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Optimization of adiabatic buncher and phase rotator

Optimization of adiabatic buncher and phase rotator. A.Poklonskiy (SPbSU, MSU), D.Neuffer (FNAL) C.Johnstone (FNAL), M.Berz (MSU), K.Makino (MSU). Key Parameters. Drift Length L D Buncher Length L B RF Gradients E B

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Optimization of adiabatic buncher and phase rotator

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  1. Optimization of adiabatic buncher and phase rotator A.Poklonskiy (SPbSU, MSU), D.Neuffer (FNAL) C.Johnstone (FNAL), M.Berz (MSU), K.Makino (MSU)

  2. Key Parameters • Drift • Length LD • Buncher • Length LB • RF Gradients EB • Final RF frequency RF (LD, LB, RF: (LD + LB) (1/) = RF) • Phase Rotator • Length LR • Vernier offset, spacing NR, V • RF gradients ER

  3. Equations

  4. Central Kinetic Energies • From buncher synchronism condition we derive following relation for kinetic energies of central particles: Puts limits on n_min and n_max => n_bunches!

  5. Final Central Kinetic Energies • From the rotator concept one could derive amount of energy gained by n-th central particle in each RF (kept const in ROTATOR) or, more generally • So for final energy n-th central particle has after the ROTATOR with m RFs we have

  6. Energies Shape after Buncher and Amount of Energy Gain they Get in Rotator

  7. Evolution of Central Energies Shape

  8. Evolution of Central Energies Shape (projecton)

  9. Objective Functions • One of the purposes of the structure is to reduce overall beam energy spread and to put particles energies close to some central energy. It seems natural to use objective function:

  10. Objective function 1 • First, we can set and get

  11. Different optimized paremters (n vs T_fin), COSY built-in optimizer

  12. Objective Function 2 • As we can use particle’s energies distribution in a beam • n energy particles % • ---------------------------------------------- • -12 963.96 1023 17.050000 • -11 510.85 692 11.533333 • -10 374.64 537 8.950000 • -9 302.98 412 6.866667 • …

  13. Objective Function 2

  14. Modeled Optimization (OBJ1), whole domain search Fixed params: Desired central kinetic energy (T_c) = 125.0000000000000 T_0 in buncher (T_0) = 125.0000000000000 Drift+Buncher length (L_buncher) = 90.00000000000000 Final frequency (final_freq) = 200000000.0000000 Varied params: 1st lever particle (n1) : -4.000000000000000 ==> 1.000000000000000 2nd lever particle (n2) : -3.000000000000000 ==> 27.00000000000000 Vernier parameter (vernier) : 0.1000000000000000 ==> 0.3000000000000000 RF gradient (V_RF) : 1.000000000000000 ==> 10.00000000000000 Number of RFs in rotator (m) : 1.000000000000000 ==> 10.00000000000000 Objective functions: !! 188624.7593430086 ==> 7434.672341694457 = 181190.0870013142 21918840.88332907 ==> 1643615.384258914 = 20275225.49907015 215.4599659295154 ==> 238.7961711271633 = -23.33620519764796 31921138.21770231 ==> 15260635.43728683 = 16660502.78041548

  15. Modeled Optimization (OBJ2), whole domain search Fixed params: Desired central kinetic energy (T_c) = 125.0000000000000 T_0 in buncher (T_0) = 125.0000000000000 Drift+Buncher length (L_buncher) = 90.00000000000000 Final frequency (final_freq) = 200000000.0000000 Varied params: 1st lever particle (n1) : -7.000000000000000 ==> 1.000000000000000 2nd lever particle (n2) : -6.000000000000000 ==> 14.00000000000000 Vernier parameter (vernier) : 0.1000000000000000 ==> 0.4000000000000000 RF gradient (V_RF) : 1.000000000000000 ==> 10.00000000000000 Number of RFs in rotator (m) : 1.000000000000000 ==> 10.00000000000000 Objective functions: 552558.8685890788 ==> 331194.3462835634 = -221364.5223055154 !! 1120051685.347023 ==> 740898336.4248258 = -379153348.9221967 790.5115736637570 ==> 714.6396495910632 = -75.87192407269379 1614049125.098601 ==> 1105871829.498042 = -508177295.6005592

  16. Other possible objective functions • We may try to incorporate information about other particles (?) • We may combine this objective function with any of the first two with any weight coefficients (?)

