glass detector used for TOF measurements. Component Chemical composition Density (g/cm 3 ) Aluminum Al alloy 2.7 Si rubber H 8.2%, C 32.4%, O 21.6%, Si 37.8% 1.1 Teflon (C 2 F 4 ) n 2.2 Glass SiO 2 56%, MgO 4%, Ce 2 O 3 4%, Al 2 O 3 18%, 6 Li 2 O 18% 2.6 Borosilicate SiO 2 81%, B 2 O 3 13%, Na 2 O 4%, Al 2 O 3 2% 2.2 μ-metal C 0.02%, Mn 0.5%, Si 0.35%, Ni 80%, Fe 14.93%, Mo 4.2% 8.75 Tape SiO 2 50% and Si rubber 50% 0.9 Table 8: List of structural materials and densities in the 6 Li-glass detector. 6 Li enrichment is 96%. The signal from the photomultiplier of each detector was split to a fast timing circuit and to a pulse-height circuit (Fig. 32). The fast timing circuit was composed of a timing filter amplifier followed by a constant-fraction discriminator. The pulse height circuit consisted of a preamplifier and a spectroscopy amplifier. The timing signal from each detector provided the TOF start signal in an allocated time-to-amplitude converter (TAC). A beam pick-up monitor, placed upstream of the target, provided a signal that was processed through a timing filter amplifier and a constant fraction discriminator and provided the common TOF stop signal to the TAC. The TOF amplitudes from the TAC were calibrated by using an ORTEC 462 time calibrator. The FWHM of the γ peak was about 4 ns, which reflects the combined time resolution of the detector and pulse width of the beam. Data for every detector were acquired independently, while the timing and pulse-height information for each detector were acquired in coincidence. Fig. 33(a) displays a raw TOF spectrum. A peak, which originates in prompt γ rays produced in the LiF target, is observed on the right of the spectrum, and the neutron events appear at longer flight times on the left of the γ peak. 46

47 Fig. 32: Electronics diagram for TOF measurements. The large amount of prompt γ rays are primarily from the 7 Li(p,p'γ), 7 Li(p,γ), 19 F(p,αγ) 16 O, and 19 F(p,γ) 20 Ne reactions. The inset, which highlights the γ peak, shows a Gaussian γ TOF distribution. Fig. 33(b) shows a two-dimensional scatter plot of TOF vs. pulse height for the 6 Li-glass detector. The pulse-height spectrum exhibits a neutron peak with a γ equivalent energy of 1.8 MeV and a FWHM of ~15% with a rather long high-energy tail. Fig. 33(b) also displays events that are scattered over the Fig. 33: (a) TOF spectrum for the 6 Li-glass detector, which shows γ s and neutrons. TOF increases toward lower channels. The inset shows a γ peak with a FWHM of ~4 ns. (b) 2D spectrum showing TOF vs. pulse height. The neutron pulse height appears as a horizontal band with a FWHM (along the vertical axis) of ~15%. 47

48 TOF and pulse height regions due to stray uncorrelated γ rays and neutrons. In addition to the 6 Li-glass detectors described above, a long counter (54-cm x 35.6-cm diameter) for neutrons, positioned at 0 at about 119 cm from the target, was used for neutron monitoring. The long counter is characterized by a large acceptance and uniform response for neutrons up to several MeV. A 4-in. x 4-in. diameter NaI detector placed at angle of ~45 and distance of ~2 m from the target was used for γ monitoring. C. Activation setup Gold activation measurements were performed for both narrow- and broad-energy proton beams. Following Ratynski and Käppeler [RAT88], we determined the total number of neutrons in the activation run by inferring the total number of 7 Be atoms produced in the 7 Li(p,n) 7 Be reaction from the measured 7 Be activity. A fresh LiF target was used for each activation run. The proton charge accumulated with electron suppression during the activation was measured by using a carefully balanced Brookhaven Products current integrator. A pair of flat gold samples, ~50 μm in thickness, was used in each of the two experiments (Fig. 31(b) and Table 9): gold sample No. 1 was 18 mm in diameter and was placed at a distance of 1 mm from the LiF target (affixed onto the outer side of the Cu target backing), gold sample No. 2 was 22 mm in diameter and was placed at a distance of 5 mm from the LiF target on a thin aluminum holder. The samples were centered on the proton-beam axis. The half cone angles subtended by the first and second gold samples for a beam spot of 3-mm diameter were 84 and 66, respectively (Table 9). Sample name - beam condition Au No. 1 - narrow energy Au No. 2 - narrow energy Au No. 1 - broad energy Au No. 2 - broad energy LiF target-au sample distance (mm) Diameter (mm) Half cone angle Weight (mg) Atomic thickness (10 20 cm -2 ) ± ± ± ± 0.01 Table 9: Parameters of the gold samples used in activation measurements. 48

49 D. Scan curves The energy spread of protons from the Van de Graaff accelerator (narrow-energy proton beam) was determined experimentally by scanning the keV resonance of the 27 Al(p,γ) 28 Si reaction, using a thick Al target. This resonance has a natural linewidth of 0.07 kev [END90]. Yields for the characteristic MeV γ-ray were measured with the NaI detector relative to the charge on target. The proton energy was decreased from 1000 to 985 kev in 1-keV steps by biasing the voltage on the insulated target from 0 to 15 kv, thereby leaving the beam optics untouched. Fig. 34 shows the measured points in the energy scan of the resonance and includes a fit to an error function with a standard deviation of 1.5 kev for the proton energy distribution. Fig. 34: Thick-target excitation function of the 27 Al(p,γ) 28 Si reaction (solid dots) around the resonance energy E R = kev. The x axis represents the beam energy determined by the 90 analyzing magnet. The solid line represents a fit to an error function with a proton energy width of σ = 1.5 kev. Threshold scans for the 7 Li(p,n) 7 Be reaction were performed before each run with the 6 Li-glass detectors and the long counter. Fig. 35(a) and Fig. 35(b) show threshold scans taken with the long counter. Fig. 35(a) shows the threshold curve taken with a narrow-energy proton beam, the data, exhibiting a sharp reaction threshold for the 7 Li(p,n) reaction. The gradual fall-off just below the threshold energy of kev Fig. 35: Threshold scan of neutrons from the 7 Li(p,n) 7 Be reaction, measured with the 6 Li-glass detector with (a) a narrow-energy proton beam and (b) a broad-energy proton beam. 49

50 is an indication of the finite energy width of the proton beam. The continuous curve represents a simulation performed with the SimLiT simulation code discussed in Sec. 2 C and includes the angular acceptance of the long counter. Fig. 35(b) shows the threshold scan with the broad-energy proton beam. Since the protons for the broad beam are degraded, the beam energy, as inferred from the NMR probe in the analyzing magnet, was reduced by 184 kev as calculated by the SRIM calculations discussed above. The threshold scan for the broad-energy proton beam is also compared to simulations performed with the SimLiT code with an energy broadening of σ = 20 kev. 2. Neutron spectra A. Neutron spectra analysis The analysis of the neutron spectra (Fig. 33) involved first placing a software window in the 6 Li-glass detector pulse height around the neutron peak, thereby eliminating most of the stray γ events. Stray events, still remaining, are attributed to γ rays that have pulse heights inside the neutron energy window and to neutrons that are not correlated with the beam pickup signal. The level for this stray neutron background was estimated at each angular position of the detector by determining the average background at a region, which should have no events, namely, between the TOF values corresponding to the prompt γ peak and those corresponding to the neutron high-energy end point. This level of background was found to be identical within statistics to the level of background at very long TOFs (i.e., low TOF channels) and at very short times (high TOF channels, prior to the γ peak), which indicates that the background at each angle is not correlated with TOF so that a constant value can be subtracted. The procedure was confirmed by a spectrum taken at 80 where no direct neutrons were kinematically expected from the 7 Li(p,n) reaction for a narrow-energy proton beam at MeV. The use of a relatively thick (1-in.) 6 Li-glass detector required taking into special consideration the added path lengths inside the detector owing to elastic neutron scattering caused by the various materials contained in the scintillator, such as silicon and oxygen, prior to a reaction with 6 Li and subsequent ionization signal from the 6 Li(n,a) 3 H reaction products. Additional structural materials in the neutron detectors, such as silicon rubber and glass-tape spacers, along with the aluminum casing, must be taken into account to extract effective flight path 50

51 lengths. Detailed simulations (10 6 neutrons), which include all known structural components of the detector, were run with GEANT4 [AGO03] to determine the effective flight path length λ(e n ) of neutrons with energies E n in 1-keV bins. In order to assign the energy that corresponded to a neutron event at a measured TOF channel, an iterative procedure was used, which started from the energy derived for the neutron TOF value by using an initial effective target-detector distance of 54 cm. The position of the γ peak in the TOF spectrum served as the reference time. The procedure was then iterated using a new effective distance interpolated from the λ(e n ) simulation values, until convergence. The efficiency of the neutron detection in the 6 Li-glass detector as a function of neutron energy was determined by simulations with the GEANT4 [AGO03] and MCNP [BRI00, BRI86] codes by using all known information on the detector structure and contents. Both codes contain up-to-date libraries for the neutronscattering and capture cross sections. Neutron efficiencies were defined for the 6 Li(n,a) 3 H reaction, following the increased path lengths caused by the elastic scatterings. Fig. 36 shows the calculated neutron detection efficiency as a function of neutron energy. We obtain consistent results with the GEANT4 and MCNP simulation codes, thereby increasing our confidence in the calculations. The differences between the calculations were used to estimate the calculation uncertainties. The calculated efficiency as a function of energy was used to correct the energy spectrum obtained from the TOF analysis described above. A significant fraction (estimated at ~9%) of emitted neutrons scatter in the Cu target backing. This effect must be taken into account in the analysis to derive the original source spectra from the measured spectra. In order to estimate this correction, GEANT4 simulations were performed to calculate a matrix R(E n,θ) of ratios between the number of neutrons emitted by a neutron source at the LiF target position and the number of neutrons that reached a detector positioned at an angle (θ, Fig. 36: Efficiency of a 2-in.-diameter, 1-in.-thick 6 Li-glass detector calculated with the GEANT4 and MCNP simulation codes. 51

52 θ+dθ) in an energy bin E n. The angular dependence and energy distribution of the neutron source were calculated with the SimLiT code (Sec. 2 C). The energy distribution, measured as described in the previous paragraph, in a detector positioned at a given angle, was corrected by multiplying by the R(E n,θ) factors. B. Experimental neutron spectra Fig. 37(a) and Fig. 37(b) show the neutron energy spectra obtained with the narrowenergy proton beam and the broad-energy proton beam, respectively, in steps of 10 (the spectrum at each emission angle θ is normalized to the corresponding solid Fig. 37: Neutron spectra at selected emission angles for the 7 Li(p,n) 7 Be reaction obtained with (a) a narrow-energy proton beam and (b) a broad-energy proton beam. Actual data were taken at 5 intervals. The curves, obtained from the experimental spectra at different angles after integrating over the azimuthal angle, were normalized to the proton charge accumulated in the respective measurement. angle). The spectra taken with the broad-energy proton beam exhibit pronounced spectral broadening compared to the spectra taken with the narrow-energy proton beam as expected. Fig. 38 shows the angle-integrated neutron spectrum for the narrow-energy proton beam and for the broad-energy proton beam. These spectra were obtained by summing the spectra from 0, 5, up to 80. The horizontal bars reflect the uncertainty in the energy determination from TOF due to the 6 Li-glass detector thickness and the iterative procedure used in the analysis. The procedure also leads to a systematic shift in measured energies, evident, in particular, as a tail of events, which extends slightly above the kinematically allowed values but also is present as an excess of events in the low-energy region. Although the individual spectra at each emission angle look markedly different for the narrow-energy and for the broad-energy proton beams, the combined spectra are remarkably similar, except in the high-energy tail above 80 kev. Also shown in Fig. 38 is a fit to the distribution 52

53 Fig. 38: Total integral neutron energy spectra for the 7 Li(p,n) 7 Be reaction for a narrow-energy proton beam (σ = 1.5 kev) and for a broad-energy proton beam (σ = 20 kev). The two curves were obtained by summing the charge-normalized angular spectra (shown, in part, in Fig. 37). The solid line represents a fit of the experimental spectrum for the broad-energy beam to a Maxwellian flux at kt = 28 kev (fit of data points at 8 < E n < 80 kev). f(e) ~ ae e E / kt, which corresponds to a Maxwellian flux at temperature T, where a is a normalizing coefficient. In the range from 8 to 80 kev, a best fit is obtained with kt = 28 kev. Although below about 80 kev, the narrow-energy and broad-energy proton beam data are very similar, it is apparent that the spectrum with the broadenergy proton beam shows considerably better agreement with the Maxwellian-flux distribution at the higher neutron energies. C. Simulated neutron spectra We developed the simulation program SimLiT [FEI12b, FRI13] as a tool for estimating the neutron spectrum expected from a thick lithium target bombarded by protons for beam energies close to the 7 Li(p,n) 7 Be reaction threshold (1.880 up to 3.5 MeV). SimLiT is a core code that estimates the neutron spectrum under the various parameters of the proton beam, which can be inserted into advanced programs, for example, GEANT4 in order to effectively plan and analyze experiments that use this reaction as a neutron source (see also code PINO by Reifarth et al. [REI09a]). SimLiT uses the Monte Carlo technique for simulation of the thick target 7 Li(p,n) reaction by using the following basic algorithm: protons are generated and are assigned spatial coordinates and energy according to beam characteristics (average energy, energy width (σ), and spatial distribution). The calculations are done based on the 53

