Low energy Positron Polarimetry at the ILC

Low energy Positron Polarimetry at the ILC Gideon Alexander, Ralph Dollan, Thomas Lohse, Sabine Riemann, Andreas Schälicke, Peter Schüler, Pavel Starovoitov, Andriy Ushakov January 23, 29 Abstract For the design of the International Linear Collider (ILC) a polarized positron source based on a helical undulator system has been proposed. In order to optimize the positron beam, i.e. to ensure high intensity as well as high degree of polarization, a measurement of the polarization close to the positron creation point is recommended. In this contribution the measurement of positron polarization at the ILC positron source is examined. A Compton transmission polarimeter was successfully used to measure the polarization of MeV positrons at the test experiment E-166. An improved version of this prototype could be used also for measurements at the ILC. Studies showed that also a Bhabha polarimeter operated at few hundred MeV is well suited to measure the positron polarization at the source. A layout for a Bhabha polarimeter at the ILC positron source is presented. Alternatively, the option to measure the positron polarization at 5 GeV using a Compton polarimeter is discussed. Tel Aviv University, Israel Humboldt University Berlin, Germany DESY, Zeuthen, Germany DESY, Hamburg, Germany NC PHEP Minsk, Belarus 1

Contents 1 Introduction 3 2 Parameters of the ILC positron source 3 3 Methods for polarimetry at the ILC positron source 5 3.1 Mott scattering................................ 6 3.2 Synchrotron radiation............................ 6 3.3 Laser Compton polarimetry......................... 6 3.4 Compton transmission polarimetry..................... 7 3.5 Bhabha polarimeter.............................. 7 3.6 Simulation tools................................ 8 4 Simulation of interactions between polarized beams and matter 8 4.1 Simulation tools for polarized processes in matter............. 9 4.2 Polarized Geant4 for the linear collider................... 1 5 Prototype: Compton transmission polarimeter 11 5.1 Compton transmission polarimetry..................... 11 5.2 The E-166 experiment............................ 12 5.3 Measurement of positron polarization.................... 15 5.4 Compton transmission polarimeter at the ILC positron source...... 16 6 Bhabha polarimeter for the ILC positron source 18 6.1 Kinematics.................................. 19 6.2 Target Heating................................ 2 6.3 Target magnetization............................. 21 6.4 Multiple scattering in the target....................... 22 6.5 Signal and background studies........................ 23 6.6 Layout of the Bhabha polarimeter...................... 25 6.7 Simulation of polarization measurement................... 27 7 Compton polarimetry at 5 GeV 3 7.1 General remarks................................ 3 7.2 The Compton scattering cross section.................... 32 7.3 The asymmetry measurement........................ 34 7.4 Simulation of the low energy Compton polarimeter............ 39 7.5 Summary Compton polarimeter at 5GeV.................. 44 8 Summary 44 2

1 Introduction The physics potential of a future linear collider will be substantially broadened if both beams electrons and positrons are polarized [1, 2]. While the production of an intense polarized electron beam is well established the production of polarized positrons is challenging. In the project of the International Linear Collider (ILC) polarized positrons are created with circularly polarized photons hitting a thin target. The spin is transferred to the pair produced electrons and positrons resulting in a net polarization of the particles emerging from the target. The positrons are captured just behind the target in a dedicated capture optics, i.e. an optical matching device (OMD) and accelerated in several steps up to 5GeV before they enter the damping ring (DR). The degree of polarization has to be maintained until the positrons reach the collision point. At the interaction point (IP), the polarization, P e and P e +, will be measured with Compton polarimeters achieving an accuracy of a few per mill to take full advantage of physics measurements with polarized beams. For the commissioning of the machine and the optimization of the ILC operation an independent check of polarization near the creation point of positrons and electrons is recommended. The polarization of electrons will be measured directly after the gun using a Mott polarimeter. To keep the positron losses as low as possible a positron polarimeter can be positioned only at energies higher than roughly 5 MeV 1 MeV. Further, the positron beam has a large transverse size of the order centimeters. Due to these features the low energy positron polarimetry turns out to be a challenging issue even if only an accuracy of a few percent is needed. An absolute polarization measurement is preferred but at least a relative measurement is required; main criteria are the robustness and reliability combined with easy handling. In this paper, the measurement of polarization at the low energies of the ILC positron source is discussed. 2 Parameters of the ILC positron source The baseline design for the ILC positron source is described in the Reference Design Report (RDR) [3]. The source uses photo production to generate positrons: After acceleration to 15 GeV, the electron beam passes through a 15-meter helical undulator to generate MeV photons directed onto a rotating.4 radiation-length Ti-alloy target located 5 meters downstream, producing a beam of electron and positron pairs. This beam is then matched using an optical-matching device into a capture system and accelerated to 125 MeV. The electrons and remaining photons are separated from the positrons and dumped. The positrons are accelerated to 4MeV, transported through the rest of the electron main linac tunnel, brought to the central injector complex, and accelerated to 5 GeV. Before injection into the damping ring, superconducting solenoids rotate the spin vector into the vertical, and a separate superconducting RF structure is used for energy compression. An overall layout of the positron source is sketched in Figure 1. 3

