compensation of transient beam-loading in clic main linac
DESCRIPTION
Compensation of Transient Beam-Loading in CLIC Main Linac. Alexej Grudiev, Oleksiy Kononenko CLIC Meeting, August 27, 2010. Contents. Introduction Calculation of unloaded/loaded voltage in AS Drive beam generation scheme Optimization of the pulse shape - using the reference pulse - PowerPoint PPT PresentationTRANSCRIPT
Compensation of Transient Beam-Loading in CLIC Main Linac
Alexej Grudiev, Oleksiy Kononenko
CLIC Meeting, August 27, 2010
Contents
• Introduction• Calculation of unloaded/loaded voltage in AS• Drive beam generation scheme• Optimization of the pulse shape
- using the reference pulse- direct energy spread minimization
• Conclusions and further steps
Motivation: Energy Spread Constraints
*CLIC-Note-764
*CLIC-Note-764
Motivation: Energy Spread Constraints
Energy Spread Minimization Scheme
Klystron (reference) pulse
Unloaded Voltage in AS- generate drive beam profile- include PETS bunch response (with/without reflections)- calculate unloaded voltage
Method 1. Minimize the differencewith the reference klystron pulse
Method 2. Minimize energy spread for the CLIC Pulse directly
Loaded Voltage in AS - calculate AS bunch response - calculate total beam loading voltage- add to unloaded voltage
Beam Loading: Steady State
0 0.05 0.1 0.15 0.2 0.250
2
4
6
8
10
12
14 x 107
z, m
G, V
/m Gloaded
Gunloaded
Gbeam
20
*Beam loading for arbitrary traveling wave accelerating structure. A. Lunin, V. Yakovlev
Unloaded Voltage in T24 structure
Considering T24 CLIC main accelerator structure
Z
Unloaded Voltage in AS (FD)
11.7 11.8 11.9 12 12.1 12.2 12.30
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 104
Frequency, GHz
Vol
tage
, V
abs(Vsync)
abs(Vasync)abs(Vtotal)
EUz (z,f) → [ exp ( ± i *z *ω/c ) ] → [ ∫ dz ] → VU (f)
0 50 100 150 200
-4000
-2000
0
2000
4000
6000
Time, ns
Vol
tage
, V
real(V(t))abs(V(t))
Unloaded Voltage in AS (TD)V(t) = ifft(V+(f))
Unloaded Voltage in AS for a Rectangular Pulse
0 50 100 150 200 250 300 350 400-3
-2
-1
0
1
2
3 x 107
real(Vunloaded)
abs(Vunloaded)Vp(t) = conv( V(t) , p(t) )
Beam Loading: Plane Wave Approach
Thanks for the idea to Valery Dolgashev (SLAC)
E0
k
Plane Wave Approach:- takes into account dispersion
- takes some time to calculate since Fast Sweeps in HFSS are not supported for the projects which involve plane wave sources, need to use Discrete Sweep
- has rather good correlation with the CST WakeField Solver
Beam Loading: Coupling Impedance
11.7 11.8 11.9 12 12.1 12.2 12.30
0.5
1
1.5
2
2.5 x 106
Frequency, GHz
Impe
danc
e, V
/A
abs(Zpw+ )
abs(Zpw- )
abs(Zpw)
Ez(z,f) → [ exp ( ± i *z *ω/c ) ] → [ ∫ dz ] → V (f) → [IHFSS = 2*π*r * E0 / Z0] → Z(f)
Beam Loading: Wake Potential
-40 -20 0 20 40 60 80-8
-6
-4
-2
0
2
4
6
8x 10
13
Time, ns
Wak
e P
oten
tial,
V/C
Wbunch Wbunch = ifft(Z+)
Beam Loading: Voltage
0 50 100 150 200-5
-4
-3
-2
-1
0
1
2
3
4
5x 10
6
Time, ns
Vol
tage
, V
real(Vbeam)
Bunches
Vbeam = q * ∑ Wbunch (t+Tbunch)
Drive Beam Generation Complex
*CLIC-Note-764
Drive Beam Combination Steps
0 50 100 150 200 250
Buncher
Delay Loop
Combiner Ring #1
Combiner Ring #2
t, ns
BuncherDelay LoopCombiner Ring #1Combiner Ring #2
fbeam = 4 * 3 * 2 * fbuncher
12 GHz
3 GHz
1 GHz
0.5 GHz
PETS: Single Bunch Response
0 5 10 15 20 25
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time, ns
Vol
tage
, a.u
.