54 Fig. 39: Comparison of the TOF neutron spectra (blue histogram) measured at angles 0 and 80 with TOF spectra (red) obtained from a full simulation (SimLiT + GEANT4) of the experimental setup (see the text) for the narrow-energy proton beam. The background from the uncorrelated neutrons and stray events were subtracted from the experimental spectra. The counts observed (in both the measured and the simulated spectra) at 80, beyond the kinematically allowed range for neutrons, result from neutron scattering, mainly in the Cu target backing. Excellent agreement between experimental and simulated spectra is observed at both angles. measurements of the 7 Li(p,n) 7 Be energy dependent cross section [NEW57, MAC58, GIB59] and on evaluations and compilations [LIS75, CHA06]. The code samples the probability for a proton making a (p,n) reaction, according to the energy dependent reaction cross section and the stopping power de/dx [ZIE08], depending on the chemical composition of the target (Li or LiF). If a (p,n) reaction occurs, the code determines the reaction energy in the center-of-mass (c.m.) system and samples the emission angle of the neutron in the c.m. system according to the differential cross section dσ(e)/dθ of the reaction [LIS75, LEE99]. The coordinates are then transformed to the laboratory system. Every iteration produces a single neutron, which can serve as input to a subsequent analysis code or can be recorded to construct an energy distribution histogram. In order to test the reliability of the code, we performed a full simulation of the experimental setup (proton-beam energy, a narrowenergy spread of σ = 1.5 kev and transverse width of σ = 1.5 mm, LiF target, and Cu backing as described in Fig. 31, neutron transport in air, detector geometry, and 54

55 Fig. 40: Measured integral spectrum of neutrons emitted by the 7 Li(p,n) 7 Be reaction (open and solid circles) for the narrow-energy proton beam and data of Ratynski and Käppeler [RAT88] (histogram) compared with simulations that use the SimLiT (dashed line) code and with the PINO (solid line) simulation code [REI09a]. Experimental and simulated spectra were normalized to the same integral over the neutron energy. structural materials as described in Table 8) by using SimLiT for the neutron source and GEANT4 for the transport thereafter. Fig. 39 shows a comparison of experimental TOF spectra and the TOF spectra generated by the full simulation at 0 and 80, both in excellent agreement. The angle 80 is beyond the kinematically allowed range of neutrons for the narrow-energy proton beam, and the similar behavior of the experimental and simulated spectra adds confidence to the validity of the treatment of neutron scattering (mainly significant in the Cu target backing). A detailed description of the SimLiT code is reported in ref. [FRI11, FRI13]. Fig. 40 shows a comparison between SimLiT and experimental data for the integral neutron spectra for the narrowenergy proton beam. Also shown Fig. 41: Double differential spectra measured at selected emission angles for the (a) narrow-energy and (b) broadenergy proton beams compared to spectra calculated with the SimLiT code (normalized for the total integral spectrum). Actual data were taken at 5 intervals. 55

56 in Fig. 40 are a comparison with the published spectrum of Ratynski and Käppeler [RAT88] and a comparison with the simulation code PINO [REI09a]. The four spectra exhibit very good agreement. Fig. 41 shows a comparison of SimLiT with the experimental data for the narrowenergy proton beam and for the broad-energy proton beam at selected emission angles of 10, 30, 50 and 60. As discussed above, the experimental results show a slightly broader distribution, both in the low-energy and higher-energy ranges, which result from the relatively thick 6 Li-glass detector and its effects on the TOF resolution. 3. Activation measurements Gold activation measurements were used by Ratynski and Käppeler [RAT88] to characterize the integral energy distribution of neutrons emitted in the 7 Li(p,n) 7 Be reaction near threshold. They determined an experimental average cross section of 586 ± 8 mb for the 197 Au(n,γ) 198 Au reaction for the neutrons produced by a 1912-keV narrow-energy proton beam on a thick Li target with the neutrons that impinge on a hemispherical gold sample. The hemispherical shape was used to provide the same sample thickness at all emission angles, thus, reducing corrections needed for the extraction of the experimental cross section. Their experimental cross section has since served as the standard for determining the energy-averaged neutron fluence in activation measurements. This section is focused on the comparison of gold activation cross sections between narrow-energy and broad-energy proton beams to validate the technique for the broad-energy proton beams at SARAF and in future facilities based on rf accelerators. The procedure for extracting the gold activation cross section can be divided into three stages: 1. Measurement of the 7 Be activity providing the total number of neutrons emitted during activation runs. The total number of protons obtained by current integration is used for determination of the n/p ratio. 2. Measurement of the gold sample activity providing the number of activated 198 Au nuclei. 3. Correction for the solid angle subtended by the Au sample, the neutron scattering in the Cu target backing, and the planar geometry of the Au sample. 56

57 A. γ-ray spectra analysis Following irradiation, the LiF targets and the Au samples were measured on the HPGe spectrometer system available at the IRMM facility. 7 Be and 198 Au activities were measured using the same detector with 100% relative efficiency, surrounded by a 10-cm lead shielding (of which the inner 3 cm are low in 210 Pb) with an inside 1-mm copper layer. The detector efficiencies at the position of the LiF target and gold sample measurements were determined with secondary-standard point sources placed at different positions on the detector end cap in order to take into account the diameter of the 7 Be and 198 Au sources. The estimated uncertainty of the absolute efficiencies is about 2%. Several activity measurements were performed for each of the Au samples and the LiF targets. The number N act ( 7 Be) and N act ( 198 Au) of 7 Be and 198 Au nuclei produced during each irradiation was determined by the measured γ spectra analyzed according to the following equation: N act S ( E ) I ( E ) ( E ) C C p att geom t t real live e 1 e t cool t real t 1 e where, for each activation run and for each activated nuclide, S γ (E) is the fitted peak area, I γ (E) is the γ emission probability, ε p (E γ ) is the detector efficiency for the measured γ photons with energy E γ, t real and t live are real and live times of the measurement, respectively, t cool is the time from the end of the irradiation until the beginning of the measurement, t irr is the time duration of the irradiation, λ = ln 2/t 1/2 is the decay constant, and t 1/2 is the nuclide half-life. C att is the photon attenuation correction due to self-absorption in the target. C geom is a correction factor due to the geometry of the activated sample with respect to the size of the germanium detector and the point source used for calibration. Table 10 lists the data and the correction factors used in the calculations. Isotope - beam condition t 1/2 (d) E (kev) I (%) p (%) irr t irr C att (%) C geom (%) 7 Be - narrow energy 53.22(6) 10.44(4) Be - broad energy [TIL02] [TIL02] Au No. 1 - narrow energy 198 Au No. 2 - narrow energy (12) 95.56(65) Au No. 1 - broad energy [CHE11] [HAM92] Au No. 2 - broad energy (1) Table 10: Numerical data used for the calculation of the number of 7 Be and 198 Au activated nuclei. 57

58 B. 7 Be and 198 Au production The numbers of 7 Be and 198 Au nuclei produced during each activation run and calculated using Eq. (1) and the corresponding integral proton charge are listed in Table 11 for both the narrow-energy and for the broad-energy proton beam Table 11: Total proton number and number of 7 Be and 198 Au nuclei produced during the activation runs. Statistical counting errors are listed. The systematic error due to photopeak efficiency and γ calibration source is 1.9%. measurements. No significant loss of 7 Be took place either during or after the activation. This was verified by measuring the residual 7 Be activity in the beam line following activation with a portable germanium detector and in the energy-degrader Au foil facing the LiF target used in the broad-energy proton-beam activation. The ratio of neutrons to protons extracted from the measured activity of 7 Be nuclei and the integrated proton current is listed in Table 12 and is compared to predictions from the PINO [REI09a] and SimLiT [FRI13] simulation codes. The experimental n/p ratios include statistical and systematic errors related to the 7 Be activation. The quoted errors in the simulated n/p ratios include the uncertainty in the mean proton energy. For the narrow-energy proton beam, this uncertainty is estimated to be ±0.5 kev, whereas, for the broadenergy proton beam, it is on the order of ±6 kev. The yields of the simulated spectra are observed to be sensitive to this uncertainty. Narrow-energy proton beam Broad-energy proton beam Total integrated proton number Be produced nuclei (1.14 ± 0.01) (1.52 ± 0.01) Au produced nuclei, target No. 1 ( < 84 ) 198 Au produced nuclei, target No. 2 ( < 66 ) (2.39 ± 0.01) 10 6 (3.64 ± 0.02) 10 6 (2.17 ± 0.02) 10 6 (2.74 ± 0.02) 10 6 Neutron per proton (10-6 ) Narrow-energy proton beam Broad-energy proton beam Experimental PINO [REI09a] SimLiT [FRI13] Table 12: Experimental n/p ratio determined from 7 Be activity and proton integrated charge. Errors include systematic errors on the number of activated nuclei. Comparison is shown with two simulations; the uncertainty in values form simulations is due to the uncertainty of the mean energy of the protons on the target. 58

59 C. 197 Au(n,γ) 198 Au cross section The experimental 197 Au(n,γ) 198 Au cross section averaged over the thick-target 7 Li(p,n) neutron spectrum is extracted from the number of 7 Be nuclei N act ( 7 Be), which provides a measure of the number of emitted neutrons and from the number of 198 Au nuclei N act ( 198 Au) as given in Table 11. The experimental cross section <σ> is then calculated by the following equation: 198 Nact ( Au) 1. (2) N ( Be) n ( Au) f The number of Au nuclei per cm 2 in the sample n t ( 197 Au) is given by: n act t m N corr Au A t ( 197 Au) (3) S Au M Au where m Au is the mass of the Au sample, N A is Avogadro s number, S Au is the area of the Au sample, and M Au is the atomic mass of gold. Table 9 lists the atomic thicknesses of the Au activation samples, determined with Eq. (3). The correction factor f corr is necessary to correct for a neutron beam incident on a planar sample with finite angular coverage and with an effective target thickness, which varies as 1/cosθ and for scattering of neutrons from the copper target backing. The effective correction factor f corr is determined by comparing a detailed simulation that contains the full experimental configuration (size and angular range of the Au planar sample and a 1- mm thick Cu target backing) with an idealized configuration that contains a spherical target that covers the angular range subtended by the Au sample (θ < 84 ) with no scatter. The simulations were performed in both cases by using the neutron angular distributions produced by SimLiT and the Monte Carlo code GEANT4 for the narrow-energy or the broad-energy proton beams. Use of the SimLiT code is justified by the good agreement with the experimental neutron spectra (Sec. 2 C and Fig. 39). The correction factor f corr, listed in Table 13 for the different cases, is taken as the calculated ratio of the activation yield of the planar gold activation sample with finite angular coverage and with scatter from copper target backing to the yield of the idealized spherical gold activation with no scatter, simulated as explained above. Although both Au samples No. 1 and No. 2 intercept all produced neutrons in the narrow-energy beam activation, in Table 13, the correction factor f corr is observed to be larger for sample No. 1 (θ < 84 ) than for sample No. 2 (θ < 66 ). This is 59

60 f corr Narrow-energy Broad-energy Au sample No. 1 ( < 84 ) 1.25 ± ± 0.04 Au sample No. 2 ( < 66 ) 1.16 ± ± 0.03 Table 13: Calculated correction factors (f corr ) for planar gold samples. attributed to neutrons scattering off the Cu target backing at large angles (66 < θ < 84 ) still hitting the Au sample with a corresponding increased effective sample thickness due to the 1/cosθ dependence. Sensitivity tests for the calculation of f corr, performed by varying geometrical parameters in the experimental setup, showed deviations in f corr of about 1.2%; an uncertainty of 2.5% was attributed to the correction factor. The activation cross sections, derived by using the experimental activities listed in Table 11 along with the correction factors of Table 13, are given in Table 14. Our measured value for the narrow-energy proton beam 616 ± 17 mb was slightly larger than the value 586 ± 8 mb obtained by Ratynski and Käppeler [RAT88]. Table 15 lists the various uncertainties used in the above measurements. Table 16 compares the experimental cross sections for the narrow-energy and broadenergy beams with cross sections <σ> calculated as a convolution of the spectrum de/dn simulated with the SimLiT code with the ENDF/B-VII.0 [CAR09] cross sections σ(e) for the 197 Au(n,γ) 198 Au reaction by using the expression: dn de E dn de de Good agreement within quoted uncertainties is observed. Similar convolutions, which used the experimental spectra (Fig. 38), were found to be too sensitive (in the range of 10% 20%) to the error bars of the neutron energies in the experimental spectra to provide useful comparison. de. Cross section (mb) Narrow energy Broad energy Au sample No. 1 ( < 84 ) 608 ± ± 17 Au sample No. 2 ( < 66 ) 626 ± ± 17 Average 616 ± ± 16 Table 14: Experimental cross section (mb) of the 197 Au(n,γ) 198 Au reaction measured for neutrons from the thick-target 7 Li(p,n) reaction. See Table 15 for the details of the uncertainties estimates. 60

61 Uncertainties (%) Narrow-energy Broad-energy Au Sample No. 1 Au Sample No. 2 Au Sample No. 1 7 Be activity Au Sample No Au activity p Sample thickness Correction factor f corr Total Table 15: Summary of estimated uncertainties in the experimental cross sections. Systematic uncertainties from the γ photopeak efficiency do not contribute to the error in the cross sections. The error listed for ε p results from the uncertainty in energy dependence of the photopeak efficiency. Narrow-energy cross section (mb) Broad-energy cross section (mb) This work Convolution of SimLiT with ENDF/B-VII ± ± 18 Table 16: Average activation cross sections of the 197 Au(n,γ) 198 Au reaction for the narrow-energy and for the broad-energy proton beams measured in this work compared with the convolution of the SimLiT simulated spectrum and ENDF/B-VII.0 cross sections [CAR09]. A 2% uncertainty was taken both for the SimLiT contribution and for the ENDF/B-VII.0 cross sections. 61