Figure 1: Layout of the positron source [3]. To allow commissioning and tuning of the positron systems while the high-energy electron beam is not available, a low-intensity auxiliary (or keep-alive ) positron source is provided. The baseline design is for unpolarized positrons, and beamline space has been reserved for an eventual upgrade to 6% polarization. But the helical undulator creates circularly polarized photons and a selection of photon polarization happens by angular acceptance due to the 5m distance between undulator and target. The spin of the photons is transferred to the electrons and positrons, the positron beam has a polarization of 3% after the capture section; positrons that match the damping ring acceptance have about 45% polarization [4, 5]. Collimation of photons before the target increases the polarization of the positron beam, the loss of yield can be compensated by using a longer undulator. Spectrum and circularly polarization of the undulator photons as well as positron yield and polarization are shown in Figure 2. The nominal design parameters of the ILC the positron beam are summarized in Table 1. The typical transverse beam size is about 1cm. The helical undulator has a period λ = 1.15cm, a strength K =.92 and the active undulator length is 147m. Following the layout of the positron source, the low energy polarimeter could be positioned behind the capture section at E e + 3 4 MeV after the pre accelerator at E e + 4 MeV or near the damping ring at E e + 5 GeV. The longitudinal spin orientation of electrons and positrons has to be rotated to transverse direction before the damping ring to avoid any destruction of the polarization. Before the main linac the spin has to be reversed back to the longitudinal direction. The design of the spin rotators before and after the damping ring is described in references [6, 7], and proposals to combine spin rotation with fast helicity reversal are presented in [8, 9]. 4

dn γ /de γ [1/(MeV e- m)].22.2.18.16.14.12.1.8.6.4.2-1 1 2 3 4 5 6 E γ [MeV] 1.8.6.4.2 - -.2 -.4 -.6 -.8 Longitudinal Polarisation Figure 2: Energy spectrum and polarization of the undulator photons at the ILC positron target (left axis, red) and positron yield and polarization (right axis, blue) after 5m drift from undulator to target. 3 Methods for polarimetry at the ILC positron source Different options to measure the polarization of positrons (or electrons) have been considered: Mott scattering laser Compton polarimeter, Compton transmission polarimeter, Bhabha/Møller polarimeter, the possibility to exploit the spin dependence of synchrotron radiation Based on the reference design given in the RDR, reasonable positions for the polarimeter are after the capture section at E e + = 125 MeV, after pre acceleration before the booster linac, at 4MeV, at energies of 5GeV either before or after the damping ring. To achieve a complete spin monitoring during commissioning and operation, a combination of polarimeters is recommended. But already during commissioning the polarization measurement at the source should be possible - that requires positron polarimetry at energies up to 4MeV. 5

Beam Parameter Symbol Value Unit Positrons per bunch n b 2 1 1 number Bunches per pulse N b 2625 number Pulse repetition rate f rep 5 Hz Positron energy (DR injection) E 5 GeV DR transverse acceptance γ(a x + A y ).9 m-rad DR energy acceptance δ ±.5 % DR longitudinal acceptance A l ±3.4 ± 2.5 cm-mev Electron drive beam energy E e 15 GeV Electron beam loss in undulator E e 3.1 GeV Positron polarization (upgrade) P > 3 (6) % Table 1: Positron source parameters from Reference Design Report (RDR) [3]. 3.1 Mott scattering Elastic electron nucleus scattering described by the Mott formula is widely used to measure the transverse polarization of electrons up to energies of few MeV. The method is destructive and requires a spin rotation in case of longitudinal polarized electrons/positrons. In the relevant energy region (3MeV 5GeV) the cross section of Mott scattering is significantly smaller than that of Bhabha/Møller scattering. Hence, a Mott polarimeter is not considered as an option for a polarimeter at the positron source. 3.2 Synchrotron radiation Synchrotron radiation is spin dependent and a procedure to observe this effect was proposed in [1] and described in detail in [11, 12]. Polarization measurements at the VEPP-4 storage ring are based on the effect that the spin magnetic moment of an electron moving in a magnetic field is a source of electromagnetic radiation (spin light). At the ILC angular asymmetries of the synchrotron radiation created in a three pole magnetic snake [12] could be used in the damping ring to monitor the transverse polarization of the positrons. The method is non destructive and non intrusive. But the expected asymmetries are very small, 1 3. The short storage period in the damping ring makes it difficult to reduce the statistical and systematic uncertainties reasonably to measure this effect. Further, with a low energy polarimeter at the damping ring the distance between creation and measurement point is large. 3.3 Laser Compton polarimetry A laser Compton polarimeter is the recommended option for a polarimeter close to the interaction point. Laser photons hit the positron (electron) beam and the distributions of scattered photons and leptons depend on the degree of polarization of the the incoming particles. With this approach it is possible to achieve very high precision in the 6

polarization measurement [13] as has been demonstrated at SLC [14] and HERA [15]. For low energy positron polarimetry the situation is different. The signal rate depends on both, the intensity of photon and positron (electron) beam. To achieve sufficient signal rates at the ILC positron source within an acceptable period either the size of the polarized positron beam has to be decreased substantially or a highest power laser would be needed. Hence, a Compton polarimeter is not the solution for a low energy positron polarimeter at the source. Behind the damping ring, at E = 5 GeV, the transverse size of the positron beam is reduced to few µm and Compton polarimetry is possible. Following the ILC design after the turnaround, before the main linac, laserwire systems are foreseen to control the emittance of electron and positron beam. In principle, it is a good idea to use the laser for both, measuring the emittance and the polarization. But there are two main differences between the configuration of a polarimeter and the laserwire: 1. The crossing angle between beam and laser is 9 for the laserwire. For Compton polarimetry a crossing angle of almost 18 is recommended to achieve a high sensitivity to the lepton beam polarization. 2. The laser spot size for the laserwire has to be significantly smaller than the electron or positron beam while the spot size for the Compton polarimeter should include the whole bunch to achieve a high rate. In Reference [16] Compton polarimetry is considered; it will be summarized in section 7. 3.4 Compton transmission polarimetry For photons of a few MeV a Compton transmission polarimeter is a well established method [17]. This procedure can also be applied to positrons (or electrons), since positrons can be converted to photons in a Bremsstrahlungs target. The polarized photons pass magnetized iron and undergo Compton scattering with the two electrons in the 3d shell of the iron atoms. The transmission of a photon beam through magnetized iron depends on the polarization of the beam photons as well as on the polarization of the iron electrons. The latter is assumed to be 2/26 7.6% in fully magnetized iron. Reversing the polarity of the magnetic field results in an asymmetry of the transmission signal at the percent level. The advantage of this method is the simple setup which can deal with very poor beam qualities. This method was successfully employed in the E-166 experiment (E e + 3 8 MeV) [18] and at ATF (E e + 3 4 MeV) [19]. The polarimeter used at E-166 is a prototype for positron polarization measurements at low energies of few MeV and will be described in section 5. 3.5 Bhabha polarimeter Møller polarimeters are widely used, e.g. in SLAC experiments and at the VEPP-3 storage ring [2, 21, 22, 23, 24]. In Bhabha polarimeters polarized positrons scatter on the shell electrons of Fe atoms in a thin magnetized iron foil. The cross sections of 7