  17. Other Optimization (OBJ1) (short structure), whole domain search Fixed params: Desired central kinetic energy (T_c) = 125.0000000000000 T_0 in buncher (T_0) = 125.0000000000000 Drift+Buncher length (L_buncher) = 75.00000000000000 Final frequency (final_freq) = 100000000.0000000 Varied params: 1st lever particle (n1) : -3.000000000000000 ==> 1.000000000000000 2nd lever particle (n2) : -2.000000000000000 ==> 4.000000000000000 Vernier parameter (vernier) : 0.1000000000000000 ==> 0.2000000000000000 RF gradient (V_RF) : 1.000000000000000 ==> 10.00000000000000 Number of RFs in rotator (m) : 1.000000000000000 ==> 10.00000000000000 Objective functions: !! 920802.1870498012 ==> 716144.2078318644 = -204657.9792179369 2906605812.448390 ==> 2289340374.907225 = -617265437.5411658 -1154.766872358291 ==> -1012.150761595708 = 142.6161107625823 2905272325.918894 ==> 2288315925.743026 = -616956400.1758685

  18. Other Optimization (OBJ2) (short structure), whole domain search Fixed params: Desired central kinetic energy (T_c) = 125.0000000000000 T_0 in buncher (T_0) = 125.0000000000000 Drift+Buncher length (L_buncher) = 75.00000000000000 Final frequency (final_freq) = 100000000.0000000 Varied params: 1st lever particle (n1) : -3.000000000000000 ==> 0.000000000000000 2nd lever particle (n2) : -2.000000000000000 ==> 5.000000000000000 Vernier parameter (vernier) : 0.1000000000000000 ==> 0.4000000000000000 RF gradient (V_RF) : 1.000000000000000 ==> 10.00000000000000 Number of RFs in rotator (m) : 1.000000000000000 ==> 10.00000000000000 Objective functions: 920802.1870498012 ==> 716325.0523539253 = -204477.1346958759 !! 2906605812.448390 ==> 2288276641.662843 = -618329170.7855473 -1154.766872358291 ==> -1015.263140233114 = 139.5037321251762 2905272325.918894 ==> 2287245882.418927 = -618026443.4999671

  19. Study 2a params (OBJ1) Fixed params: Desired central kinetic energy (T_c) = 200.0000000000000 T_0 in buncher (T_0) = 200.0000000000000 Drift+Buncher length (L_buncher) = 150.0000000000000 Final frequency (final_freq) = 200000000.0000000 Varied params: 1st lever particle (n1) : 0==> 3.000000000000000 2nd lever particle (n2) : 18==> 6.000000000000000 Vernier parameter (vernier) : 0.032==> 0.08 RF gradient (V_RF) : 8==> 9.000000000000000 Number of RFs in rotator (m) : 10 ==> 10.00000000000000 Objective functions: 619593.7642709546 ==> 522561.7532899606 = -97032.01098099403 !! 750907264.4334378 ==> 615875434.3135488 = -135031830.1198890 -1066.685941047459 ==> -869.7924497231580 = 196.8934913243012 749769445.5366095 ==> 615118895.4079534 = -134650550.1286561

  20. Study 2a params (OBJ2) Fixed params: Desired central kinetic energy (T_c) = 200.0000000000000 T_0 in buncher (T_0) = 200.0000000000000 Drift+Buncher length (L_buncher) = 150.0000000000000 Final frequency (final_freq) = 200000000.0000000 Varied params: 1st lever particle (n1) : 0==> 3.000000000000000 2nd lever particle (n2) : 18==> 6.000000000000000 Vernier parameter (vernier) : 0.032==> 0.07 RF gradient (V_RF) : 8==> 9.000000000000000 Number of RFs in rotator (m) : 10 ==> 10.00000000000000 Objective functions: 619593.7642709546 ==> 522561.7532899606 = -97032.01098099403 !! 750907264.4334378 ==> 615875434.3135488 = -135031830.1198890 -1066.685941047459 ==> -869.7924497231580 = 196.8934913243012 749769445.5366095 ==> 615118895.4079534 = -134650550.1286561

  21. Summary • Model of central energies shape optimization for buncher and phase rotator is proposed. • Code is written and debugged (hope so), It allows to perform optimization on any set of supported parameters (length of the buncher and rotator, final frequency, central energy, E field gradient, phases). • Some example results are presented

  22. To do • Check results in (t,E) space as more important (problem: energy is changing  ) • Different RF field waveform? • Check optimized parameters for the whole beam distribution (COSY, ICOOL?) Is it really better? • Switch to 3D-motion simulation and optimization

  23. Overall RFs Effect

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