62 Chapter 5: Nuclear Astrophysics at SARAF Using a Liquid Lithium Target 1. Introduction Aiming for experiments in nuclear astrophysics using LiLiT for neutron production, a set of measurements was performed at SARAF in order to characterize the proton beam (energy, energy spread) at low intensity. A dedicated setup, presented in sections 3 and 4, was built for the characterization of the proton beam and for gold activation. Since the SARAF accelerator does not provide fast timing required for characterization of the neutron spectrum using the TOF technique as described in the previous chapter (see however [SHO12] for future development) the characterization of the SARAF proton beam becomes very important. Good confidence in the proton beam energy distribution together with benchmarked simulations tools can give good evaluation for the neutron spectrum characteristics. Since the SARAF is a state-ofthe-art RF accelerator, ad-hoc techniques need to be developed for the characterization of the proton beam with good precision at target position at reasonable time, cost and efforts. Proton Rutherford Back Scattering (RBS) and TOF diagnostics systems for the measurements of the proton beam energy and energy spread were used, each having however limitations. As shown in chapter 3, space charge changes significantly the energy spread along the beamline for high current beams and therefore, it is important to characterize the beam close to the target position. RBS and TOF non-destructive diagnostics systems are positioned about 10 m upstream the target position, at the diagnostic table (D-plate) between the PSM and the first 45 bending magnet (Fig. 3 and Fig. 6). The Solid-LiF Target (SoLiT) RBS diagnostics system which we developed is positioned very close to the LiF target but is a destructive diagnostics and can be operated only for very low currents (measurements were performed with duty cycle of 3% and an average current of 100 na). The proton beam TOF 62

63 measurement is a non-destructive diagnostics but is limited to high currents because of the weak inductive signal of the bunches [PIE07]. A method was developed for systematic determination of the optimized acceleration conditions followed by systematic characterization of the proton beam energy aiming at neutron production with proton beam energy of ~1912 kev and energy spread of ~20 kev. Systematic measurements and analysis were performed based on the available diagnostics of SARAF and SoLiT and will be presented in sections 2 and 3. Neutron production and Au activations, performed with SoLiT and a low intensity proton beam will be presented in section 4. A first experiment using LiLiT with full power (2 kw) proton beam was performed as well. Activations of gold monitors and of a target of natural Zr were performed. Based on the proton beam characteristics and detailed simulations using the tools developed (described in chapter 4), measurements of the MACS for the stable isotopes 94,96 Zr were performed. The high-intensity experiment will be presented in sections Determination of the optimized acceleration conditions for the proton beam A. Diagnostics systems The determination of the optimized accelerating conditions for neutron production by protons of energy E ~ 1912 kev and energy spread of 20 kev (1σ) was done using the D-plate (see Fig. 5) RBS and beam-tof diagnostics systems. The D-plate RBS diagnostics includes a thin gold foil that can be inserted into the halo of the intense proton beam. The scattered protons are measured by a surface barrier detector and the spectrum is analyzed to give the energy of the proton beam. The TOF diagnostics system includes 2 pickoffs; the time difference between the signals (176 MHz) of both pickoffs is determined. Due to the cables lengths and distance between pickoffs, a bunch and the fifth bunch following are employed to determine the energy. B. The method used for determination of the acceleration conditions Based on beam dynamics calculations, a rough tune was set for the accelerator. Fine tuning of the last operating cavity phase was done by RBS and TOF and will be shown on sections C and D. The dependency of the proton energy as function of the 63

64 Energy (kev) last operating cavity phase was measured by D-plate RBS and compared to TOF measurement. The dependency of the energy measured by TOF with the beam current was measured and the accelerating phase for current of 1.5 ma was determined by TOF measurement. Once the acceleration conditions for a high current beam are determined, it is considered as a reference. Due to accelerator instabilities, every few hours, the conditions were verified, fine tuning and small corrections were made if needed to the last operating cavity phase based only on a quick TOF measurement. C. Characterization of the energy dependence on the phase of the last operating cavity by D-plate RBS and TOF measurements The energy as a function of the last cavity phase was measured by the D-plate RBS and by TOF (Fig. 42). The operating phase of a cavity is defined as the difference between the SARAF master oscillator phase and the cavity phase. Note that the operating phase defined here is the negative of the absolute phase used in chapter 3. We adopted here an accelerator tune, with only cavities 1,2 and 4 operating, different from the one described in chapter 3 in order to allow us to scan the beam energy in a relatively wide range of ~100 kev around the 7 Li(p,n) threshold. With this requirement, the energy of 1912 kev was achieved for a relative phase of φ rel -30. The RBS and TOF measurements were performed for cavity 4 operating phases between φ operating =100 and φ operating =350, each TOF data point is an average of 5 measurements. For operating phases between 200 and 300 the bunch induced signal was hard to measure by the TOF pickoffs therefore the data for those phases is D-plate RBS TOF Cavity 4 operating phase (deg) Fig. 42: D-plate RBS and TOF measurements of the energy dependency on cavity 4 operating phase. 64

65 Energy (kev) Energy (kev) Energy (kev) presented in Fig. 42 only for the RBS measurements. TOF measurements were performed with higher resolution for SARAF phases between φ operating =100 and φ operating =200 focusing on phases which result in energy close to 1912 kev (Fig. 43 (left)). Each TOF data point is an average of 5 measurements, the average value with statistical errors is presented in Fig. 43 (right). The measurements were performed for beam current of 1 ma D-plate RBS TOF 1 ma D-plate RBS TOF 1 ma Cavity 4 operating phase (deg) Cavity 4 operating phase (deg) Fig. 43: Beam energy dependency on cavity 4 operating phase (TOF measurements for operating phases between 100 and 200 ). Left - compared to D-plate RBS measurement, right - the TOF measurements are presented with statistical errors (5 measurements each data point). D. High current TOF measurement for phase determination The dependency of the beam energy on the beam intensity was checked in order to verify the energy stability. The beam energy was measured by TOF while changing the beam current keeping cavity 4 operating phase at φ operating =176. The results are presented in Fig. 44, each TOF data point is an average of 5 measurements. For high current proton beam, the TOF signal increases therefore the measurements become more accurate. Surprisingly, we found a significant dependency of beam energy on Intensity (ma) Fig. 44: Measured energy vs. proton beam intensity. Cavity 4 operating phase is φ operating =

66 Energy (kev) Energy (kev) the intensity that may be caused by a space charge effect in the RFQ, beam loading or other current related effect. This energy-intensity dependency should be investigated and compensated for future high current experiments while tuning the SARAF beam with low current. In order to find the acceleration optimal phase for high current experiments, TOF measurements were performed for proton beam intensity of 1.5 ma and for phases which result in energy close to 1912 kev. The measurements (each TOF data point is an average of 5 measurements) show a small reduction in beam energy than for beam intensity of 1 ma (Fig. 45). The optimal phase was determined by a linear fit done for 8 data points. The fit and the data points with statistical error bars are presented in Fig. 46. For φ operating =171 the calculated energy using the fit equation is kev therefore this was the chosen operating phase for cavity D-plate RBS TOF 1 ma TOF 1.5 ma Cavity 4 operating phase (deg) Fig. 45: TOF measurements of the energy dependency with cavity 4 operating phase for beam intensity of 1.5 ma compared to D-plate RBS and TOF (1 ma) measurements Energy (kev) = *phase Cavity 4 operating phase (deg) Fig. 46: TOF measurements of the energy dependency with cavity 4 operating phase for a 1.5 ma proton beam and a linear fit. Error bars calculated for statistics of 5 measurements for each data point. 66

67 3. Proton beam energy characterization with SoLiT RBS diagnostic system The neutron spectrum produced by the 7 Li(p,n) 7 Be reaction is sensitive to the proton beam energy and energy spread hence the energy characterization of the beam is essential. We characterized the proton beam close to the LiF target by RBS using a surface barrier detector. The information is complementary with the measurements done using the D-plate diagnostics. Both the proton beam energy and energy spread were extracted. A code was written for simulating quantitatively the RBS spectrum for protons scattered into a well defined solid angle from a thin layer of Au evaporated on a thin Ti foil. The simulation takes into account the irradiation integrated current and other parameters (detector resolution and dead layer, proton energy loss and straggling in Ti, Au and Si, etc.). The analysis was based on energy calibration of the surface barrier detector done with a 228 Th α source. The proton beam parameters were extracted by an iterative optimization procedure A. RBS experimental setup A rotatable stage cooled by air flow inside the SoLiT chamber enables choosing between 3 stations cooled collimator, quartz disk for beam tuning and thin gold target on Ti foil attached to a 20 mm diameter Al collimator for the RBS characterization. The Au layer (15 μg/cm 2 ), 6 mm in diameter, was evaporated on the center of the Ti foil (1.3 mg/cm 2 ). The setup configuration (Fig. 47 and Fig. 48) Si detector Cu collimator Al collimator Ti foil Au layer Proton beam Fig. 47: Right - SoLiT chamber and the Ti+Au foil on the Cu rotatable stage. Left - The Ti+Au foil on the Cu stage, the thickness of the Cu stage is 23 mm and the center of the Au target is 22 mm above the Cu stage base level. 67

68 included in addition to the SoLiT chamber and the copper stage, a tilted port fixing the Si detector at a distance of 0.5 m from the Ti+Au target, a 2 mm dia. collimator and a surface barrier Si detector (Ortec B ). A movable holder for the α source enabled inserting it in front of the Si detector or taking it out to enable the RBS measurements. Precise measurement of the angle of the scattered protons that reach the Si detector is important for the determination of the proton beam energy and the accuracy of the result. The scattering angle between the beam direction and the center of the (off-axis) collimator in front of the Sidetector was determined as ± 0.7. SoLiT chamber Collimator B. Extracting the beam parameters from the RBS spectrum α source Si detector Fig. 48: The setup for SoLiT RBS measurements, the α source can be inserted in front of the Si detector. The proton beam enters from the right. The spectrum measured using the SoLiT Si detector is shown in Fig. 49. It includes in addition to the RBS Ti + Au peaks, 4 α lines originating from 220 Rn. In order to extract the proton beam energy and energy spread from the RBS spectrum a Matlab Ti 220 Rn 216 Po Au 212 Bi 212 Po Fig. 49: The RBS Ti+Au spectrum of the proton beam and the α lines of the 228 Th source. 68

69 Counts Counts code (App. 12) was written to reproduce the spectrum and optimize it to the experimental spectrum while changing the calculation parameters and optimizing the energy and energy spread. Using Rutherford differential cross section the spectrum was calculated quantitatively for the Ti+Au layers for a proton beam with an average energy E and Gaussian energy distribution with standard deviation de. The quality of the fit was determined and χ 2 optimization was done in order to evaluate E and de. C. Energy calibration Energy calibration of the Si detector was done using the 228 Th α source. During the RBS measurement, the 228 Th source was retracted but α lines emitted from the 220 Rn daughters were observed and served as continuous energy monitor. The calibration was done using 4 lines listed in Table 17. The α line centroid was determined by fitting a Gaussian function to the high energy part of the line as presented in Fig. 50 (left) for the 216 Po line. Fitting the whole line (Fig. 50 (right)) would result in a shift in the centroid energy of ~5 channels for that isotope due to a slight smearing of the lowenergy part. There are 2 alphas for 212 Bi: kev (69.9%) and kev (27.1%), only the high energy group was fitted for that isotope σ=13.9 kev σ=16.7 kev ±3.4 centroid= ± ±0.6 centroid= ± Channel x Channel x 10 4 Fig. 50: The 216 Po peak and two fits for channels (left) and (right). For B series ORTEC surface barrier Si detector the silicon equivalent dead layer thickness is 800 Å. The α particles average energy after the dead layer was calculated using TRIM. The energy calibration was determined by a linear fit to be: Energy (kev) = X Channel

70 Isotope Energy (kev) Energy after the Peak centroid dead layer (kev) (channel) 212 Po Po Rn Bi Table 17: α lines energy, effect of the detector dead layer and fitted centroids. Even though the error in the peak centroid channel is very low, the error projected on energies of ~2 MeV is significant (±9 kev) because of large lever arm between calibration energy and beam energy. D. Simulation of the RBS spectrum The code written for the simulation of the RBS spectrum reconstructs the Ti and the Au peaks based on the foil thicknesses and irradiation parameters. The measured spectrum is presented in Fig. 51. The Ti peak is seen between channels The low energy slope is smaller than that of the high energy edge due to both the roughness of the Ti foil and energy straggling. The Au peak is centered at channel 2711 and is much smaller because of the small thickness of the evaporated gold layer. For the 7.5 nm Au layer and 2.9 μm Ti foil (Table 18), the energy spectrum of the scattered protons was calculated. In order to evaluate the energy loss and energy spread in the Ti backing TRIM calculations were performed for foils of thicknesses between 0.1 μm and 3.4 μm. The initial conditions for the proton beam energy and energy spread were E initial = 1910 kev and de initial = 0 kev. For thin (few μm) Ti foil the energy loss (de/dx) gets a constant value of: de/dx = 43.1 kev/μm The effect of the Ti foil can be described as: Energy spread Layer Density (g/cm 3 ) Thickness (μg/cm 2 ) Ti thickness m kev Thickness Ti μm Au nm Table 18: Nominal Ti foil and Au layer parameters. The calculated energy loss for 1912 kev protons in Au is 91.5 kev/μm and the calculated average contribution of the Au layer to the energy spread is 0.9 kev. The 70