Bhabha (and Møller) scattering depend on the polarization of positrons and electrons. Assuming a known polarization of the electrons in iron atoms, P e, the polarization of the incident particle beam can be determined by reversing the magnetization in iron. The asymmetry between the counting rates of scattered electrons and positrons for +P e and P e is a measure for the polarization of the incoming positron beam. A Bhabha polarimeter is sketched in Figure 3. Figure 3: Sketch for a Bhabha polarimeter at the positron source of the ILC. A Bhabha polarimeter can be operated at positron energies of few hundred MeV. This corresponds to a position after the pre accelerator, before the booster linac where the positrons have an energy of 4MeV. A Bhabha polarimeter is a favored option for polarimetry at the positron source, details will be presented in section 6. 3.6 Simulation tools The interaction of polarized particles with matter is treated in dedicated simulation programs. A major program is Geant4 [25]: A powerful geometry package allows the creation of complex detector configurations. The physics performance is based on a huge list of interaction processes. Particle tracking in arbitrary magnetic fields is possible. But for a complete simulation of polarized processes as obtained, e.g. at the ILC positron source target and low energy polarimeter, all relevant processes have to be available with polarization. However, polarization played only a minor role so far. A new extension in the library of electromagnetic physics was created and is dedicated to polarization effects in beam applications [26, 27, 28, 29]. A short overview on its purpose and potential is given in section 4. 4 Simulation of interactions between polarized beams and matter All polarimeter options and analyses of the test experiment discussed in this paper require simulation studies with Monte Carlo programs including polarized processes. Two different scenarios are of interest in this context: 8

a) the interaction of polarized beams with unpolarized matter Creation of polarized positrons using a polarized photon beam that hits on a thin unpolarized target. In order to understand and to optimize the resulting positron yield and degree of polarization, a robust simulation of all involved processes is essential. The emphasis lies here on the polarization transfer from the mother particle to the daughter particles in the electromagnetic cascade. b) the interaction of polarized beams with polarized matter In order to optimize the operation of the positron source an independent check of the polarization near the source is recommended. This low energy polarimetry requires reasonable simulations and modelling to evaluate the analyzing power. For a complete simulation of the low energy polarimeter setup all processes that are relevant for tracking polarized particles through matter, i.e. spin dependence of Compton scattering, Bhabha/Møller scattering, annihilation into photons and photoelectric effect, as well as the polarization transfer via bremsstrahlung and pair production have to be taken into account. 4.1 Simulation tools for polarized processes in matter Several simulation packages for the description of electromagnetic showers in matter have been developed. A prominent example of such codes is EGS (Electron Gamma Shower)[3]. For this simulation framework some extensions including the treatment of polarized particles exist [31, 32, 33, 34]; the most complete code has been developed in [31, 32]. It is based on the matrix formalism [35], which enables a very general treatment of polarization. The EGS extensions, however, concentrate only on the evaluation of polarization transfer, i.e. the effects of polarization induced asymmetries are neglected and interactions with polarized media are not considered. Some effort has been made to include polarization in Geant3 [36, 18, 37], but these extensions are not publicly available. The package Geant4 is the newest member on the simulation front and is entirely written in C++. It has a wide range of applications, and slowly replaces the Fortran based simulation toolkit. In Geant4 all particles possess a three component polarization vector, therefore the description of spin precession in a magnetic field exists. However, in the past polarized processes were not included. This gap is currently being filled by two independent projects. The first project is located in the low energy package. It is dedicated to astrophysics and space based experiments, concentrating on the interactions of polarized optical photons with unpolarized materials. So far polarized versions of Compton scattering, Rayleigh scattering and the photoelectric effect have been implemented. A polarized version of pair production is under development. The second project [29] concentrates on the needs given by the linear collider experiment. It is available in a public Geant4 release since version 8.2 (December 26) [26, 27]. With this new extension it is possible to track the polarization in electromagnetic showers. Special emphasis has been put on the proper treatment of polarized matter, that 9

