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)

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+ + + e

– e– + e + and/or

IIT NFMCC Meeting ‘06

Buncher and Rotator

Drift (Length LD ) Buncher (Length LB, RF Gradients EB, Final RF frequency

RF) Phase Rotator ( Length LR, Vernier offset, spacing NR, V,

RF gradients ER )

IIT NFMCC Meeting ‘06

Longitudinal Motion (2D simulations)

Drift Buncher

(E) rotator Cooler

System would capture both signs (+, -)

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:

1

111

1)1,,(

20

cc

c

cc

n

WnT

Puts limits on n_min and n_max => n_bunches!

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,…

12

121 2sin),,,,(

nn

nnEnnEnT RFRF

,...)(,...)(,...),( nTmnTmnT

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

21 ),...),(( cTmnTI

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 …

22 )),(( cn TmnTcI

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) =

200000000.0000000Varied 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 ==> 10.00000000000000Objective 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

-100

0

100

200

300

400

500

600

-5 0 5 10 15 20 25 30

T0 [

MeV

]

0

200

400

600

800

1000

1200

1400

-5 0 5 10 15 20 25 30

Num

ber

of

part

icle

s

n (number of reference particle from central T = 200 MeV)

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) =

200000000.0000000Varied 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 ==> 10.00000000000000Objective 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

-100

0

100

200

300

400

500

600

-5 0 5 10 15 20 25 30

T0 [

MeV

]

0

200

400

600

800

1000

1200

1400

-5 0 5 10 15 20 25 30

Num

ber

of

part

icle

s

n (number of reference particle from central T = 200 MeV)

IIT NFMCC Meeting ‘06

Palmer’s Baseline OptimizationREF 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

IIT NFMCC Meeting ‘06

Reference

IIT NFMCC Meeting ‘06

OBJ1 Optimized (?)

IIT NFMCC Meeting ‘06

OBJ2 (Optimized?)

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?