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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
E N D
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 LD • Buncher • Length LB • RF Gradients EB • Final RF frequency RF (LD, LB, RF: (LD + LB) (1/) = RF) • Phase Rotator • Length LR • Vernier offset, spacing NR, V • RF gradients ER
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!
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
Energies Shape after Buncher and Amount of Energy Gain they Get in Rotator
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:
Objective function 1 • First, we can set and get
Different optimized paremters (n vs T_fin), COSY built-in optimizer
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 • …
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
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
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 (?)
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
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
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
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
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
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