is essential for the simulation of low energy polarimetry. The following polarization dependent processes have been considered so far: Compton scattering, Bhabha/Møller scattering, Pair production, Bremsstrahlung, Annihilation in flight, Photoelectric effect. In the subsequent section some details of this implementation are presented. 4.2 Polarized Geant4 for the linear collider The implementation of polarized processes is based on the use of Stokes vectors and allows a convenient description of the polarization transfer by applying the matrix formalism [35]. In this formalism, a three component polarization vector ξ is assigned to each particle and characterizes completely the polarization state of any lepton or photon. For the simulation of polarized media, a possibility has to be provided to assign Stokes vectors to physical volumes. The general procedure is very similar to the polarization extension of the code EGS [32]. Any interaction is described by a transfer matrix T, which characterizes the process completely. The transfer matrix usually depends on kinematic variables like energy and angles, but it can also depend on the polarization states (of the media, for instance). The final state polarization ξ is determined via multiplication of the transfer matrix with the incoming Stokes vector ξ, ( I ξ ) = T ( I ξ ). (1) The components I and I in Equation (1) refer to the incoming and outgoing intensities, respectively. In this framework the transfer matrix T is of the form S A 1 A 2 A 3 T = P 1 M 11 M 21 M 31 P 2 M 12 M 22 M 32. (2) P 3 M 13 M 23 M 33 The matrix elements T ij can be identified as (unpolarized) differential cross section (S), polarized differential cross section (A j ), polarization transfer (M ij ), and (de)polarization (P i ). In the EGS extension the elements A j and P i have been neglected, thus concentrating on polarization transfer only. Using the full matrix the polarization implementation in Geant4 all polarization effects into account. A more detailed documentation is available in [26, 27]. 1

5 Prototype: Compton transmission polarimeter As shown in the positron source layout (Figure 1) the polarized positrons are created in a conversion target, captured using an optical matching device (OMD) and accelerated to 125MeV using normal conducting L-band RF with solenoidal focusing. Then positrons are separated from electrons and photons with a dogleg. Here, at 125 MeV, it would be a first reasonable position to verify the degree of positron polarization, especially during commissioning. At this energies the transverse dimension of the positron beam is centimeters. Compton transmission and Bhabha polarimetry are the candidates for positron polarimetry at the source. The Compton transmission polarimeter option is presented in this section including the proof of principle experiment E-166 where this type of polarimeter was used. The Bhabha polarimeter will be discussed in section 6. 5.1 Compton transmission polarimetry Compton transmission polarimetry is a simple method and works best for photon energies of few MeV to few 1MeV, in this energy range the interaction of circularly polarized photons with (polarized) electrons in iron is dominated by Compton scattering. Figure 4 illustrates this. The Compton cross section for particles with polarizations P γ and P e, 6 5 σ [barns/atom] 4 3 2 1 Total Compton Pair production 1 1 1 1 photon energy [MeV] Figure 4: Cross section of Compton scattering and pair production in iron depending on the energy of the incident photon (data taken from [38]). includes the unpolarized cross section, [( σ unpol = πr2 1 2 2 k k k 2 σ C = σ unpol + P γ P e σ pol (3) ) ln(1 + 2k ) + 1 2 + 4 k ] 1, (4) 2(1 + k ) 2 11

and the polarized cross section, σ pol = 2πr2 k [ 1 + 4k + 5k 2 1 + k ] ln(1 + 2k (1 + 2k ) 2 ) 2k, (5) where r = e 2 /mc 2 is the classical electron radius and k = E γ /mc 2. The transmission probability T ± (L) for photons of helicity P γ through magnetized iron of thickness L can be expressed as T ± (L) = exp nlσ C = exp( nlσ unpol ) exp(±nlp e P γ σ pol ), (6) where n is the number density of atoms in iron and the signs (+) and ( ) in T ± indicate whether the electron spins in iron are parallel or anti-parallel to the direction of incident photons. Reversing P e, an asymmetry, δ, in the transmission of photons through iron can be obtained: δ(l) = T + (L) T (L) T + (L) = T (L) = tanh(nlp ep γ σ pol ) nlp e P γ σ pol. (7) The analyzing power, A γ, for transmission polarimetry, A γ δ(l) P e P γ (8) can be used to to determine the polarization of he photons if the polarization of electrons in magnetized iron, P e, is known; P γ = δ(l) P e A γ (9) Compton transmission polarimetry can also be used for polarimetry of MeV positrons: In a relatively thick target ( 4 radiation lengths) positrons undergo annihilation and Bremsstahlungs processes and are converted to photons. The polarization of the positrons is transferred to the photons that are analyzed in a Compton transmission polarimeter. The positron polarization can be obtained with P e + = δ, (1) P e A e + where the analyzing power for positrons has to be determined by simulating all processes of the polarization transfer from positrons to photons and the transmission of the photons through the iron absorber. A prototype of a Compton transmission polarimeter was used in the E166 experiment. 5.2 The E-166 experiment The E-166 experiment [18, 39, 4] has been performed to demonstrate that the undulatorbased scheme can produce polarized positron beams of sufficient quality for use at the proposed International Linear Collider. The main elements of the experiment were the 12

SLAC linac [41], the Final Focus Test Beam (FFTB) [42], a pulsed helical undulator and detectors to measure the photon and positron polarizations schematically in Fig. 5. The experiment operated with an electron beam energy of 46.6±.1GeV at a repetition rate of 1Hz with 1-4 1 9 e/pulse. The normalized beam emittances were γǫ x (γǫ y ) 2.2 (.5) 1 5 mrad, and the transverse spot size was tuned to σ x σ y 35 µm. The electron beam passed through the 1-m-long undulator whose aperture was only.9mm, and was then deflected away from the produced photon beam by a string of permanent magnets. The circularly polarized photon beam of peak energy 8 MeV drifted approximately 35 m to the diagnostic detectors, shown in the lower part of Fig. 5. e - BT 's from undulator BPM1 PRT C1 T1 BPM2 D1 's to HSB1 HSB2 detectors undulator OTR WS HCOR PRD e -dump e - dump C2 D2 gamma diagnostics e + diagnostics Figure 5: Conceptual layout (not to scale) of the E-166 experiment. A 46.6-GeV electron beam entered from the left and was deflected by magnet D1 after traversing the undulator. Part of the beam of 8-MeV circularly polarized photons created in the undulator was converted to positrons in a target 35 m downstream of the undulator, and the rate and polarization of the positrons and unconverted photons were subsequently diagnosed in the spectrometer D2. BPM = beam-position monitor, BT = beam toroid, C = collimator, HCOR = horizontal-correction magnet, HSB = hard-soft-bend magnet, OTR = opticaltransition-radiation monitor, PR = beam-profile monitor, T1 = target, WS = wire scanner. The photon beam impinged upon a.2-radiation-length tungsten target T1 to produce positrons and electrons which were separated in spectrometer D2, and the polarization and rate of the positrons were measured in transmission polarimeter TP1 [17]. The unconverted photons were monitored in a second transmission polarimeter, TP2. The undulator had bifilar, helical windings of wires with currents flowing in opposite directions, resulting in a transverse magnetic field whose direction rotated with period 2.54 mm and whose strength was.71 T on axis, corresponding to an undulator strength parameter of K =.17. The calculated energy spectrum and longitudinal polarization of the photons produced by the undulator are shown in Fig. 6. For an electron beam energy of 46.6GeV and K =.17 the first-harmonic photon energy cutoff is E γ = 7.9 MeV, at 13