71 routine for the calculation of the Ti peak takes into account the energy loss in the Au layer and Ti slices to determine the proton energy before the scattering - E beforerbs. The energy of the scattered proton E afterrbs is determined by the kinematic factor k: E afterrbs = k E beforerbs m k p cos m p m 2 target m m where m p is the proton mass, m target is the mass of the target nucleus (Ti or Au nucleus) and θ is the RBS angle. After scattering in the Ti or Au layer, the proton energy is reduced according to the de/dx in Ti and Au. The proton energy measured in the silicon surface barrier detector is a bit smaller because of energy loss in the Si detector dead layer. The reduction in energy was calculated according to the de/dx of protons for 800 Å silicon equivalent dead layer. This calculation is iteratively repeated for slices of a Gaussian representing the proton beam energy distribution. Another iterative calculation is done for the silicon detector energy resolution represented by a Gaussian distribution with σ = 12 kev. For each iteration the equivalent channel is increased by the calculated contribution for the slice. The proton beam average energy and energy spread can be extracted from the high-energy edge half-maximum channel and slope, respectively. The plateau absolute height can give information about the normalization parameters and the moderate slope should behave like Rutherford differential cross section. In addition, the Ti foil thickness and roughness can be extracted from the low energy peak fall off half maximum channel and slope. The parameters used in the calculations are listed in appendix 12. Optimization of the Ti foil thickness together with a roughness parameter led to reduction of 7% in the bulk Ti foil thickness and addition of a roughness layer with linear decrease in density of thickness 0.84 μm. The fit corresponds to an average thickness of the Ti foil of 3.1±0.2 μm and a roughness whose amplitude is ~0.4 μm. Optimization of the energy and energy spread was done iteratively for channels The best fit was achieved for energy of 1908 kev and energy spread of σ = 14 kev. Fig. 51 shows the optimized simulation for the Ti peak and the results are summarized in Table 19 and found consistent with expected values. It can be seen from Fig. 51 that the simulation predicts a stronger Au peak, it is possible that during the measurement, the time integrated proton beam was not fully target 2 p sin

72 Fig. 51: The RBS Ti and Au spectrum (blue) and an optimized simulation for the Ti peak (green). The best fit is achieved for proton energy of 1908 kev and energy spread of 14 kev (1 STD). focused and centered therefore a significant charge percentage hit the Ti foil on area with no evaporated gold layer. Ti spectrum parameter Information obtained Nominal value Extracted value High energy edge average channel High energy slope Proton beam energy ± 4.3 kev 1908 ± 9 kev Proton beam energy spread (1 σ) Unknown 14 ± 3 kev Plateau height Normalization Low energy edge average channel Ti foil thickness 2.9 μm 3.1 ± 0.2 μm Low energy edge slope Ti foil roughness Unknown 0.84 ± 0.05 μm Table 19: Quantitative parameters extracted by the code. 72

73 4. Neutron production using SoLiT Neutron production and Au activation were performed using SoLiT with a lowintensity proton beam [FEI12c]. Those experiments were the first to produce quasi- Maxwellian neutrons at SARAF. The limited diagnostics and experience in accelerator operation enabled only low accuracy measurements but helped towards following experiments with LiLiT. The experimental setup design (Fig. 52) is based on a solid Li/LiF target used for MACS measurements [RAT88]. The transversal properties of the proton beam at target position should enable activation of a gold sample of reasonable dimensions. The total proton charge on target required for the activation is of the order of 10 mc and is easily collected for a ~5 µa beam which correspondingly requires to dissipate ~10 W of beam power. The setup for Au activations consists of a solid-lif target LiF cup, connected to the SoLiT chamber. LiF is evaporated on a 1 mm thickness Cu backing, soldered to a water cooled copper cup, to produce a thick neutron-producing target (>1 µm) with a diameter of 8 mm. The electrically-floating LiF cup enables proton current measurement in order to determine the n/p ratio and improve the abilities to tune the beam on the center of the target; a permanent magnet was used to suppress secondary electrons for current measurements. The proton beam transversal dimensions were shaped by 3 collimators the 4-jaw rectangular cooled collimator at the end of the beamline (Fig. 3), a 14 mm cooled collimator inside the chamber (Fig. 47) and a 6 mm collimator very close to the LiF layer. Peripheral water cooling removed the heat from the target without interfering with the neutron spectrum. The Au foil was centered and attached tightly to the LiF cup Cu backing as can be seen in Fig. 52 (Left). The distance between the Delrin insulators LiF target backing Ø12, 1mm thick Cu LiF cup Teflon insulator cup+target holder water-cooled Cu ODØ29 housing ODØ31, 65 mm long SS 0.5 mm thick Suppressing magnets Au activation target Proton beam direction insertion collimator Cu Ø6 4.5 CF flange Fig. 52: Left SoLiT chamber positioned at the end of the beamline, gold secondary target is attached to the LiF cup, Right 3D drawing of the LiF cup. 73

74 Au target and the neutron source was approximately the Cu backing thickness 1 mm. Only low accuracy cross section measurements were performed because of 7 Be losses due to target damage and low accuracy and stability of the proton beam during the activations; in addition, difficulties in current measurements caused large variations in the n/p ratio. In order to get a more reliable measurement with lower error the following improvements of the experimental setup are suggested: The LiF cup design should be optimized to enable better suppression and improve the current measurement. The proton beam current during irradiation should be reduced and a better design should be made for the setup for better handling of targets in order to prevent 7 Be losses during and after irradiation. The methods developed here for the proton beam energy and energy spread characterization should be used. 5. The Liquid-Lithium Target (LiLiT) for nuclear astrophysics The development of the windowless liquid-lithium target was based on the specifications determined for LiLiT setup (see below). It included hydrodynamics similarity experiments (appendix 13), detailed design and construction of the target, circulation tests and heat removal tests using an electron gun. The circulation tests and heat removal experiments are discussed in details in [HAL13a, HAL13b, HAL14]; the experimental setup for activations and the first activation experiment are discussed in details in this chapter. A. LiLiT specifications The Liquid-Lithium Target (LiLiT) was designed to operate with a high-intensity proton beam. Aiming at optimizing the conditions for precise cross section measurements, a detailed set of specifications for LiLiT was defined (appendix 1). The main requirements are the following: 1. Proton energy: kev 2. Maximum proton current: 3.5 ma 3. Rectangular collimation by the 4-jaw collimator of a radial Gaussian beam 74

75 4. Lithium jet velocity: < 20 m/s 5. Secondary target diameter: < 30 mm 6. Optimized wide exit port for neutrons Based on these requirements and on calculations that include the 7 Li(p,n) 7 Be reaction cross section, heat removal analysis, beam dynamics simulations and the physical, practical and safety constraints of the nuclear astrophysics experiments, the specifications for LiLiT were determined and defined in details [FEI08a]. Based on this document, a general design was made for LiLiT (Fig. 53). For a smooth lithium surface and a mono-energetic (1912 kev) proton beam, neutrons are created in the first 4 µm, after which the proton energy becomes smaller than the reaction threshold. A minimum thickness of 160 µm of lithium is required to stop the 1912 kev proton beam but for safety and hydrodynamics reasons, the lithium jet thickness was designed to be 1500 µm. Leaving safety margins for irradiating by a ~8 mm width (rectangular) proton beam, the jet width was planned to be 18 mm. Our calculation predicted that in order to sustain a 6 kw proton beam (with R RMS = 3 mm) and preventing boiling or excessive evaporation, a 16 m/s lithium jet flowing on a curved back wall at a pressure of 10-5 Torr is required. For base lithium temperature of 195 C in these conditions, the maximal local temperature stays below the vapor pressure temperature of 350 C and the average temperature rise of the total Li volume after being heated by the proton beam is 7 C. The heat is removed from the lithium by an oil heat exchanger followed by an air-oil heat exchanger. The design enables to position a secondary sample, 27 mm in diameter, at a Proton beam distance of ~3 mm from the neutron source (the lithium surface) and minimize the mass of structural materials in a cone of 70 from the neutron source [FEI08b, FEI09]. Detailed information can be found in appendix 1. Lithium circulation Fig. 53: LiLiT 3D scheme. The red arrow represents the proton beam direction. 75

76 B. Experimental setup LiLiT loop The LiLiT setup (see [HAL11, HAL13a] for details) is built as a loop circulating liquid lithium at a temperature of ~200ºC and producing a jet onto a thin concave supporting wall. The liquid lithium is collected in a reservoir housing a heat exchanger with a mineral-oil closed loop (Fig. 54, left). The SARAF liquid-lithium LiLiT vacuum chamber Proton beam Flow-meter Nozzle Lithium tank + heat exchanger EM pump loop Fig. 54: Left - 3D scheme of LiLiT loop. Right - LiLiT at early stage of its construction. Proton beam Fig. 55: Left - 3D scheme of LiLiT nozzle. Right - liquid lithium flow during circulation. 76

77 target loop was built in a separate ad-hoc laboratory (Fig. 54, right). 8 kg of lithium were loaded into the loop under argon atmosphere. In order to circulate the lithium, the loop is heated to >200 C and the lithium is driven by a rotating magnet inductive electromagnetic pump [FEI09, HAL13a]. The lithium flowing on the concave wall during circulation can be seen in Fig. 55 (right). During irradiations, the proton beam is focused on the free surface of the lithium jet (Fig. 55, left). Thermal tests simulating the energy deposition of the proton beam were performed using a 20-kW e-gun [HAL13a]. C. Experimental setup - cross section measurements with LiLiT Minimization of the neutron cone diameter at target location depends on the beam parameters but the most important parameter is the distance between the neutron source (the jet surface) and the sample - Δz. For a point source and cone opening of ±70, the cone diameter can be approximated as 5.5 Δz. In order to optimize the conditions for MACS measurements using LiLiT, special care was given for the design of the lithium jet back wall, the vacuum window (10" diameter) and the sample holder. As schematically illustrated in Fig. 56, the design enables placing the sample (target sandwich) close to LiLiT vacuum window. A thin stainless steel (SS) back wall (0.35 mm) and a thin SS vacuum window (0.5 mm) create a compact design which allows reducing the distance between the sample and the neutron source. Proton beam Fig. 56: The setup scheme for activations with LiLiT. Proton beam direction is indicated by the red arrow. 77

78 The actual distances established in our first experiments are listed in Table 20. The jet waviness of the order of <0.5 mm is negligible. Layer Thickness (mm) Jet thickness 1.5 Concave wall 0.35 Distance between jet wall and window 4.0 Vacuum window 0.5 Vacuum window to sample distance 2.0 Total 8.3 ± 1.0 Table 20: Distances of layers between the neutron source and the sample. The setup for cross section measurements was built taking into account the safety constraints for operating a high-intensity machine. In case of major instability in the lithium flow on the back concave wall or large transversal deviation of the high intensity proton beam, a hole may be punctured in the 0.5 mm thickness SS back wall. Keeping the vacuum conditions is critical for superconducting accelerators air and lithium vapor reaching the PSM may freeze on the cavities surface and cause severe damage. In order to protect the accelerator, beamline and LiLiT while enabling activations, a dedicated secondary vacuum (~0.1 mbar) chamber (LiLiT activation chamber), was built and installed downstream the LiLiT loop (Fig. 57). During operation, the chamber was kept in vacuum (separate) and served as a safety beam dump in case of failure. As illustrated in Fig. 58, the sample is placed close to the LiLiT vacuum window. For the setup design we minimized the materials and components to reduce the effect of scattered neutrons. LiLiT activation chamber LiLiT chamber Proton beam Fig. 57: LiLiT activation chamber connected to LiLiT chamber. 78

79 One of the main objectives of LiLiT is to conduct cross section measurements for reactions of product nuclei with short half life. In that case the measurement of the activated sample should be made shortly after the irradiation. The target holder is utilized for fast dismounting of the irradiated target using a shaft with a bayonet connector. After irradiation, the mounting port is opened (Fig. 58), the shaft is inserted into the chamber and the sample is pulled out. LiLiT activation chamber Sample holder LiLiT vacuum window Mounting port Fast dismounting shaft Fig. 58: LiLiT activation chamber. The sample is fixed close to the neutron source, fast dismounting after irradiation is done by the shaft. 6. Methodology for cross section measurements with LiLiT A. Proton beam characterization The determination of the SARAF proton beam energy and energy spread is planned to be done by RBS as successfully proved in SoLiT experiments. An RBS diagnostics system positioned close to LiLiT will be used to characterize the proton beam. As described in details in the beginning of the chapter, the systematic characterization of the proton beam energy will also be based on the D-plate (see Fig. 5) RBS and TOF diagnostics systems. The evaluation of the SARAF proton beam current upstream from LiLiT is planned to be achieved by 2 current transformers located at the D-plate and at the end of the beamline. In addition, an independent measure of the proton beam current will be supplied by calibrated measurement of the 478 kev γ line of the 7 Li(p,p ) 7 Li * reaction during the irradiation. B. Neutron beam characterization Two main limitations of SARAF and LiLiT prevent us from characterizing experimentally the neutron yield and spectrum. After an irradiation with LiLiT, we 79

