muon colliders ‘2004 14 december 2004 optimization of adiabatic buncher and phase rotator for muon...
Post on 19-Dec-2015
214 views
TRANSCRIPT
14 December 2004 Muon Colliders ‘2004
Optimization of adiabatic buncher and phase rotator for Muon Accelerators
A.Poklonskiy (SPbSU, MSU), D.Neuffer (FNAL)C.Johnstone (FNAL), M.Berz (MSU), K.Makino
(MSU)
14 December 2004 Muon Colliders ‘2004
Adiabatic buncher + () Rotator (David Neuffer)
• Drift (90m) decay, beam develops correlation
• Buncher (60m) (~333Mhz200MHz, 04.8MV/m) – Forms beam into string of bunches
Rotator (~12m) (~200MHz, 10 MV/m)– Lines bunches into equal energies
• Cooler (~50m long) (~200 MHz)– Fixed frequency transverse cooling system
Replaces Induction Linacs with medium-frequency RF (~200MHz)
14 December 2004 Muon Colliders ‘2004
Longitudinal Motion (2D simulations)
Drift Buncher
(E) rotator Cooler
System would capture both signs (+, -)
14 December 2004 Muon Colliders ‘2004
Adiabatic Buncher overview
• Array of RF cavities• Fix RF frequency at the
end to 200 Mhz 1.5m, desired central energy and total length of the buncher
• RF phase is set to be 0 for reference energy through all buncher
• Find the condition for particles velocities to pass last RF in 0 phase (no energy change) and set frequencies in all RFs in buncher to maintain this condition
Example: rf : 0.901.5m
RF
L
14 December 2004 Muon Colliders ‘2004
Adiabatic Buncher overview
• Adiabatically increase RF gradient:
mMVzL
zz
L
zzC
L
zzBzE
D
DDDRF /8.4)( 2
2
2
2
01.0
150
5.1111
1 Lc
nTn n
cn
,111
1
)( LLRF
cnnT
vvLttt RF
RFc
c
11 n,
14 December 2004 Muon Colliders ‘2004
Rotator overview
• At end of buncher, change RF to decelerate high-energy bunches, accelerate low energy bunches, i.e. rotation in phase space
• With central reference particle at 0 phase, set rf a bit less than bunch spacing (increase RF frequency)
• Places low/high energy bunches at accelerating/decelerating phases
• Change frequency along channel to maintain phasing
Example: rf : 1.4851.517m;
14 December 2004 Muon Colliders ‘2004
Rotator overview
• At end of buncher, choose:– Second reference particle TN– Vernier offset
• Example:– T0 = 125 MeV – Choose N= 10, =0.1– T10 starts at 77.28 MeV
• Along rotator, keep second ref particle at (N + ) rf spacing 10 = 36° at =0.1– Bunch centroids change:
• Use Erf = 10MV/m; L=8.74m– High gradient not needed– Bunches rotate to ~equal
energies.
RRFR zEeTzT )sin()0()( 101010 Example: rf : 1.4851.517m;
14 December 2004 Muon Colliders ‘2004
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
14 December 2004 Muon Colliders ‘2004
Central Energies Optimization Approach
• This is how rotator could look like in reality• This is “transit time factor” (percent of the acceleration from
maximum which particle could gain in changing E field):
g – length of the cavity,
w – cyclic frequency,
v – particle’s velocity
For 1. We can use kick approximation for the particle energy gain
2. We “forget” about the influence of cavity phases and gradients on all beam particles dynamics (could be added lately)
Study dynamics of the central particles of the bunches separately: T_final = T(n,…)
2
2sin
...d
v
dv
FTT
97.0...86.0...333...200,1000...50 FTTMhzMeVT
14 December 2004 Muon Colliders ‘2004
Centroids Kinetic Energies
• From buncher synchronism condition one could derive following relation for kinetic energies of central particles:
nTn n
cn
,111
1
111
1)1,,(
20
cc
c
cc
n
WnT
Puts limits on n_min and n_max => n_bunches!
14 December 2004 Muon Colliders ‘2004
Final Centroids Kinetic Energy
– From the rotator concept one could derive amount of energy gained by n-th synchronous particle in each RF (kept const by changing frequency)
or, more generally
– So for final energy n-th bunch central particle has after the ROTATOR consists of m RFs we have
12
121 2sin),,,,(
nn
nnEnnEnT RFRF
)()(,...),( nTmnTmnT
)2sin(),,,(N
nENEnT RFRF
14 December 2004 Muon Colliders ‘2004
Energies shape in buncher and amount of kick they get in rotator
14 December 2004 Muon Colliders ‘2004
Objective Functions
– The idea of the whole structure is to reduce overall beam energy spread and to put particles energies around some central energy. So we have general objective function:
2)),(( cn TmnTcI
14 December 2004 Muon Colliders ‘2004
Objective function 1
– First, we can set and getnCn ,1
21 ),...),(( cTmnTI
14 December 2004 Muon Colliders ‘2004
Different optimized paremters (n vs T_fin), COSY built-in optimizer
14 December 2004 Muon Colliders ‘2004
Different optimized paremters (T_0 vs T_fin), COSY built-in optimizer
14 December 2004 Muon Colliders ‘2004
Objective Function 2
– As we can use particle’s energies distribution in a beam
22 )),(( cn TmnTcI
nc
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 …
14 December 2004 Muon Colliders ‘2004
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) = 200000000.0000000Varied 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 ==>
10.00000000000000Objective 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
14 December 2004 Muon Colliders ‘2004
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) = 200000000.0000000Varied 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 ==>
10.00000000000000Objective 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
14 December 2004 Muon Colliders ‘2004
Other possible objective functions
• We may try to incorporate information about buckets widths and lengths
• We may combine this objective function with any of the first two with any weight coefficients
14 December 2004 Muon Colliders ‘2004
Other Optimization (OBJ1) (asked by David), whole domain searchFixed 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) = 100000000.0000000Varied 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 ==>
10.00000000000000Objective 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
14 December 2004 Muon Colliders ‘2004
Other Optimization (OBJ2) (asked by David), whole domain searchFixed 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) = 100000000.0000000Varied 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 ==>
10.00000000000000Objective 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
14 December 2004 Muon Colliders ‘2004
Summary
Model of central energies shape optimization for buncher and phase rotator is proposed.
Ready-to-use program is written, 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). We can search for optimal parameters values in any desired range and check some previously chosen params for optimality. (It could take long… )
Some example results are presented
14 December 2004 Muon Colliders ‘2004
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
2
1
s
s v
dst