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Simulation of Particle Distribution and Emittance Growth in Charged Particle Beams

This report presents a simulation approach by Alexander Molodozhentsev for studying charged particle distribution and emittance growth in a particle beam. Key parameters include transverse and longitudinal distributions with various initial conditions, such as Binomial and Gaussian distributions. A notable feature is the estimation of incoherent tune shifts and their effects on beam dynamics. The simulation results highlight the behavior of RMS emittance and its variation over multiple turns, providing insights into the underlying causes of emittance growth, particularly due to the influence of chromatic sextupoles and space charge effects.

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Simulation of Particle Distribution and Emittance Growth in Charged Particle Beams

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  1. MR: Space chargedifferent particle distribution& working points Alexander Molodozhentsev for MR-Group June 21, 2006

  2. Simulation approach… Qx = 22.42 / Qy = 20.82 … for some reason (not clear yet) Number of macroparticles = 15104 Transverse bin points = 128128 CPU_time/turn ~ 130 sec Single processor Longitudinal bin points = 128 Number of kicks per element = 2 Space Charge - ON Initial: Binomial Transverse distribution Uniform Longitudinal distribution RF - ON Chromatic Sextupoles - ON

  3. What… • (1) • Initial (transverse) particle distribution to provide reasonable / practical • Incoherent tune shift…

  4. Estimation of Incoherent tune shift Bunching-factor Form-factor Form_Factor=1(NO chamber) or 2 (image coefficients) Distribution_Factor=1(Uniform)_1.56…2(Gaussian) … as a function of Bunching_Factor Distribution-factor Beam from RCS: QINC ~ -0.15 Bf ~ 0.33

  5. Initial transverse distributions (#1.3) Footprint without walls Uniform MJoho=1, RMS=100%/2(MJoho+1) Qx0 = 22.42 Qy0 = 20.82 RMS = 54/4 = 13.5 xMAX = (4)1/2RMS

  6. Initial transverse distributions (#2.3) Footprint without walls Binomial - Parabolic MJoho=2, RMS=100%/2(MJoho+1) Qx0 = 22.42 Qy0 = 20.82 RMS = 54/6 = 9 xMAX = (6)1/2RMS

  7. Initial transverse distributions (#3.3) Footprint without walls Binomial - Gaussian MJoho=3, RMS=100%/2(MJoho+1) Qx0 = 22.42 Qy0 = 20.82 RMS = 54/8 = 6.75 xMAX = (8)1/2RMS

  8. X-Y plane: Initial particle distribution MJoho=2 MJoho=1 MJoho=3

  9. RMS and 99% emittance MJoho=2, RMS=100%/2(MJoho+1) Binomial - Parabolic RMS = 54/6 = 9 Qx0 = 22.42 Qy0 = 20.82 xMAX = (6)1/2RMS 600 turns

  10. RMS emittance variation during 10 turns MJoho=2, RMS=100%/2(MJoho+1) Binomial - Parabolic RMS = 54/6 = 9 Qx0 = 22.42 Qy0 = 20.82 xMAX = (6)1/2RMS Initial RMS-Emittance RMS,X = 9.0023 RMS,Y = 9.0017

  11. 99% emittance: Gaussian & Parabolic Qx = 22.42 / Qy = 20.82

  12. Emittance variation Qx = 22.42 / Qy = 20.82 TD: Binomial - Parabolic 1000 turns

  13. What is going on here? What is the source for the emittance growth?

  14. Wp3: Qx=22.42, Qy=20.82 What is going on here? What is the source for the emittance growth? “testHerd” which feels “mainHerd” 300 turns X0 = 5, 10, 15, 20, 25 mm X0/ = Y0 = Y0/ = 0 NO Coupling.

  15. Wp3: Qx=22.42, Qy=20.82 What is going on here? What is the source for the emittance growth? “TAIL” particles “testHerd” which feels “mainHerd” 300 turns X0 = 20, 22, 24, 26, 28 mm X0/ = 0 Y0 = 23, 25, 27, 29, 30 mm Y0/ = 0 Coupling…Sources: CCSX & SpCh

  16. Wp3: Qx=22.42, Qy=20.82 What is going on here? What is the source for the emittance growth? “testHerd” which does NOT feel “mainHerd” Effect of Chromatic Sextupole Field… [4,0] 300 turns X0 = 20, 22, 24, 26, 28 mm X0/ = 0 Y0 = 23, 25, 27, 29, 30 mm Y0/ = 0 Coupling…Sources: CCSX !!!

  17. ATAC’2 meeting, March 7, 2003 Beam survival:scanning of QX: 22.20…22.50 COSY Infinity

  18. ATAC’2 meeting, March 7, 2003 Betatron tune-shift budget

  19. Wp3: Qx=22.42, Qy=20.82 What is going on here? What is the source for the emittance growth? Resonance region for the 54  mm.mrad particles TAIL CORE 4Qx = 90 Structure resonance

  20. What is going on here? What is the source for the emittance growth? “testHerd” which does NOT feel “mainHerd” Effect of Chromatic Sextupole Field… 300 turns X0 = 20, 22, 24, 26, 28 mm X0/ = 0 Y0 = 23, 25, 27, 29, 30 mm Y0/ = 0 Wp3: Qx=22.333, Qy=20.774

  21. What is going on here? What is the source for the emittance growth? “testHerd” which feels “mainHerd” Effect of Sextupole Field & SpaceCharge 300 turns X0 = 20, 22, 24, 26, 28 mm X0/ = 0 Y0 = 23, 25, 27, 29, 30 mm Y0/ = 0 Wp3: Qx=22.333, Qy=20.774

  22. What is going on here? What is the source for the emittance growth? “testHerd” which feels “mainHerd” Effect of Sextupole Field & SpaceCharge Initial conditions for the Test_Particle are NOT changed !!! 300…600 turns X0 = 20, 22, 24, 26, 28 mm X0/ = 0 Y0 = 23, 25, 27, 29, 30 mm Y0/ = 0 Wp3: Qx=22.333, Qy=20.774

  23. What is going on here? What is the source for the emittance growth? “testHerd” which feels “mainHerd” Effect of Sextupole Field & SpaceCharge Initial conditions for the Test_Particle are NOT changed !!! 600…1000 turns X0 = 20, 22, 24, 26, 28 mm X0/ = 0 Y0 = 23, 25, 27, 29, 30 mm Y0/ = 0 Wp3: Qx=22.333, Qy=20.774

  24. RMS_emittance behavior w2: Qx = 22.333 Qy = 20.774 w3: Qx = 22.42 Qy = 20.82

  25. 99% emittance behavior w2: Qx = 22.333 Qy = 20.774 w3: Qx = 22.42 Qy = 20.82

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