80 lack the ability to evaluate the number of neutrons produced based on 7 Be activity as performed with solid targets [RAT88, FEI12c] since the 7 Be accumulated during the irradiation cannot be measured with good accuracy. The number of neutrons incident on target during the irradiation should be evaluated then by monitoring using the gold foils. In addition, since TOF measurements are not presently available at SARAF, we cannot measure the neutron spectrum with good resolution and must rely on detailed simulations as developed and benchmarked in chapter 4. C. Methodology of MACS determination The cross section determination of a sample irradiated with LiLiT is performed relative to a Au standard. Two gold foils on both sides of the activated sample are used as a neutron monitor. The experimental cross section is calculated based on the activities of the Au foils and the investigated sample. The eventual goal of the activation experiments is the determination of the MACS at ~30 kev for stable and unstable nuclei based on the measurement of the energy-averaged cross section and the experimental neutron spectrum. The first step of the cross section measurement of the investigated nucleus is the determination of the number of neutrons n 0 incident on the target assembly during the irradiation. A detailed simulation based on the SimLiT code (chapter 4 sec. 2B) and on Geant4 supply us with the required neutron spectrum data. The simulation requires determination of the proton beam parameters E and de to be used as the initial conditions of the calculation. The evaluation of n 0 can be done in principle based on these simulations and on the activity of the gold foils or based on simulations and integrated current measurement: 1) Evaluation by Au activity: based on the proton beam energy and energy spread measurement, a SimLiT + Geant4 simulation (see chapter 4) is performed in order to evaluate the neutron spectrum at the position of each Au foil. n 0 is calculated by convolutions of the simulated neutron spectra for each Au foil with ENDF/B-VII Au(n,γ) cross section and the measured Au foils activities. 2) Evaluation by integrated current measurement: the proton beam energy, energy spread and integrated current during the irradiation are measured. The evaluation of n 0 is achieved by SimLiT+Geant4 simulation based on those parameters. 80

81 Consistency of those 2 methods is important in order to have confidence in our simulation code to describe reliably the effects related to the neutron spectrum for LiLiT geometry - scattering in the SS walls, effective target thickness, etc. and also increase the confidence in our E, de and current measurements. However, the reliability of current measurement in our experiment turned out to be low and we relied therefore exclusively on normalization to Au measured activity. The second step relies on the activation measurement of the investigated nucleus target. Once we have n 0 and based on the target thickness and activity of the investigated nucleus, we can obtain the experimental averaged cross section. We rely on the ENDF-2011 libraries to describe qualitatively the neutron capture cross section in the region of interest (E n kev) and calculate an average cross section over the simulated neutron spectrum. The ratio between the experimental and calculated averaged cross section gives us an experimental normalization factor (CSNF) of the library data. The MACS at kt = 30 kev of the investigated nucleus is then obtained from the ENDF-2011 library multiplied by CSNF. This procedure has been widely used for MACS calculations [TOU90, HEI08] Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr cross section measurements with LiLiT A first high-current operation of LiLiT at SARAF for activation was performed. The target (see [HAL13a] for details) operated steadily dissipating the heat created by the proton beam and with a natural Zr target, the (n,γ) cross sections of 94 Zr and 96 Zr were measured using two gold foils for monitoring the neutron flux [FEI14]. The case of nat Zr was selected because of a series of existing measurements [TOU90, DIL09] and its astrophysical significance [LUG13]. The A Zr neutron capture cross sections have 95 Mo 96 Mo 97 Mo 95 Nb 96 Nb 97 Nb 94 Zr 95 Zr 96 Zr 97 Zr Fig. 59: Activation of 94 Zr and 96 Zr and consecutive β - decays. 81

82 an impact on the understanding of the s-process (see Fig. 59) and the origin of presolar grains. The isotopic compositions of presolar grains extracted from primitive meteorites are different from the solar system composition and provide unique information on their formation environments in astrophysical sites. Cross section measurements were also performed recently by time-of-flight at n-tof [TAG11a, TAG11b, TAG13]. Predictions of the Zr isotopic ratios in presolar grains produced by the s-process were compared for different MACS measurements and discussed in [LUG13]. A. nat Zr activation with LiLiT The target for the irradiation was made as a disk, 24 mm in diameter and 21.1 μm in thickness. Two gold disks of same diameter were used to monitor the neutron fluence on both sides of the Zr sample, the thicknesses of the Au disks were 21.7 μm for the Fig. 60: γ spectrum of the activated Zr sample. disk closer to the neutron source and μm for the second gold disk. During the activation the total proton charge irradiating LiLiT was ~1 ma hr with peak current of ~1 ma. After the irradiation, the Au and Zr targets were brought to a separate laboratory for γ measurement and placed at a distance of 2 cm from a calibrated HPGe detector. The γ spectrum (Fig. 60) shows the γ lines of 95,97 Zr activated nuclei. 82

83 B. MACS of the 94 Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr reactions Based on the half life and decay radiation of 95 Zr and 97 Zr (Table 21), the number of activated nuclei produced by the 94 Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr reactions were determined (Table 22). The measured Au activations were similar for both foils and were consistent with proton beam energy of 1908 kev and energy spread of 15 kev. These values were used for the SimLiT+Geant4 simulations. Natural abundance 94 Zr 17.38% 96 Zr 2.8% Nuclei Half life 95 Zr 64 d Product nuclei γ lines Energy (kev) I γ % % 97 Zr 16.8 hr % Daughter nuclei γ lines Half Nuclei Energy life (kev) I γ 95 Nb 35 d % 97 Nb 1.23 hr % Table 21: Zr isotopes and daughter nuclei data. The 94 Zr and 96 Zr energy-dependent cross sections were taken from ENDF/B-VII.1 [CAR09] and the CSNF for 94 Zr and 96 Zr was determined from the γ measurement results (Table 23). MACS calculation for kt = 30 kev was done by convoluting the ENDF/B-VII.1 cross section multiplied by CSNF with the neutron Maxwellian distribution at kt = 30 kev. Random and systematic uncertainties which affected our results have been investigated. The stability of the value for the MACS has been checked for variations in beam parameters (E, de), setup geometry and the uncertainty resulting from the Monte Carlo-based analysis. We evaluate our present overall uncertainty at 5-7%. We believe that Isotope Number of nuclei produced 95 Zr (3.82 ± 0.05) Zr (2.72 ± 0.03) Au 1 (6.78 ± 0.08) Au 2 (6.73 ± 0.08) 10 9 Table 22: Number of 95 Zr and 97 Zr nuclei produced during the activation runs. Isotope CSNF 94 Zr 1.03 ± Zr 1.32 ± 0.09 Table 23: CSNF for 94 Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr. reducing this uncertainty is achievable after finalizing the optimization of the setup, diagnostics, accelerator operation and analysis codes. The results of this first experiment are listed in Table 24 compared to reported data. 83

84 MACS (mb) Isotope This work KADoNiS v0.3 [DIL09] Toukan Wyrick Musgrove Boldeman Macklin Tagliente Tagliente [TAG11a] [TAG11b] [TOU90] [WYR83] [MUS78] [BOL76] [MAC67] 94 Zr 29.0 ± ± ± 4 33 ± ± ± Zr 13.1 ± ± ± ± ± 0.6 Table 24: MACS at 30 kev of the 94 Zr(n,γ) 95 Zr and 96 Zr(n,γ) 97 Zr reactions. The KADoNiS recommended value was measured by Toukan et al.. 84

85 Chapter 6: Discussion and Conclusions Activation measurements with neutrons produced by the near-threshold thick-target 7 Li(p,n) reaction have provided extensive data on weak s-process reactions that occur in massive stars. High-current rf accelerator facilities currently being planned will allow more sensitive MACS measurements and will extend the measurements to unstable nuclides, small cross sections, or cases in which decay radiation is hard to detect. The new machines, based on rf technologies, will allow for much higher proton-beam intensities in the milliampere and even tens of milliamperes ranges. The rf accelerators, which typically consist of rf quadrupole structures often followed by rf resonators, have the drawback of a broader energy width as compared to the traditional Van de Graaff machines. At SARAF, we anticipate a proton beam of few ma and an energy standard deviation σ, which ranges from 7 to 20 kev. At higherintensity facilities being planned, for example, the FRANZ facility, higher-energy broadenings yet are considered [REI09a, RAT10]. Detailed beam dynamics simulations were performed for SARAF phase I linac and beamline. The simulation started at the RFQ exit based on a reference initial distribution. We focused on performing a reliable feasibility study for the planned experiments tuning the accelerator and beamline and simulating the expected beam at target position. GPT routines were written in order to visualize the "S-shape" beamline and to ease the beamline magnets optimization. The SARAF phase I accelerator, beamline and target chambers lattice were implemented in the GPT simulation code. We confirmed that the SARAF SC linac can supply with a beam with the required energy (1912 kev) and energy spread (~10-20 kev) including the transport of the beam through the beamline. The accelerator tune was optimized for minimal energy spread for a low current and high current beam. Minimal energy spread of 4.5 kev was achieved at the PSM exit for low and high current beam. At the end of the beamline the beam energy spread did not change significantly for low 85

86 current (100 μa) beam but for high current of 3.5 ma, the energy spread was increased to ~8.5 kev by the space charge effect. From the beam dynamics studies we learned about the importance of beam collimation by the 4-jaw collimator. The calculations showed that the position of the 4-jaw is close enough to target position to allow the required collimation of the beam and will also protect the lithium nozzle SS "ears" during high power operations with LiLiT. The operational conditions of the beamline magnets and 4-jaw collimation were optimized by detailed studies. The current position of the 4-jaw was found to be appropriate for high current operations with LiLiT for the nuclear astrophysics experiments. Based on the optimized beamline magnets tune and 4-jaw collimation the required transversal dimensions of the beam of r rms 3 mm were achieved. The feasibility of large spot operations was also proved, based on the 4-jaw collimation. The losses for high current experiments were evaluated and proved to be low enough considering heat removal limitation of the accelerator and beamline components. We have presented a comparison of neutron spectra and gold foil activation studies with a narrow-energy proton beam as is typical of a Van de Graaff facility (σ ~ 1.5 kev) and with a broad-energy proton beam as expected at the SARAF accelerator (σ ~ 20 kev). Results for the narrow-energy proton beam neutron spectra compare favorably to existing measurements [RAT88]. The angle-integrated neutron spectra were found to be nearly identical for the two measurements, except for the tail region where the spectrum obtained with the broad-energy proton beam showed better agreement with the high-energy tail of a Maxwellian distribution (at the cost of a larger angular spread). The extent to which this factor is significant in astrophysical measurements of s-process reactions depends on the contribution of the higher-energy neutrons at the tail to the MACS. The SimLiT code reproduces well the experimental spectra and angular distributions for both narrow-energy and broad-energy proton beams. We have measured gold activation with the semi-maxwellian neutrons on planar gold samples and have obtained good agreement with previous measurements [RAT88]. Experiments with SARAF were performed both with SoLiT and LiLiT. The experiments included the tuning of the accelerator to obtain the required proton beam, characterization of the proton beam and activation of a nat Zr sample. 86

87 We study the systematics and develop methods to tune the linac followed by a method for characterizing the proton beam energy and energy spread. The tuning of the linac and characterization of the proton beam were performed with 3 diagnostics systems: D-plate RBS, D-plate TOF and SoLiT RBS, each have its limitations. Since there is no available precise diagnostics for the neutron beam, it is important to perform the final proton beam characterization as close as possible to the neutron production position. The SoLiT RBS diagnostics system was proved as a reliable diagnostics for the proton beam characterization. For future setup installed for LiLiT, it should be tested in comparison to other diagnostics (e.g. 7 Li(p,n) threshold scan). Precise calibration of the Si detector should be done with a very thin α source (e.g. 220 Rn gas from 228 Th source). Energy-current dependency was discovered and should be investigated in order to understand the origin of the correlation. First activation with LiLiT was performed for a nat Zr sample. The MACS was calculated and compared to known data. Even though the experiment was aimed only at performing a preliminary measurement of the cross section, the results obtained were consistent with the literature taking into account the measurement uncertainties. LiLiT as a neutron source was proved to be able to dissipate the power of a ~1 ma proton beam and produce a high intensity stellar neutron flux. Future development of LiLiT will reduce MACS measurements uncertainties. Main recommendations for future experiments Based on the broad experience accumulated, it is recommended to study and develop the following systems and experimental methods for LiLiT future high current experiments: 1) Upgrade the beam dynamics code to include the influence of neighbor bunches 2) Beam dynamics code benchmark with measurements 3) Optimize the operation of the 4-jaw and last beamline doublet in order to get better transversal beam shaping 4) Implement a RBS system for LiLiT 5) Repeat the systematic tune and characterization of the proton beam with LiLiT setup and accelerator new tune 87

88 6) Verify the reproducibility of the measurements and the operational characteristics focusing on cross section measurements of a specific nucleus and proton beam parameters 7) Verify stability in time of main parameters (energy, energy spread, current) 8) Standardize the setup and measurements when possible (target diameter, proton beam transversal dimensions, gold foil thickness, accelerator and beamline magnets tune, beam collimation, target position Δz, integrated current) We recommend on the following diagnostics systems for precise characterization of the SARAF high intensity proton beam: 1) Energy: D-plate TOF 2) Energy spread: LiLiT RBS system 3) Current: D-plate current transformer (MPCT) Summarizing the work done towards high current activations at SARAF with LiLiT we report of a broad study performed for developing a high intensity neutron source to be operated in a high intensity machine and first successful operation of the systems. The study proved the feasibility and advantages of a broad energy spread proton beam to be used to irradiate LiLiT in order to get a high intensity stellar neutron source. Simulation tools were developed as well as experimental method for reliable operation of the accelerator and beamline, lithium irradiation and secondary target irradiation by the stellar neutrons aiming at precise MACS measurements. 88

