Positron Capture Optimization Using AMD Field and RF Structure Length

Positron capture optimization: AMD field and RF structure length Positron capture optimization: AMD field and RF structure length V. Mytrochenko1,3 , F. Alharthi1, A. Bacci2, E. Bulyak3, I. Chaikovska1, R. Chehab1, M. Rossetti2 1Universit Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France 2INFN, Milano, Lombardia, Italia 3NSC KIPT, Kharkiv, 61108, Ukraine mytrochenko@ijclab.in2p3.fr 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Outline Outline Introduction: FCC ee positron capture linac Version 0 consisting of HTS coils as a matching device and the five 3- meter-long 9/10 large aperture L-band accelerating sections. Tasks of this study. Simulation technique. Results and discussion. Conclusion. 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Introduction Introduction Version 0 of a FCC ee capture linac (CL) with five 2 GHz 3-meter-long 9/10 sections Usage of high temperature superconducting coils as a matching device make it possible to keep constant aperture with diameter of 60 mm along the linac starting from the target. It provide high positron yield (at least 9) at the linac exit. It is unclear now how much of these positrons can be accepted into 1.5 GeV damping ring. We suggest that longitudinal acceptance would be 1.54 3.8% GeV of energy spread ( 59 MeV) and 16.7 mm of longitudinal spread. Version 0 of CL (from CHART Scientific Report 2022) Great work was done to establish Version 0 configuration 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Tasks of this study Tasks of this study Version 0 of FCC ee positron CL is hardware based. The aim of this work was to find features of a bunch formation in a positron CL that is less hardware-based and consisting of an AMD with theoretical field and 2 GHz large aperture 9/10 section (or sections). At simulations, the field drop rate of the matching device, as well as the RF field phase and accelerating section length were varied to find better configuration. 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Simulation technique Tracking of particles from positron generating target through positron accelerator were performed with the Astra (A Space Charge Tracking Algorithm) program package. Initial positron distribution at the exit of the target was obtained with GEANT4 (We use the same distribution that was used at Version 0 simulation). Parameters of positron beam at the target exit are listed below. To study influence of the field drop rate of the AMD on beam performances, axial on-axis magnetic field was represented in a form of superposition of the AMD field, and constant solenoidal field: ?0 1 + ??+ ???? The study was carried out in several stages. At the first B0 = 12 T and Bsol = 0.5 T were fixed to investigate influence of the in the range of 10 m-1 to 60 m-1 on beam performances. Initial positron beam parameters Parameter Positron yield Beam sizes x, y rms emission time t Average kinetic energy Energy spread Transverse beam emittances b. The 9/10 section of variable number of cells from 28 through 112 including the two couplers was placed downstream the target. Influence of accelerating section length was studied. Two options of CL layout were considered. a. The 9/10 section containing 60 cells and two couplers was placed downstream the target. Influence of the field drop rate of the matching device, as well as the RF field phase on beam parameters was studied. Then, the CL with four such accelerating sections was considered. ??? = Value 13.6 1.3 4.4 50.54 123 1.9 104 Units ne+/ne- mm ps MeV MeV mm mrad 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Simulation technique Simulation technique Normalized brightness was used as figure of merit at the first section exit: ?? ???= ?? . Then, after promising solution was found 2? ?? ? ??? ?? ? ???, 2? simple formula was used to bring particle energy up to damping ring energy to estimate accepted yield. ???= W + 1.54 ?0cos + 2 z ?0 In most cases we carried out 2D scanning of following parameters to find the best solution: AMD field drop rate; RF phase; accelerating section length. Acceleration gradient was in most cases of 16 MeV/m. It is some lower than that for Version 0. For section length up to 74 cells simulations were performed also for 8 MeV/m and 12 MeV/m. To variate more parameters, we are trying to use a Giotto algorithm. The work is in progress. Some preliminary results have been obtained that will be reported later. It is necessary to note that with the Giotto algorithm more physical magnetic field distribution was used: AMD field in the region where it is higher than constant solenoid field and constant solenoid field downstream that region. 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Results Results We simulate 60-cell long section in auto phase mode to get maximum acceleration. At slow field drop more positrons are collected but phase length of the bunch is larger because of bunch lengthening. It should be noted that the transverse emittance is lower with greater particle loss. The dependence of the brightness on the field phase has two ridges that grow with increasing . The highest peak corresponds to acceleration of the initial bunch tail and the other one to acceleration the head of the bunch. Analysis of the particle dynamics showed that at the maximum brightness the first RF bucket contains 99% of the particles. Field drop rate actually For four 60-cell-long sections. W/W = 1.0%, Z = 2.7 mm, Yield= 8.0 Normalized brightness vs and field phase Total positron yield and bunch phase length vs 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Results Results To show how accelerating section length influences beam bunching scan of RF field phase for the sections containing different number of cells was carried out at =60 m-1. Dependence has two ridges structure. The ridges correspond to the acceleration of the head or the tail of the initial positron longitudinal distribution. The last one provides a higher positron yield for the long structures. Although the figure does not show an optimal section length, calculations have indicated a decrease in acceptable yield after a length of 100 cells. Accepted yield is 8.3, 1 W/W is 1.0% and 1 Z = 2.48 mm. for 100 cells. Evolution of positron longitudinal phase space along the linac with 112-cell accelerating section. Actual distance between adjacent distributions is 1 m. The distributions artifactually shifted back and placed with period of a halve of wavelength. . RF phase is set to accelerate a tail of the initial bunch, so phase space is rotating along the linac that lead to short bunch formation. 4/16/2025

Comparison Comparison So far the best results is presented below with comparison with Version 0 parameters. The best means that without knowing damping ring acceptance we can not say for sure what really is the best. Parameter Maximum accelerating gradient Mean energy at DR entrance 1 W/W at DR entrance 1 Z at DR entrance Accepted positron yield n rms x,y One 100-cell-long structure was replaced with two 50-cell-long structure that were acting as one. There were only minor changes in beam performances (accepted yield drops to 8.0) maybe because of two additional couplers involved. Comparison with results for lower field amplitudes shows that brightness just increasing with field increase. To provide high accepted yield it is necessary apply strong bunching keeping almost all particles in the first RF bucket. Essential here is configuration of magnetic field between the positron producing target and an accelerating section. For example, changing magnetic field distribution from superposition of AMD and solenoid field to AMD field in the region where it is higher than constant solenoid field and constant solenoid field downstream that region causes only slight change of beam parameters (yield drops from 8.3 to 8.0). But substituting to that layout field map from Version 0 changes beam parameters drastically. Particles spread over several RF buckets, accepted yield drops almost to Version 0 yield. This study 16 1.54 1.0 2.5(6.0) 8.3 13 FCC-ee V0 Units MeV/m GeV 20 1.54 1.6 % mm ( ) ne+/ne- mm rad 3.0(7.2) 6.6 13 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Conclusion Conclusion AMD field drop rate, as well as the RF field phase and accelerating section length can be optimized to provide short bunch formation withing one RF bucket with accepted positron yield of 8.3. The feasibility of the magnetic field distribution obtained need to be checked. It is necessary to stress that configuration of magnetic field between the positron producing target and an accelerating section is essential for short bunch formation. It seems the 5D normalized brightness is useful parameter to optimize linac settings especially for the few first sections. There are two picks in beam normalized brightness dependence on a field phase of the first accelerating section, which correspond to acceleration the head or the tail of the initial longitudinal distribution. The last one provide higher positron yield. We hope that Giotto can help in further optimization of the capture linac. 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN

Thank you for your attention 4/16/2025 The FCC-ee Pre-Injector: CHART collaboration meeting, INFN