which energy the longitudinal polarization P γ is.98, differing from unity due to the small admixture of second harmonic photons. Photons per MeV.1.9.8.7.6.5.4.3.2.1-1 5 1 15 2 25 3 (MeV) E γ 1.8.6.4.2 - -.2 -.4 -.6 -.8 Figure 6: Solid line: calculated photon number spectrum per beam electron of undulator radiation integrated over angle, plotted as a function of photon energy E γ for electron beam energy 46.6GeV, undulator period 2.54mm and undulator strength parameter K =.17. The peak energy of the first harmonic (dipole) radiation was 7.9MeV. Dashed line: longitudinal polarization P γ of the undulator radiation as a function of energy. The diagnostics for the positrons, electrons and photons is illustrated in Figure 7. The photon beam was monitored in the transmission polarimeter TP2. The flux of photons was determined by aerogel Čerenkov counters, A1, A2, and by silicon-diode detectors, S1, S2, before and after a 15-cm-long cylinder of iron whose axial magnetization was reversed periodically. The total energy of photons that passed through the iron cylinder was monitored in a W-plate calorimeter GCAL read out by interleaved Si diodes. The asymmetry δ γ = (S γ S+ γ )/(S γ + S+ γ ) (11) in the observed signals S γ ± of photons transmitted through the iron cylinder with reversed magnetization (±) was in good agreement with a simulation combining the energy and polarization distributions with the spin-dependence of Compton scattering of the polarized photons off polarized atomic electrons in the magnetized iron [43]. For details see References [39, 4]. Polarization 14

Figure 7: Schematic of the photon and positron diagnostics. A1, A2 = aerogel Čerenkov detectors, C2-C4 = collimators, D2 = dipole spectrometer magnet, CsI = 3 3 array of CsI crystals, GCAL = Si-W calorimeter, J = movable W jaws, P1, S1, S2= Si-diode detectors, SL = solenoid lens, T1 = positron production target, T2 = reconversion target, TP1 = positron transmission polarimeter solenoid, TP2 = photon transmission polarimeter solenoid. The detectors were encased in lead and tungsten shielding (not shown). 5.3 Measurement of positron polarization The scheme to measure positron (electron) polarization follows is shown in Figure 7: Positrons (and electrons) produced from undulator photons in the W target T1 were focused to a parallel beam by solenoid lens SL and then energy-selected and separated from the electrons and unconverted photons in spectrometer D2 consisting of a pair of dipole magnets. The energy spread of positrons at the reconversion target T2 was 5% (FWHM). The positron flux (typically 2-6 1 4 /pulse with undulator on and 1% of this with undulator off) was monitored by Si-diode detector P1. The polarization of the positrons was determined by first reconverting them into polarized photons by a.5-radiation-length W disk, and then using transmission polarimeter TP1 to measure the longitudinal polarization of the photons. This polarimeter consisted of a 7.5-cm-long magnetized iron cylinder followed by a 3 3 array of CsI crystals. Data were collected with the undulator on and off during successive electron beam pulses. The sign of the magnetization of polarimeter TP1 (and that of TP2 as well) was reversed after every 15 undulator-on beam pulses; for cross checks beam-off and targetout runs were interspersed throughout the data sets. Data were taken with positrons at five energies from 4.6 to 7.4MeV, and with electrons at a single energy (6.7MeV) for which the current in dipole spectrometer D2 was reversed. Data samples for each energy ranged from 2-2 1 5 beam pulses and a total of more than 8 1 6 events were recorded during the experiment. The positron (or electron) polarization is derived from the asymmetry δ e ± = (S CsI S+ CsI )/(S CsI + S+ CsI ) (12) 15