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94 Appendices Appendix 1: LiLiT design parameters and operational characteristics The specifications for LiLiT were determined and defined in the "User Requirement Specifications for LiLiT" [FEI08a]. The specifications are based on calculations that include the 7 Li(p,n) 7 Be reaction, heat removal analysis, beam dynamics calculations and the physical, practical and safety constraints of the nuclear astrophysics experiments. The specifications are based on 5 main requirements: 1. Proton energy: 1912 kev 2. Proton current: ~3.5 ma 3. Rectangular collimation by the 4-jaw collimator of a radial Gaussian beam 4. Lithium jet velocity: ~20 m/s 5. Secondary target diameter: < 30 mm 6. Optimized wide exit port for neutrons The analysis of the thermal behavior of the target was based on the physical properties and realistic geometry of the target and considered the proton beam parameters. For a smooth lithium surface and a mono-energetic (1912 kev) proton beam, neutrons are created in the first 4 µm, after which the protons energy becomes smaller than the reaction threshold. A minimum thickness of 160 µm of lithium is required to stop the 1912 kev proton beam but for safety and hydrodynamical reasons, the lithium jet thickness was designed to be 1500 µm. The proton beam transversal distribution was assumed to be a radial Gaussian. In order to irradiate a small secondary target (dia. < 30 mm) the proton beam should be focused into a small spot size on the Li jet surface. The beam focusing together with minimizing the distance between the neutron source and the secondary target Δz are stringent demands for the operation of LiLiT. Minimization of Δz shows that a value of σ=2.2 mm (R rms =3.1 mm) is required for the proton beam transversal distribution. Based on the beam energy and initial current, the power is 6.6 kw. Cutting first with the x (horizontal) plates of the 4-jaws at 1.8σ reduces the current by 7.2% and absorbs 240 W on each plate. The y (vertical) plates cut the beam at 1.5σ. The cut reduces the 94

95 current by 13.4% and absorbs 410 W on each plate of the 4-jaws. The total power absorbed by the 4-jaws is P 4-jaws = 1.3 kw therefore the remaining beam power stopped in the lithium jet is P LiLiT = 5.3 kw. The beam dimensions after the 4-jaws cut is 7.9 X 6.6 mm. The beam dimensions may change between the 4-jaw and the Li jet position, keeping safety margins the jet width was determined to be at least 15 mm. Note that the final design value was 18 mm. For a distance lithium surface to sample of Δz ~ 3 mm, a sample diameter of 27 mm subtends the ±70 opening cone of the neutrons. For power density and heating calculations we assume jet velocity of 16 m/s which corresponds in lithium flow rate of 21.6 lit/min. In order to investigate the lithium heating we calculate the parameter determining the maximum temperature rise at the center of the beam the horizontal power density (integrated over the Y axis) at the center of the beam. For a 2 MeV, I = 2 ma, σ = 2.04 mm proton beam and jet velocity of V = 20 m/s, the calculated maximum temperature rise is ΔT = 80. The horizontal power density (perpendicular to flow direction) for that case is 0.78 kw/mm. The horizontal power density for the nominal beam and jet velocity is 1 kw/mm. Assuming linearity of the horizontal power density with the reciprocal velocity and independency with σ y we get for the maximal temperature rise: ΔT = 130 C. The average lithium temperature rise is ΔT average = 7 C. Parameter Value Parameter Value Proton energy 1912 kev Proton current at PSM exit 3.5 ma Proton current at lithium jet position 2.8 ma Beam spot at lithium jet position (σ / R RMS ) 2.2 mm / 3.1 mm Cut x = 1.8 σ 3.96 mm Cut x = 1.5 σ 3.3 mm Proton beam width (2 Cut x) 7.9 mm Proton beam height (2 Cut y) 6.6 mm Proton beam power at PSM exit 6.65 kw Proton beam power at target position 5.3 kw Jet velocity 16 m/s Vacuum in the jet chamber 10-5 mbar Vacuum in the sample chamber 10-2 mbar Table A1: LiLiT specifications summary. Nozzle thickness 1.5 mm Nozzle width 15 mm Δz 3 mm Sample diameter 27 mm ΔT 130 C Q 21.6 lit/min P HX 7 kw HX coolant temperature 195 C Working temperature 225 C HX entrance lithium temperature 232 C Maximal average loop temperature 270 C Maximal temperature in the lithium jet 355 C 95

96 Appendix 2: SARAF phase I PSM and beamline lattice "wcs" coordinate system elements and lengths in meters element name element length end of element "wcs" position radius dr_rfq_end dr_ap dr_mebt quad dr_mebt quad dr_mebt quad dr_mebt z_psm_ dr_b09c_entry sol_psm HWR / dr_b09c_interhwr HWR / sol_psm HWR / dr_b09c_interhwr HWR / sol_psm HWR / dr_b09c_interhwr HWR / dr_b09c_end end of element distance from z_psm_end z_psm_end dr_psm_ionpump dr_ionpump quad1_eff dr_quad1_ quad2_eff dr_quad2_dplate dr_dplate dr_dplate_exit Dplate_collimator dr_vg dr_vg_bellow z_dplate_end dr_pre_bend bend_length z_wcs_end Table A2: The lattice of the "wcs" coordinate system elements. 96

97 "CS_interband" coordinate system elements and lengths in meters element name element length end of element "CS_interbend" position radius end of element in "wcs" position bend_length dr_bends bend_length z_cs_interbend_end Table A3: The lattice of the "CS_interband" coordinate system elements. "CS_shifted" coordinate system elements and lengths in meters element name element length end of element "CS_interbend" position radius end of element in "wcs" position bend_length dr_post_bend dr_after_bend dr_pre_quad quad3_eff dr_post_quad dr_steerer dr_tube dr_pre_quad quad45_eff dr_doublet_mid quad45_eff dr_post_quad dr_bellow dr_4jaw dr_post_4jaw dr_solit dr_solit_stage_collimator dr_solit dr_solit_cup_collimator z_end Table A4: The lattice of the "CS_shifted" coordinate system elements. 97

98 Appendix 3: Beamline magnets specifications The beamline magnets specifications are specified in Tables A5 and A6: Manufacturer 1 st doublet Quadrupole 2 nd doublet High Voltage Engineering DANFYSIK Auckland Nuclear Accessory Company ANAC Model ED-1086-M, 2'' doublet ANAC 3515, 3'' doublet Aperture diameter (mm) Effective pole length (mm) Effective element separation (mm) Field gradient (T/m) Table A5: Beamline quadrupoles specifications. 45 dipole Manufacturer DANFYSIK Model 45 bending magnet Bending radius (mm) 1350 Internal free height in vacuum chamber (mm) 46 Internal free width in vacuum chamber (mm) 100 Bending angle 45 Entrance angle (magnetic field) 25.6 Exit angle (magnetic field) 26.6 Maximum magnetic field (T) 1 Table A6: 45 bending magnet specifications. 98

99 Appendix 4: Custom GDFA Program - SoLiTpiperrms /* SoLiTpiperrms.c: R RMS calculation for vacuum pipe for SoLiT beamline */ /* Developed by Gitai Feinberg, SARAF 2012 */ #include <math.h> #include "gdfa.h" int SoLiTpiperrms_func(double *result) { int i, num, tmpnum, tmpnum2; double Rxz, R2, sumr2=0, sumnr2=0, sumn=0; double *x, *y, *nmacro, *z; if(gdfmgetarr("x",&x,&num) num<1 gdfmgetarr("y",&y,&tmpnum) tmpnum!=num gdfmgetarr("z",&z,&tmpnum2) tmpnum2!=num gdfmgetarr("nmacro",&nmacro,&tmpnum) tmpnum!=num) return(1); for(i=0 ; i<num ; i++) { if (z[i]<8.592) {R2=(x[i]*x[i]+y[i]*y[i]);} else {if (x[i]<(-1)*z[i] ) {Rxz=1.35-sqrt((z[i]-8.592)*(z[i]-8.592)+(x[i]-1.35)*(x[i]-1.35)); R2=Rxz*Rxz+y[i]*y[i];} else {if (x[i]<(-1)*z[i] ) {R2=0.5*(x[i]-z[i]+9.151)*(x[i]-z[i]+9.151)+y[i]*y[i];} else {if (z[i]<11.21) {Rxz=1.35-sqrt((z[i]-11.21)*(z[i]-11.21)+(x[i]-0.150)*(x[i]-0.150)); R2=Rxz*Rxz+y[i]*y[i];} else {R2=(x[i] )*(x[i] )+y[i]*y[i];} } } } sumr2+=r2; sumnr2+=nmacro[i]*r2; sumn+=nmacro[i]; } if (sumn==0) *result=sqrt(sumr2/num); else *result=sqrt(sumnr2/sumn); return(0); } 99

100 Appendix 5: Custom GDFA Program - SoLiTrmax /* SoLiTrmax.c: rmax calculation for SoLiT beamline */ /* Developed by Gitai Feinberg, SARAF 2012 */ #include "gdfa.h" int SoLiTrmax_func( double *result ) { int i, num, tmpnum, tmpnum2; double Rxz, R2, r2max=0.0; double *x, *y, *nmacro, *z; if(gdfmgetarr("x",&x,&num) num<1 gdfmgetarr("y",&y,&tmpnum) tmpnum!=num gdfmgetarr("z",&z,&tmpnum2) tmpnum2!=num gdfmgetarr("nmacro",&nmacro,&tmpnum) tmpnum!=num) return(1); for(i=0 ; i<num ; i++) { if (z[i]<8.592) {R2=(x[i]*x[i]+y[i]*y[i]);} else {if (x[i]<(-1)*z[i] ) {Rxz=1.35-sqrt((z[i]-8.592)*(z[i]-8.592)+(x[i]-1.35)*(x[i]-1.35)); R2=Rxz*Rxz+y[i]*y[i];} else {if (x[i]<(-1)*z[i] ) {R2=0.5*(x[i]-z[i]+9.151)*(x[i]-z[i]+9.151)+y[i]*y[i];} else {if (z[i]<11.21) {Rxz=1.35-sqrt((z[i]-11.21)*(z[i]-11.21)+(x[i]-0.150)*(x[i]-0.150)); R2=Rxz*Rxz+y[i]*y[i];} else {R2=(x[i] )*(x[i] )+y[i]*y[i];} } } } if (R2>r2max) r2max=r2; } *result=sqrt(r2max); return(0); } 100

101 Appendix 6: Custom GDFA Program - SoLiTavgrXZ /* SoLiTavgrXZ.c: calculate avgr only for XZ plane for SoLiT beam line */ /* Developed by Gitai Feinberg, SARAF 2013 */ #include "gdfa.h" int SoLiTavgrXZ_func(double *result) { int i, num, tmpnum, tmpnum2; double Rxz, sumrxz=0, sumnrxz=0, sumn=0; double *x, *nmacro, *z; if(gdfmgetarr("x",&x,&num) num<1 gdfmgetarr("z",&z,&tmpnum2) tmpnum2!=num gdfmgetarr("nmacro",&nmacro,&tmpnum) tmpnum!=num) return(1); for(i=0 ; i<num ; i++) { if (z[i]<8.592) {Rxz=x[i];} else {if (x[i]<(-1)*z[i] ) {Rxz=1.35-sqrt((z[i]-8.592)*(z[i]-8.592)+(x[i]-1.35)*(x[i]-1.35));} else {if (x[i]<(-1)*z[i] ) {if ((x[i]-z[i]+9.151)>0) Rxz=sqrt(0.5*(x[i]-z[i]+9.151)*(x[i]-z[i]+9.151)); else Rxz=(-1)*sqrt(0.5*(x[i]-z[i]+9.151)*(x[i]-z[i]+9.151));} else {if (z[i]<11.21) {Rxz=(-1)*(1.35-sqrt((z[i]-11.21)*(z[i]-11.21)+(x[i]-0.150)*(x[i]-0.150)));} else {Rxz=x[i] ;} } } } sumrxz+=rxz; sumnrxz+=nmacro[i]*rxz; sumn+=nmacro[i]; } if (sumn==0) *result=sumrxz/num; else *result=sumnrxz/sumn; return(0); } 101

102 Appendix 7: Custom GDFA Program - SoLiTxrms /* SoLiTxrms.c: X RMS calculation for SoLiT beamline */ /* Developed by Gitai Feinberg, SARAF 2013 */ #include "gdfa.h" int SoLiTxrms_func(double *result) { int i, num, tmpnum, tmpnum2; double Xxz, X2, sumx2=0, sumnx2=0, sumn=0; double *x, *nmacro, *z; if(gdfmgetarr("x",&x,&num) num<1 gdfmgetarr("z",&z,&tmpnum2) tmpnum2!=num gdfmgetarr("nmacro",&nmacro,&tmpnum) tmpnum!=num) return(1); for(i=0 ; i<num ; i++) { if (z[i]<8.592) {X2=x[i]*x[i];} else {if (x[i]<(-1)*z[i] ) {Xxz=1.35-sqrt((z[i]-8.592)*(z[i]-8.592)+(x[i]-1.35)*(x[i]-1.35)); X2=Xxz*Xxz;} else {if (x[i]<(-1)*z[i] ) {X2=0.5*(x[i]-z[i]+9.151)*(x[i]-z[i]+9.151);} else {if (z[i]<11.21) {Xxz=1.35-sqrt((z[i]-11.21)*(z[i]-11.21)+(x[i]-0.150)*(x[i]-0.150)); X2=Xxz*Xxz;} else {X2=(x[i] )*(x[i] );} } } } sumx2+=x2; sumnx2+=nmacro[i]*x2; sumn+=nmacro[i]; } if (sumn==0) *result=sqrt(sumx2/num); else *result=sqrt(sumnx2/sumn); return(0); } 102

