1. IIT NFMCC Meeting ‘06 Recent Optimization Studies of Adiabatic Buncher and Phase Rotator A.Poklonskiy (SPbSU, MSU), D.Neuffer (FNAL) C.Johnstone (FNAL), M.Berz (MSU), K.Makino (MSU)

2. IIT NFMCC Meeting ‘06 R&D goal: “affordable” e,  -Factory Improve from baseline: Collection Induction Linac  “high-frequency” buncher Cooling Linear Cooling  Ring Coolers Acceleration RLA  “non-scaling FFAG”  +  e + + n  + e  –  e – + n e +  and/or

3. IIT NFMCC Meeting ‘06 Buncher and Rotator Drift (Length L D ) Buncher (Length L B, RF Gradients E B, Final RF frequency RF ) Phase Rotator ( Length L  R, Vernier offset, spacing N  R,  V, RF gradients E  R )

4. IIT NFMCC Meeting ‘06 Longitudinal Motion (2D simulations) DriftBuncher (  E) rotator Cooler System would capture both signs (  +,  - )    

5. IIT NFMCC Meeting ‘06 Calculating Final Kinetic Energy 1 Moving to (T,n) phase space to study motion of the central particles from the buncher concept we derive following relation: Puts limits on n_min and n_max => n_bunches!

6. IIT NFMCC Meeting ‘06 Calculating Final Kinetic Energy 2 From the rotator concept we derive amount of energy gained by n- th central particle in each RF (kept const in ROTATOR) So final energy n-th central particle has after the BUNCHER+ROTATOR is a function of n,m,…

7. IIT NFMCC Meeting ‘06 Objective functions Minimize the distances from desired central energy As weight 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 …

8. IIT NFMCC Meeting ‘06 Optimization with 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

9. IIT NFMCC Meeting ‘06 Optimization with 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

10. IIT NFMCC Meeting ‘06 Palmer’s Baseline Optimization REF T0 = 200 MeV n1 = 0 n2 = 18 Vernier = 0.032 V_RF = 12 n_RFs = 72 OBJ1 1st lever particle (n1) : ==> 2.000000000000000 2nd lever particle (n2) : ==> 10.00000000000000 Vernier parameter (vernier) : ==> 0.6000000000000000E-01 RF gradient (V_RF) : ==> 8.000000000000000 Number of RFs in rotator (m) : ==> 50.00000000000000 OBJ2 1st lever particle (n1) : ==> 5.000000000000000 2nd lever particle (n2) : ==> 6.000000000000000 Vernier parameter (vernier) : ==> 0.1000000000000000E-02 RF gradient (V_RF) : ==> 16.00000000000000 Number of RFs in rotator (m) : ==> 150.0000000000000

11. IIT NFMCC Meeting ‘06 Reference

12. IIT NFMCC Meeting ‘06 OBJ1 Optimized (?)

13. IIT NFMCC Meeting ‘06 OBJ2 (Optimized?)

14. IIT NFMCC Meeting ‘06 Status Optimization algorithm invented and implemented. Seems to work for central energies, although not everything is explored (more than one harmonics, more objective functions) Simulated optimized parameters in ICOOL (?), but it is not clear if optimization scheme is working for the whole beam or not?