of signals S ± CsI that are proportional to the (integrated) energies E± CsI of reconverted photons observed in the central CsI. The outer eight crystals of the CsI array were not used in the final analysis because of poorer signal to background ratio. The photon energies E ± CsI were corrected for background using the undulator-off data, and normalized to the beam current rates observed in the Si-diode detector P1. The asymmetry (12) was calculated for each pair of 15 undulator-on beam pulses with opposite magnetization of the polarimeter. The longitudinal polarization P e ± of the positrons (electrons) is deduced from the measured asymmetry δ e ± using the relation P e ± = δ e ± A e ±P Fe e, (13) where Pe Fe =.695±.21 is the longitudinal polarization of the atomic electrons in the iron cylinder, and A e ± is the analyzing power determined by numerical simulation. The latter was performed with an enhanced version of the Geant4 toolkit that included six new routines to deal with circularly polarized photon beams and longitudinally polarized electron beams (see also section 4). The relative systematic uncertainty on the analyzing power is estimated to be 7%. The longitudinal polarizations P e ± of electrons and positrons deduced using Equation (13) are shown together with simulations in Figure 8 as a function of particle energy. The shift between the curves arises because for photon energies that peak near E γ = 7.9MeV the maximum energy of a positron from pair production is E e + = E γ mc 2 7.4MeV, while electrons from Compton scattering and the photoelectric effect have maximum energies E C e E γ +mc 2 /2 8.2MeV and E PE e = E γ +mc 2 8.4MeV, respectively, where mc 2 = 511 kev is the rest energy of the electron. The uncertainties shown in the figure include both statistical and systematic effects. The results of this experiment are in agreement with Geant simulations that positron polarization of 8% is obtainable when GeV electrons pass through a helical undulator, producing MeV photons that are converted in a thin target. A Compton transmission polarimeter is appropriate to measure the polarization of the low energetic positron beam. 5.4 Compton transmission polarimeter at the ILC positron source The experiment E-166 demonstrated that the technique of undulator-based production of polarized positron works well. It can be scaled up to provide polarized positron beams for the next generation of linear colliders. The polarization of the positron beam near it s creation can be measured using a Compton transmission polarimeter. At the ILC positron source the best position to use a Compton transmission polarimeter would be after the capture section at E e + 35 MeV. But to maintain a high efficiency of positron production, the capture section is immediately followed by a pre accelerator; hence the first realistic possibility to place a Compton transmission polarimeter is after pre acceleration to E e + 125 MeV. At this energy the Compton transmission method 16

longitudinal polarization (%) 1 8 6 4 2 + e - e + expected e polarization - expected e polarization 3 4 5 6 7 8 (MeV) E e ± Figure 8: Longitudinal polarization P e ± as a function of energy E e ± of positrons and electrons as determined from the asymmetries observed in the central CsI crystal. The smaller error bars show the statistical uncertainty, and the larger bars indicate the statistical and systematic uncertainties combined in quadrature. Also shown are predictions by a Geant4 simulation of the experiment. is still usable, but thicknesses of the reconversion target and the magnetized iron have to be adjusted. However, if positrons of E e + 125 MeV hit the reconversion target mainly photons with energies larger 1MeV are produced. As illustrated in Figure 4, for these photons pair-production processes dominate in the magnetized iron and hence smaller asymmetries will be measured. Table 2 summarizes the parameters for the reconversion target and the iron absorber of a Compton transmission polarimeter for the ILC positron source. For the simulation of the polarization measurement at the ILC positron source a 2 radiation lengths thick tungsten reconversion target and an iron absorber of 7 radiation lengths have been assumed. Compton transmission polarimetry is destructive for the beam, so only few bunches can be used to monitor the polarization. Due to the high intensity at the ILC already few bunches per pulse will heat the target substantially. As illustrated in Figure 9 a tungsten reconversion target hitted by 2 bunches per pulse would be heated up to 115K if no cooling is applied; 1 bunch per pulse will yield 545K. To perform the measurement with few bunches selected from the pulses a fast kicker is needed accomplished by an additional bend to compensate the spin rotation by the kicker. In principle, one ILC bunch used for the polarization measurement provides similar statistics as was evaluable in the E-166 experiment for one energy point. Hence, the measurement is not limited by statistics but by the energy deposition in the reconversion target, in the iron absorber and in the calorimeter: The measured bunches are dumped into these polarimeter components (see also Table 2). Finally it should be remarked that helicity related uncertainties can only be reduced 17

Positron beam energy material thickness E dep per e + [MeV] [X / mm] [MeV/1e + ] Target 35 W 1 / 3.5 13.7 Absorber Fe 17.6 / 1 6.8 Target 35 W 2. / 7. 22.4 Absorber Fe 26.7 / 15 6.9 Target 125 W 2. / 7. 38.1 Absorber Fe 26.7 / 15 61.6 Table 2: Energy deposition per incident positron in the reconversion target and the absorber for different positron energies and material thicknesses. by fast spin reversals. For the undulator-based source such a system is not foreseen at 125 MeV and it would demand significant effort to realize it. But for routine checks of positron polarization at the source the uncertainty reached with a simple design should be sufficient. 6 Bhabha polarimeter for the ILC positron source As mentioned in section 1, also Bhabha scattering is well suited to measure the beam polarization at the ILC positron source. The differential cross section for Bhabha scattering of longitudinal polarized beams may be written in the center-of-mass system as dσ dω = r2 (1 + cosθ ) 2 16γ 2 sin 4 θ { (9 + 6 cos 2 θ + cos 4 θ ) P e +P e (7 6 cos 2 θ cos 4 θ ) }, (14) where θ is the polar angle in the center-of-mass system. Mass effects have been neglected. Only if both incoming particles are longitudinally polarized, an asymmetry can be measured by reversing the polarization. In Bhabha polarimetry the electron polarization is flipped by choosing opposite magnetizations of the analyzing iron foil: A = σ(p e ) σ( P e ) σ(p e ) + σ( P e ) (15) An asymmetry A up to 7/9P e +P e can be obtained at scattering angles near to π/2, if both, electrons and positrons, are 1% polarized. In a Bhabha polarimeter a positron beam with polarization P e + < 1 hits electrons in a magnetized iron foil (polarization P e 7%). Figure 1 shows the asymmetries A as function of the scattering angle in the Lab and c.m.s. system for two different choices of polarizations. These asymmetries are related to that reached with 1% polarized 18