103 Appendix 8: Custom GDFA Program - SoLiTxmax /* SoLiTxmax.c: xmax (max abs(x)) calculation for SoLiT beamline */ /* Developed by Gitai Feinberg, SARAF 2013 */ #include "gdfa.h" int SoLiTxmax_func(double *result) { int i, num, tmpnum, tmpnum2; double Xxz, X2, temp=0.0; double *x, *nmacro, *z; if(gdfmgetarr("x",&x,&num) num<1 gdfmgetarr("z",&z,&tmpnum2) tmpnum2!=num gdfmgetarr("nmacro",&nmacro,&tmpnum) tmpnum!=num) return(1); for(i=0 ; i<num ; i++) { if (z[i]<8.592) {X2=x[i]*x[i];} else {if (x[i]<(-1)*z[i] ) {Xxz=1.35-sqrt((z[i]-8.592)*(z[i]-8.592)+(x[i]-1.35)*(x[i]-1.35)); X2=Xxz*Xxz;} else {if (x[i]<(-1)*z[i] ) {X2=0.5*(x[i]-z[i]+9.151)*(x[i]-z[i]+9.151);} else {if (z[i]<11.21) {Xxz=1.35-sqrt((z[i]-11.21)*(z[i]-11.21)+(x[i]-0.150)*(x[i]-0.150)); X2=Xxz*Xxz;} else {X2=(x[i] )*(x[i] );} } } } if (X2>temp) temp=x2; } *result=sqrt(temp); return(0); } 103

104 Appendix 9: Custom GDFA Program - SoLiTyrms /* SoLiTyrms.c: Y RMS calculation for SoLiT beamline */ /* Developed by Gitai Feinberg, SARAF 2013 */ #include "gdfa.h" int SoLiTyrms_func( double *result ) { int i, num, tmpnum; double Y2, sumy2=0; double *y, *nmacro; if(gdfmgetarr("y",&y,&num) num<1 gdfmgetarr("nmacro",&nmacro,&tmpnum) tmpnum!=num) return(1); for(i=0 ; i<num ; i++) {Y2=y[i]*y[i]; sumy2+=y2;} *result=sqrt(sumy2/num); return(0); } 104

105 Appendix 10: Custom GDFA Program - SoLiTymax /* SoLiTymax.c: ymax (max abs(y)) calculation for SoLiT beamline */ /* Developed by Gitai Feinberg, SARAF 2013 */ #include "gdfa.h" int SoLiTymax_func(double *result) { int i, num, tmpnum; double Y2, temp=0.0; double *y, *nmacro; if(gdfmgetarr("y",&y,&num) num<1 gdfmgetarr("nmacro",&nmacro,&tmpnum) tmpnum!=num) return(1); for(i=0 ; i<num ; i++) { Y2=y[i]*y[i]; if (Y2>temp) temp=y2; } *result=sqrt(temp); return(0); } 105

106 Appendix 11: GPT Input File /* Developed by Gitai Feinberg, SARAF 2013 */ I=0.1; RFQ_aperture=0.005; m=mp; q=-qe; w=2*pi* ; # mp= MeV MEBT_quad_field_1=13.35; MEBT_quad_field_2=-10.14; MEBT_quad_field_3=0.6688; phi1=42; phi2=0; phi3=252; phi4=23; phi5=0; phi6=70; HWR1=0.22; HWR2=0.0; HWR3=0.4; HWR4=0.27; HWR5=0.0; HWR6=0.071; #MaxAmp=1 muni_psm= ; ni_psm=muni_psm/(6* e-06); sol1=1.6*ni_psm; sol2=1.79*ni_psm; sol3=1.3*ni_psm; BL_quad1_field= ; BL_quad2_field= ; BL_quad3_field=0.5222; BL_quad4_field= ; BL_quad5_field=0.9796; bend_radius=1.35; bend_length=0.559; # bend_length=bend_radius*tan(pi/8) E_MeV=1.9132; beta_gamma=sqrt((e_mev/ )^2-1); bend_field=-1*m*c*beta_gamma/(q*bend_radius); bend_dl= ; bend_b1=30; t_start=0; t_end=900e-9; interval=0.5e-9; setfile("beam","..\set1_rotated.gdf"); setnmacro("beam",(i/4.0)*( /5000)); spacecharge3dmesh(); #RFQ+MEBT (start=0, end=0.687) dr_rfq_end=0.037; dr_ap=0.02; quad=0.07; bore_drift=0.015; dr_mebt1=0.110; dr_mebt2=0.075; dr_mebt3=0.075; dr_mebt4=0.160; z_rfqdr=dr_rfq_end/2; z_ap = dr_rfq_end + dr_ap/2; z_mebt_0 = z_ap + dr_ap/2; z_mebt1=z_mebt_0+dr_mebt1/2; z_mebt_quad1 = z_mebt1 + dr_mebt1/2 + quad/2; z_mebt2 = z_mebt_quad1 + quad/2 + dr_mebt2/2; z_mebt_quad2 = z_mebt2 + dr_mebt2/2 + quad/2; z_mebt3 = z_mebt_quad2 + quad/2 + dr_mebt3/2; z_mebt_quad3 = z_mebt3 + dr_mebt3/2 + quad/2; z_mebt4 = z_mebt_quad3 + quad/2 + dr_mebt4/2; z_psm_0=z_mebt4+dr_mebt4/2; drift("wcs","z",z_rfqdr, dr_rfq_end, 0.01); drift("wcs","z",z_ap, dr_ap, RFQ_aperture); drift("wcs","z",z_mebt1, dr_mebt1, bore_drift); quadrupole("wcs","z",z_mebt_quad1, quad, MEBT_quad_field_1);rmax("wcs","z",z_MEBT_quad1, 0.015, quad); drift("wcs","z",z_mebt2, dr_mebt2, bore_drift); quadrupole("wcs","z",z_mebt_quad2, quad, MEBT_quad_field_2);rmax("wcs","z",z_MEBT_quad2, 0.015, quad); drift("wcs","z",z_mebt3, dr_mebt3, bore_drift); quadrupole("wcs","z",z_mebt_quad3, quad, MEBT_quad_field_3);rmax("wcs","z",z_MEBT_quad3, 0.015, quad); drift("wcs","z",z_mebt4, dr_mebt4, bore_drift); 106

107 #PSM (start=0.687, end=3.199) dr_b09c_entry=0.155; dr_b09c_interhwr=0.050; dr_b09c_end=0.155; sol_psm=0.244; HWR09=0.22; bore_sol = 0.019; sol_psm_eff= ; sol_rad= ; z_b09c_entry = z_psm_0 + dr_b09c_entry/2; z_b09c_c1_sol = z_b09c_entry + dr_b09c_entry/2 + sol_psm/2; z_b09c_c1_hwr1 = z_b09c_c1_sol + sol_psm/2 + HWR09/2; z_b09c_c1_dr = z_b09c_c1_hwr1 + HWR09/2 + dr_b09c_interhwr/2; z_b09c_c1_hwr2 = z_b09c_c1_dr + dr_b09c_interhwr/2 + HWR09/2; z_b09c_c2_sol = z_b09c_c1_hwr2 + HWR09/2 + sol_psm/2; z_b09c_c2_hwr1 = z_b09c_c2_sol + sol_psm/2 + HWR09/2; z_b09c_c2_dr = z_b09c_c2_hwr1 + HWR09/2 + dr_b09c_interhwr/2; z_b09c_c2_hwr2 = z_b09c_c2_dr + dr_b09c_interhwr/2 + HWR09/2; z_b09c_c3_sol = z_b09c_c2_hwr2 + HWR09/2 + sol_psm/2; z_b09c_c3_hwr1 = z_b09c_c3_sol + sol_psm/2 + HWR09/2; z_b09c_c3_dr = z_b09c_c3_hwr1 + HWR09/2 + dr_b09c_interhwr/2; z_b09c_c3_hwr2 = z_b09c_c3_dr + dr_b09c_interhwr/2 + HWR09/2; z_b09c_end = z_b09c_c3_hwr2 + HWR09/2 + dr_b09c_end/2; z_psm_end = z_b09c_end + dr_b09c_end/2; drift("wcs","z",z_b09c_entry, dr_b09c_entry, bore_drift); drift("wcs","z",z_b09c_c1_sol, sol_psm, bore_sol); bzsolenoid("wcs","z",z_b09c_c1_sol, sol_rad, sol_psm_eff, sol1); HWR("wcs","z",z_B09C_C1_HWR1, "..\EH-09.gdf", "x","y","z","ex","ey","ez","hx","hy","hz", HWR1*1.969, phi1*pi/180, w); drift("wcs","z",z_b09c_c1_dr, dr_b09c_interhwr, bore_drift); HWR("wcs","z",z_B09C_C1_HWR2, "..\EH-09.gdf", "x","y","z","ex","ey","ez","hx","hy","hz", HWR2*1.969, phi2*pi/180, w); drift("wcs","z",z_b09c_c2_sol, sol_psm, bore_sol); bzsolenoid("wcs","z",z_b09c_c2_sol, sol_rad, sol_psm_eff, sol2); HWR("wcs","z",z_B09C_C2_HWR1, "..\EH-09.gdf", "x","y","z","ex","ey","ez","hx","hy","hz", HWR3*1.969, phi3*pi/180, w); drift("wcs","z",z_b09c_c2_dr, dr_b09c_interhwr, bore_drift); HWR("wcs","z",z_B09C_C2_HWR2, "..\EH-09.gdf", "x","y","z","ex","ey","ez","hx","hy","hz", HWR4*1.969, phi4*pi/180, w); drift("wcs","z",z_b09c_c3_sol, sol_psm, bore_sol); bzsolenoid("wcs","z",z_b09c_c3_sol,sol_rad, sol_psm_eff, sol3); HWR("wcs","z",z_B09C_C3_HWR1, "..\EH-09.gdf", "x","y","z","ex","ey","ez","hx","hy","hz", HWR5*1.969, phi5*pi/180, w); drift("wcs","z",z_b09c_c3_dr, dr_b09c_interhwr, bore_drift); HWR("wcs","z",z_B09C_C3_HWR2, "..\EH-09.gdf", "x","y","z","ex","ey","ez","hx","hy","hz", HWR6*1.969, phi6*pi/180, w); drift("wcs","z",z_b09c_end, dr_b09c_end, bore_drift); # BEAM LINE before 45 deg bend (start=3.199, end=8.456) dr_psm_ionpump=0.075; dr_ionpump=0.930; quad1_eff=0.231; dr_quad1_2=0.118; quad2_eff=0.231; dr_quad2_dplate=0.317; dr_dplate=2.301; dr_dplate_exit=0.374; Dplate_collimator=0.050; dr_vg=0.480; dr_vg_bellow=0.150; z_psm_ionpump=z_psm_end+dr_psm_ionpump/2; z_ionpump=z_psm_ionpump+dr_psm_ionpump/2+dr_ionpump/2; z_quad1=z_ionpump+dr_ionpump/2+quad1_eff/2; 107

108 z_quad1_2=z_quad1+quad1_eff/2+dr_quad1_2/2; z_quad2=z_quad1_2+dr_quad1_2/2+quad2_eff/2; z_quad2_dplate=z_quad2+quad2_eff/2+dr_quad2_dplate/2; z_dplate=z_quad2_dplate+dr_quad2_dplate/2+dr_dplate/2; z_dplate_exit=z_dplate+dr_dplate/2+dr_dplate_exit/2; z_dplate_collimator=z_dplate_exit+dr_dplate_exit/2+dplate_collimator/2; z_vg=z_dplate_collimator+dplate_collimator/2+dr_vg/2; z_vg_bellow=z_vg+dr_vg/2+dr_vg_bellow/2; z_dplate_end=z_vg_bellow+dr_vg_bellow/2; drift("wcs","z",z_psm_ionpump,dr_psm_ionpump, bore_drift); drift("wcs","z",z_ionpump, dr_ionpump, ); quadrupole("wcs","z",z_quad1,quad1_eff,bl_quad1_field); rmax("wcs","z",z_quad1, , quad1_eff); drift("wcs","z",z_quad1_2,dr_quad1_2, ); quadrupole("wcs","z",z_quad2,quad2_eff,bl_quad2_field); rmax("wcs","z",z_quad2, , quad2_eff); drift("wcs","z",z_quad2_dplate,dr_quad2_dplate, ); drift("wcs","z",z_dplate,dr_dplate, ); drift("wcs","z",z_dplate_exit,dr_dplate_exit, ); drift("wcs","z",z_dplate_collimator,dplate_collimator, 0.029); drift("wcs","z",z_vg,dr_vg, ); drift("wcs","z",z_vg_bellow,dr_vg_bellow, ); # 45 deg bending magnets (start=8.456, end=11.346) dr_pre_bend1=0.136; dr_bends=1.003; dr_post_bend2=0.136; z_pre_bend1=z_dplate_end+dr_pre_bend1/2; z_bend1=z_pre_bend1+dr_pre_bend1/2+bend_length; z_interbend=bend_length+dr_bends/2; z_bend2=z_interbend+dr_bends/2+bend_length; z_post_bend2=bend_length+dr_post_bend2/2; z_bends_end=z_post_bend2+dr_post_bend2/2; ccs("wcs", 0,0,z_bend1, 1,0,-1, 0,1,0, "CS_interbend"); ccs("cs_interbend", 0,0,z_bend2, 1,0,1, 0,1,0, "CS_shifted"); drift("wcs","z",z_pre_bend1,dr_pre_bend1, ); sectormagnet("wcs", "CS_interbend", bend_radius, bend_field, , , bend_dl, bend_b1, 0.0); drift("cs_interbend","z",z_interbend, dr_bends, ); sectormagnet("cs_interbend", "CS_shifted", bend_radius, bend_field, , , bend_dl, bend_b1, 0.0); drift("cs_shifted","z",z_post_bend2, dr_post_bend2, ); # end of beam line (start=11.346, end=15.311) dr_after_bend2=0.415; dr_pre_quad3=0.086; quad3_eff=0.106; dr_post_quad3=0.086; dr_steerer=0.27; dr_tube=0.556; dr_pre_quad4=0.326; quad45_eff=0.314; dr_doublet_mid=0.183; dr_post_quad5=0.147; dr_bellow=0.148; dr_4jaw=0.242; dr_post_4jaw=0.772; z_after_bend2=z_bends_end+dr_after_bend2/2; z_pre_quad3=z_after_bend2+dr_after_bend2/2+dr_pre_quad3/2; z_quad3=z_pre_quad3+dr_pre_quad3/2+quad3_eff/2; z_post_quad3=z_quad3+quad3_eff/2+dr_post_quad3/2; 108