T [K] 11 1 9 8 7 6 5 4 3 2 4 6 8 1 12 14 16 time [s] Figure 9: Heating of the tungsten reconversion target (2X ) assuming positrons with an energy of 125 MeV and no additional cooling. The numbers of bunches per pulse hitting the target are 2 (upper curve) and 1 (lower curve). beams by A 1 = A(P e + = 1, P e = 1) = A(P e +, P e ) P e + P e. (16) 6.1 Kinematics For a single Bhabha (or Møller) scattering event the polar angle and kinetic energy of the final state are related. In the Lab system, the outgoing particle carries a kinetic energy fraction ǫ and is scattered with angle θ, ǫ = 2 cos 2 θ (γ 1) sin 2 θ + 2 sin 2 θ = 2(1 ǫ) ǫ(γ 1) + 2. (17) The corresponding scattering angle in the CMS frame, θ, is sin 2 θ = 4ǫ(1 ǫ), (18) yielding θ = π/2 for ǫ = 1/2. Following Figure 1, with electrons or positrons scattered into a certain angular and energy range a high sensitivity to the polarization of the initial beams is reached. In first studies of [44, 45], the energy and angular distribution for the scattered electrons and positrons was considered for the Bhabha and background processes. Main source of background is Bremsstrahlung. It turns out that for positron energies of few tens MeV the signal-background separation is less significant than for energies of few hundred MeV 19

Asymmetry (CMS).5.4 P beam P target =.8.7 Asymmetry (LAB).5.4 P beam P target =.8.7.3.3.2.2.1 P beam P target =.6.7.1 P beam P target =.6.7-1 -.8 -.6 -.4 -.2.2.4.6.8 1 cos θ*.2.4.6.8.1.12.14 θ [rad] Figure 1: Angular dependence of the asymmetry in Bhabha polarimetry for different positron beam and target polarizations for E beam = 4 MeV. Left: Asymmetries in cms system. Right: Asymmetries in Lab system. and higher. Hence, a Bhabha polarimeter located after the pre accelerator working at energies of 4 MeV is an option to measure the positron polarization at the source and is considered in detail. Potential problems are heating of the target foil due to passage of intense positron beam and multiple scattering in the target foil resulting in large emittance growth of the positron beam. The target is tilted at an angle 21 and placed into a magnetic field in order to get a longitudinal polarization component. The polarization along the beam direction is about 7%. 6.2 Target Heating A challenge will be the iron target: the intense positron beam must not destroy the foil. In that particular case the large transverse size of the positron beam helps: The temperature at the target can be kept within reasonable limits. The evolution of the target temperature is shown in Figures 11 and 12 assuming a Gaussian beam profile with σ = 1 cm, N e + = 2 1 1 particles per bunch and an energy of 4MeV. The target is assumed to be tilted to 21. A heating of 15 K per pulse is obtained. Assuming a cooling by radiation the peak temperature in the equilibrium is 5 K taking into account all bunches and a pulse repetition rate of 5Hz. To obtain a high polarization of the electrons the target has to be magnetized; target heating would reduce the polarization as shown in Figure 13. For an easy measurement procedure it is desired to use the full beam and keeping the average target temperature 2

38 T [K] T [K] 4 35 3 25 36 34 32 3 28 2 8 6 4 2 y [cm] -2-4 -6-8 -8-6 -4-2 2 x [cm] 4 6 8 26 24 22 2 Figure 11: Peak temperature of a 3µm tilted (21 ) iron foil in a Bhabha polarimeter. well below the critical temperature of T c = 143 K. This temperature limit will be easily exceeded if an intense beam with a small diameter hits the target. But the large positron beam size and radiation cooling between the pulses ensures a stable working temperature of about 5 K for a target perpendicular to the beam [48, 49] or correspondingly 4 K for a tilted target (21 ). This target temperature lowers the polarization of the electrons in iron; in the equilibrium it is reduced to approximately 97% for the tilted and 93% for the perpendicular target (compare with Figure 13). The polarization of the electrons in the iron foil is only slihtly reduced P e =.97.7. The temperature variation within a pulse yields can be neglected for the required accuracy of the polarization measurement. The heated target will expand and due to gravitation the tilt yields a sagging of the foil in the heated area. The beam positrons have to pass a foil of different effective thickness leading to an additional uncertainty in the polarization measurement. A rough estimate taking into account a linear thermal expansion coefficient of α = 12.2 1 6 K 1, the expansion of the target foil is about.3%. This can be neglected for the given precision requirements. It should be remarked that in case of a recently discussed minimal machine the number of positron bunches per pulse will be reduced by a factor two what reduces the heat load in the Bhabha target. 6.3 Target magnetization The electrons in the iron foil have to be longitudinally oriented to achieve a high counting rate (see Equation (14). There are two possibilities to realize this: either a target is mounted perpendicular to the beam, but this requires a strong magnetic field (few T) to magnetize the iron. Or, a target tilted by 21 with respect to the beam direction is 21

T [K] 4 38 36 34 32 3 28 5 1 15 2 25 3 35 4 45 time [s] Figure 12: Time dependence of peak temperature of a 3µm tilted (21 ) iron foil in a Bhabha polarimeter. used and magnetized with Helmholtz coils. The tilt reduces the effective longitudinal polarization in the iron, P eff e = cos 21 P e and increases the effective thickness of the target foil, d eff = d/ sin21. 6.4 Multiple scattering in the target The Coulomb scattering distribution is roughly Gaussian for small deflection angles. The width of this distribution is approximately given by [5] 13.6 MeV θ = z ] x/x [11 +.38 ln(x/x ) (19) βcp where p, βc and z are momentum, velocity, and charge number of the beam particle, x is the foil thickness, and X is the radiation length. For iron the radiation length is [51, 52] X Fe = 1.76 cm. (2) For electrons and positrons with momentum 4 MeV, and an effective foil thickness of d eff = d/ sin 21 56µm (d = 2µm) the mean scattering angle is θ = 1.5 mrad (21) This can be compared with the intrinsic beam spread. For a normalized emittance of ǫ = 3.6cm mrad [3] and transverse beam size σ x,y = 1 cm (σ x,y =.5 cm), the angular divergence is given by θ x,y = ǫ γσ x,y = 4.6 mrad (9.2 mrad) (22) 22

M(T)/M() 1.8.6.4.2.2.4.6.8 1 T/T c Figure 13: Magnetization of iron depending on the temperature (see [46, 47]). corresponding to an emittance increase of 5.2% (1.3%). 6.5 Signal and background studies Simulations of distributions of scattered electrons, positrons and photons and the resulting asymmetries have been performed using the polarized Geant4. The positron beam parameters used for the simulation are: beam energy 4MeV 1 8 positron beam particles per target polarization angular spread of.5deg energy spread of 1% target material 2 µm iron foil target electron polarization ±1% positron beam polarization 1% To derive realistic results beam and target polarization and number of particles have to be scaled. Observables are the particle distributions after the scattering process, in the energy scattering angle plane, (E, θ), for different target polarizations, +P e and P e, 23

EUROTeV-Report-28-91 number of scattered electrons and positrons, asymmetry of electrons and positrons, significance distribution for electrons and positrons. The significance is defined as S= A N N A 2 + s N + N+ (N + 1)(N + + 1) (23) Number E [MeV] where N and N + are the numbers of particles in the bin for different polarities, + and. Figures 14 16 show the results of simulating Bhabha scattering of the positron beam in a magnetized iron foil: depicted are the distributions of scattered electrons and positrons for opposite magnetizations of the iron target, the corresponding asymmetries and their significances. In the left plot of Figure 14 the separation of the different particle types by energy and scattering angle is visible. Particles scattered into the angular range 3 mrad < θ < 1 mrad can be well separated and have only minor photon background. Asymmetries and their significances are shown in Figure 15 for the electrons and in Figure 16 for the positrons. The significance considered immediately after the target is slightly higher for scattered electrons than for positrons, but in principle both, electrons and positrons, can be used for measurements. Since no high precision measurement is necessary, it should be sufficient to analyze only the scattered electrons of the Bhabha process. The electrons scattered into the sensitive angular and energy range have to be lead into a detector with an adequate polarimeter layout. 3 5 1 25 2 14 15 13 1 5 12.4.6.8.1.12.14 θ [rad] 5 1 15 2 25 3 35 4 E [MeV] Figure 14: Energy and angular distributions of positrons (red), electrons (blue and cyan for opposite polarizations) and photons (green) after scattering positrons on a 3 µm thick iron foil assuming realistic beam parameters and 1% positron and electron polarization. Only particles with θ >.25 rad were considered. 24

Number 12 1 8 6 4 E [MeV] 4 35 3 25 2 15 1.8.6.4.2 -.2 -.4 E [MeV] 4 35 3 25 2 15 8 6 4 2 2 1 5 -.6 -.8 1 5 5 1 15 2 25 3 35 4 E [MeV].5.1.15.2.25.3 θ [rad] -1.5.1.15.2.25.3 θ [rad] Figure 15: Electron distributions after scattering polarized positron on a 3 µm thick iron foil assuming realistic beam parameters and 1% positron and electron polarization. Left: Electron distribution for positve and negative target polarization for.5 rad< θ <.9 rad. Middle: Asymmetry determined with scattered electrons. Right: Significance distribution. Number 8 7 6 E [MeV] 4 35 3 1.8.6.4 E [MeV] 4 35 3 5 4 5 25.2 25 3 4 3 2 2 15 1 -.2 -.4 -.6 2 15 1 2 1 1 5 -.8 5 5 1 15 2 25 3 35 4 E [MeV].5.1.15.2.25.3 θ [rad] -1.5.1.15.2.25.3 θ [rad] Figure 16: Positron distributions after scattering polarized positron on a 3 µm thick iron foil assuming realistic beam parameters and 1% positron and electron polarization. Left: Positron distribution for positive and negative target polarization for.5 rad< θ <.9 rad. Middle: Asymmetry determined with scattered positrons. Right: Significance distribution. 6.6 Layout of the Bhabha polarimeter Thanks to the large beam size at the positron source the Bhabha polarimeter can be designed with a target foil placed in the beamline over a longer period of alignment and/or polarization measurement. The schematic of a Bhabha polarimeter is presented in Figure 17. The positron beam passes the tilted target foil which is magnetized using Helmholtz coils. The scattered Bhabha electrons pass a.5mm thick stainless steel window. This window together with mask behind the window allow a selection of the relevant angular region for the scattered particles. With a spectrometer magnet the scattered electrons can be separated from positrons and by energy. The detector for the electrons is placed about 6.2 m behind the target, 1 m behind the spectrometer. The detector has not yet been specified but a charge sensitive detector material with 2 cm 2 cm pads has been assumed for the studies. For the studies a large detector plane was assumed to obtain signals and background and to find the sensitive area for the under realistic conditions. 25

Figure 17: Schematic for a Bhabha polarimeter layout. The spectrometer magnet is sketched in Figure 18, it s specifications used for the simulations are Bdl =.1Tm, gap: 2 cm, B gap =.5 T, length in z direction: 2cm, thickness of yoke: 7.7 cm, coil: about 8kA turns in total, corresponding to 2 1 turns with 4A each, conductor: 8 8mm 2 copper with 3mm water channels for cooling 3, cm 1, cm 15, cm 7,5 cm 14,2 cm 25, cm 7,5 cm Figure 18: Schematic for a spectrometer magnet, shown is one quadrant. 26