109 z_steerer=z_post_quad3+dr_post_quad3/2+dr_steerer/2; z_tube=z_steerer+dr_steerer/2+dr_tube/2; z_pre_quad4=z_tube+dr_tube/2+dr_pre_quad4/2; z_quad4=z_pre_quad4+dr_pre_quad4/2+quad45_eff/2; z_doublet_mid=z_quad4+quad45_eff/2+dr_doublet_mid/2; z_quad5=z_doublet_mid+dr_doublet_mid/2+quad45_eff/2; z_post_quad5=z_quad5+quad45_eff/2+dr_post_quad5/2; z_bellow=z_post_quad5+dr_post_quad5/2+dr_bellow/2; z_4jaw=z_bellow+dr_bellow/2+dr_4jaw/2; z_post_4jaw=z_4jaw+dr_4jaw/2+dr_post_4jaw/2; end_of_beam_line=z_post_4jaw+dr_post_4jaw/2; drift("cs_shifted","z",z_after_bend2, dr_after_bend2, ); drift("cs_shifted","z",z_pre_quad3, dr_pre_quad3, ); quadrupole("cs_shifted","z",z_quad3, quad3_eff, BL_quad3_field); rmax("cs_shifted","z",z_quad3, , quad3_eff); drift("cs_shifted","z",z_post_quad3, dr_post_quad3, ); drift("cs_shifted","z",z_steerer, dr_steerer, ); drift("cs_shifted","z",z_tube, dr_tube, 0.048); drift("cs_shifted","z",z_pre_quad4, dr_pre_quad4, ); quadrupole("cs_shifted","z",z_quad4, quad45_eff, BL_quad4_field); rmax("cs_shifted","z",z_quad4, , quad45_eff); drift("cs_shifted","z",z_doublet_mid, dr_doublet_mid, ); quadrupole("cs_shifted","z",z_quad5, quad45_eff, BL_quad5_field); rmax("cs_shifted","z",z_quad5, , quad45_eff); drift("cs_shifted","z",z_post_quad5, dr_post_quad5, ); drift("cs_shifted","z",z_bellow, dr_bellow, ); drift("cs_shifted","z",z_4jaw, dr_4jaw, ); drift("cs_shifted","z",z_post_4jaw, dr_post_4jaw, ); # SoLiT (start=15.311, end=15.829) dr_solit1=0.329; dr_solit_stage_collimator=0.01; dr_solit2=0.169; dr_solit_cup_collimator=0.01; z_solit1=end_of_beam_line+dr_solit1/2; z_solit_stage_collimator=z_solit1+dr_solit1/2+dr_solit_stage_collimator/2; z_solit2=z_solit_stage_collimator+dr_solit_stage_collimator/2+dr_solit2/2; z_solit_cup_collimator=z_solit2+dr_solit2/2+dr_solit_cup_collimator/2; z_lif=z_solit_cup_collimator+dr_solit_cup_collimator/2; drift("cs_shifted","z",z_solit1, dr_solit1, 0.09); drift("cs_shifted","z",z_solit_stage_collimator, dr_solit_stage_collimator, 0.007); drift("cs_shifted","z",z_solit2, dr_solit2, 0.09); drift("cs_shifted","z",z_solit_cup_collimator, dr_solit_cup_collimator, 0.003); tout(t_start,t_end,interval); dtmax=interval; screen("wcs","i",1.33); screen("wcs","i",1.59); screen("wcs","i",2.06); screen("wcs","i",2.33); screen("wcs","i",2.79); screen("wcs","i",3.06); 109

110 Appendix 12: RBS simulation code In order to calculate the absolute spectrum the following parameters were included in the simulation: 1. The RBS angle 2. Au and Ti natural abundances, masses and densities 3. The Si detector collimator diameter and distance from the Ti foil (effective solid angle) 4. The integrated current during the measurement 5. RBS differential cross section 6. de/dx and straggling in Ti, Au and the detector dead layer 7. Si detector resolution 8. Au layer thickness 9. Ti layer thickness and roughness 10. Energy calibration The number of protons of energy E scattered by a 10 nm Ti slice into a solid angle Ω is calculated by the following equation: N scattered N p d N d Ti where N p is the number of irradiated protons, d kz1z 2e d 4E 2 2 sin 4 1 / 2 is Rutherford differential cross section ( k Nm C 2 ) and N Ti is the number of Ti atoms per unit area in a 10 nm slice. 15 For an irradiation period of 2583 sec and average current of 100 na - N The solid angle created by the detector collimator (diameter = 2 mm), positioned at a distance of 45 cm from the Ti foil is d d sin sr. For Ti we get: / E kg/ m 20 2 and: N Ti m kg/ mol therefore: N scattered E 8 1 The following code includes those parameters for the calculation. 2 p E 2 110

111 %RBS for Ti+Au code2: optimized absoluterti, with Ti roughness clear %Ti abundances and masses mp=1.01; mti46=45.95; mti47=46.95; mti48=47.95; mti49=48.95; mti50=49.94; Avector=[mTi46/mP mti47/mp mti48/mp mti49/mp mti50/mp]; abundance=[ ]; mau=196.97; AAu=mAu/mP; % parameters flange_angle=156.3; angle=flange_angle*pi/180; kev_to_ch_a=0.6688; % linear calibration parameter a kev_to_ch_b=52.7; % linear calibration parameter b Si_detector_resolution=12; % Si detector resolution: sigma=12 kev chisquare=zeros(30,2000); de_au=0.686; %energy loss in Au layer Au_thickness=7.5; %Au layer thickness in nm Ti_thickness=2.70; %Ti layer thickness in um Ti_roughness=0.84; %Ti layer roughness in um %Absolute calculations parameters kelec=8.988e9; unitcharge=1.6e-19; kevtojoule=1000*1.6e-19; omega=(pi*0.1^2)/(45^2); %Si collimator diameter=2 mm, (Si diameter = 20 mm) totalprotons=2583*(100*1e-9/(1.6e-19)); %livetime*100na csti=(kelec*1*22*unitcharge^2)^2/16/(kevtojoule^2)/(sin(156.3*pi/180/2)^4); N10nmTi=1e4*6.02e23*1e-6*4.506/47.867; %cm^2_to_m^2*navogadro*10nm_of_cm*density/molar mass absoluterti=(csti*omega*n10nmti*totalprotons)*1.009; % best fit for the plateau csau=(kelec*1*79*unitcharge^2)^2/16/(kevtojoule^2)/(sin(156.3*pi/180/2)^4); N1AngAu=1e4*6.02e23*1e-8*19.3/196.97; %cm^2_to_m^2*navogadro*1ang_of_cm*density/molar mass absoluterau=(csau*omega*n1angau*totalprotons); for Efit=1908:1908 for sig=14:14 E0=Efit; %initial proton beam energy proton_sigma=sig; %proton beam sigma simulation=zeros(1,16384); smoother=3; for g=0:(10*au_thickness) %number of Au slices in 0.1 nm for j=-40*smoother:40*smoother % proton energy spread scan EbeforeRBS=E0+j/smoother *g; %de/dx=91.5 kev/um EafterRBS=EbeforeRBS*(cos(angle)+sqrt(AAu^2-(sin(angle))^2))^2/(1+AAu)^2; Edetector=EafterRBS-( *g)/cos(pi-angle)-2.16; % energy loss in dead layer = 2.16 kev proton_sigma_total=sqrt((proton_sigma)^2+1.05^2); % energy spread after Au degrader = 0.9 kev, 1.05=0.5*( /cos(23.7)) frac_protonbeam=exp(- (j/smoother)^2/(2*proton_sigma_total^2))/sqrt(2*pi*proton_sigma_total^2); for s=-30:30 frac_si=exp(- s^2/(2*si_detector_resolution^2))/sqrt(2*pi*si_detector_resolution^2); channel=round(((edetector+s)-kev_to_ch_b)/kev_to_ch_a); simulation(channel)=simulation(channel)+frac_si*frac_protonbeam*(absoluterau/smoother) /(EbeforeRBS^2); end end end for abundance_index=1:5 A=Avector(abundance_index); frac_abundance=abundance(abundance_index); %for abundance_index=1:1 % A=Avector(3); % frac_abundance=1; for i=1:(100*ti_thickness) %number of Ti slices in 10*nm for j=-40:40 EbeforeRBS=E0+j-dE_Au *i; %de/dx=43.14 kev/um 111

112 EafterRBS=EbeforeRBS*(cos(angle)+sqrt(A^2-(sin(angle))^2))^2/(1+A)^2; Edetector=EafterRBS-(0.4314*i)/cos(pi-angle)-dE_Au/cos(pi-angle)-2.4; % energy loss in dead layer = 2.4 kev proton_sigma_total=sqrt((proton_sigma)^2+1.05^2+(5.755*sqrt(i/100))^2); frac_protonbeam=exp(- j^2/(2*proton_sigma_total^2))/sqrt(2*pi*proton_sigma_total^2); for s=-30:30 frac_si=exp(- s^2/(2*si_detector_resolution^2))/sqrt(2*pi*si_detector_resolution^2); channel=round(((edetector+s)-kev_to_ch_b)/kev_to_ch_a); simulation(channel)=simulation(channel)+frac_abundance*frac_si*frac_protonbeam*absolut erti/(ebeforerbs^2); end end end for i=100*ti_thickness:(100*ti_thickness+100*ti_roughness) %degrader roughness effect for j=-40:40 EbeforeRBS=E0+j-dE_Au *i; %de/dx=43.14 kev/um EafterRBS=EbeforeRBS*(cos(angle)+sqrt(A^2-(sin(angle))^2))^2/(1+A)^2; Edetector=EafterRBS-(0.4314*i)/cos(pi-angle)-dE_Au/cos(pi-angle)-2.4; % energy loss in dead layer = 2.4 kev proton_sigma_total=sqrt((proton_sigma)^2+1.05^2+(5.755*sqrt(i/1000))^2); frac_protonbeam=exp(- j^2/(2*proton_sigma_total^2))/sqrt(2*pi*proton_sigma_total^2); frac_roughness=1-(i-100*ti_thickness)/(100*ti_roughness); %effective Ti surface caused by linear roughness for s=-30:30 frac_si=exp(- s^2/(2*si_detector_resolution^2))/sqrt(2*pi*si_detector_resolution^2); channel=round(((edetector+s)-kev_to_ch_b)/kev_to_ch_a); simulation(channel)=simulation(channel)+frac_abundance*frac_si*frac_protonbeam*frac_ro ughness*absoluterti/(ebeforerbs^2); end end end end % X axis for q=1:16384 x16384ch(q)=q; end %Y axis file=fopen('raw.txt'); for i=1:16384 raw(i)=fscanf(file,'%f',[1]); end fclose(file); chi2=0; for ch=2515:2565 % Ti high energy slope %for ch=2650:2763 % Au peak %for ch=2515:2763 % Ti high energy slope + Au peak %for ch=2000:2763 % Ti + Au %for ch=2250:2450 % Ti plateau %for ch=2100:2180 % Ti low energy slope chi2=chi2+(raw(ch)-simulation(ch))^2/simulation(ch); end chisquare(sig,efit)=chi2; end end smooth=zeros(1,16384); for w=3:16300 smooth(w)=(raw(w-2)+raw(w-1)+raw(w)+raw(w+1)+raw(w+2))/5; end ystairs(:,1)=raw'; ystairs(:,1)=smooth'; ystairs(:,2)=simulation'; %Plots stairs(x16384ch,ystairs) axis([ ]) 112

113 Appendix 13: Hydrodynamics similarity experiments The hydrodynamic behavior of the lithium jet was modeled using water. Since the kinematic viscosity of lithium and water is similar, a 1:1 scale (for both hydraulic diameter and velocity) water setup was built producing a stable 20 m/s water jet. Another setup was built to check the jet hydrodynamics keeping both the Reynolds and Weber numbers (60,000 and 2,020 respectively) constant and therefore simulating the effects related to viscosity and surface tension. Those demands for the similarity experiment result in enlarging the hydraulic diameter by a factor of 7.3 and reducing the velocity by a factor of 6 for the water setup. A smooth and steady water jet was produced in these experiments as can be seen in Fig. 61. Fig. 61: 108 mm wide and 13 mm thick water similarity modeling of the lithium jet. Front view (left) and side view (right), proton beam direction indicated by red arrow. 113