kindly provided by Alessandro Cappelletti, Igor Syratchev (CERN)
PETS: Generated Rectangular Pulse
trise ≈ 1.5 ns
0 5 10 15 20 250
1
2
3
4
Switch Number
Del
ay T
ime,
ns
No delays, just nominal (~240ns) switch times in
buncher
Rectangular Pulse in Main LinacEnergy Spread ≈ 6%
0 50 100 150 200 250 300 350 400 450-3
-2
-1
0
1
2
3 x 107
Time, ns
Vol
tage
, V
real(Vloaded)
abs(Vunloaded)
real(Vbeam)
Bunches
Method N1. Reference Pulse
Unloaded Voltage
Loaded Voltage
Klystron Pulse(reference pulse)
CLIC Pulse
tiK etAtp )()(
),,()( SWITCHPETSCLIC Trtptp
Minimization of the Energy Spread in Main Beam
0)()(max tptp CLICKt
Note: unfortunately we can’t use any deterministic algorithm for the optimization. Pulse shape dependence on the delay times is significantly nonlinear so it seems like only probabilistic algorithms can be used here. Exhaustive search is also not a good idea either, because the total number of the possible combinations is ~ 1024
Reference Pulse Shape
Time
Pul
se A
mpl
itude
0
Ar
A
6*TRF
trisetfilling tbeam trise
tfilling
Arise ≈ 0.62A
Trapezoidal Pulse in Main Linac
50 100 150 200 250 300 350
-3
-2
-1
0
1
2
x 107
Time, ns
Vol
tage
, V
real(Vloaded)
abs(Vunloaded)
real(Vbeam)
Bunches
0 50 100 150 200 250 300 350-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Bunch Number
Vol
tage
Spr
ead,
%
Bunch Voltage Spread
Energy Spread ≈ 0.17%
Comparison of the Ramp Types
0 50 100 150 200 250 300 350-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Bunch Number
Vol
tage
Spr
ead,
%
Linear PulseParabolic PulseCubic Pulse
Energy Spread ≈ 0.17 %Energy Spread ≈ 0.15 %Energy Spread ≈ 0.14 %
0 50 100 150 200 250 300 350-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Bunch Number
Vol
tage
Spr
ead,
%
tr = 27 nstr = 54 ns
tr = 13. 5 ns
tr = 81 ns
Comparison of the Rise Times
Note: efficiency ~ tB/tP , so increasing tr we decrease the efficiency.
tr = 81 ns, efficiency decrease by a factor of 0.8
Energy Spread ≈ 0.60 %Energy Spread ≈ 0.17 %Energy Spread ≈ 0.04 %Energy Spread ≈ 0.03 %
Approximating the reference pulse by the CLIC one
Monte Carlo Tdelays(i,Tstep)
pi(t) = p(t,Tswitch(i))
εi = | pi(t)-p0(t) |
i < NshotsYesi = i + 1
No
i = 0Tstep = C / f buncher
Tswitch(i) = Tswitch + Tdelays(i)
min(εi) < ε
No
Tswitch = Tswitch(imin)ε = εimin
Yes
ε < ε1Check energy
spread
Tswitch = Tnominal
ε = ε0
Yes
No
Brief Description:
- generate ‘reference’ pulse
- generate random pulses
- find the minimal difference
- adjust delay step
- check energy spread
Disadvantages:
- need to know the reference pulse
- no guaranty it can be approximated by the CLIC pulses
Pulse Shape Optimization Utility
Optimized Pulse Shape
0 50 100 150 200 250 300 350
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time, ns
Vol
tage
, a.u
.
PETS PulsePerfect PulsePulse Difference
0 5 10 15 20 250
10
20
30
40
50
60
70
80
90
100
Switch Number
Del
ay T
ime,
ns
Corresponding switch delays in buncher
Optimized Pulse in Main Linac
50 100 150 200 250 300 350 400
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
x 107
Time, ns
Vol
tage
, V
real(Vloaded)
abs(Vunloaded)
real(Vbeam)
Bunches
0 50 100 150 200 250 300 350-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Bunch Number
Ene
rgy
Spr
ead,
%
Linear Reference PulseCLIC pulse
Voltage Spread ≈ 0.22 %Voltage Spread ≈ 0.17 %
PETS: Single Bunch Response
0 5 10 15 20 25
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time, ns
Vol
tage
, a.u
.
*Alessandro Cappelletti, Igor Syratchev
Full PETS Bunch Response Calculations
0 50 100 150 200 250 300
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time, ns
Vol
tage
, a.u
.
PETS PulsePerfect PulsePulse Difference
0 5 10 15 20 250
10
20
30
40
50
60
70
80
90
100
Switch Number
Del
ay T
ime,
ns
The same switch delays as for the simplified
bunch response in PETS
Full PETS Bunch Response Calculations
50 100 150 200 250 300 350 400
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
x 107
Time, ns
Vol
tage
, V
real(Vloaded)
abs(Vunloaded)
real(Vbeam)
Bunches
0 50 100 150 200 250 300 350-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Bunch Number
Ene
rgy
Spr
ead,
%
Full PETS ResponseSimplified PETS Response
Voltage Spread ≈ 0.25 %Voltage Spread ≈ 0.22 %
Method 2. Energy Spread Minimization
Unloaded Voltage
Loaded Voltage
Klystron Pulse(reference pulse)
CLIC Pulse
tiK etAtp )()(
),,()( SWITCHPETSCLIC Trtptp
Minimization of the Energy Spread in Main Beam
0),),((max,1
LSWITCHINJLNn
VTTntVB
12 23 3 3 Vbeam(Tinj)X X X X
Nr Nr Nr Nr Nr Vbeam(Tinj+TMB)X X X X X
Np Np Np Np Np Vbeam(Tinj+(NB-1)TMB)X X X X
Nr+Np-3 Nr+Np-3 Nr+Np-3Nr+Np-2 Nr+Np-2
Nr+Np-1
1 2 3 X Nr X Np2 3 X Nr X Np . X3 X Nr X Np X Nr+Np-3X Nr X Np X Nr+Np-3 Nr+Np-2
Nr X Np X Nr+Np-3 Nr+Np-2 Nr+Np-1
rAS(t)
pCLIC(t,Tswitch)
pCLIC(t,Tswitch)
Unloaded Voltage VU(t) = conv ( pCLIC, rAS )
Loaded Voltage VL(t) = VU(t) + VBEAM(t)
NB rows
Method 2. Energy Spread Minimization
Energy Spread Minimization in CLICBrief Description:
- fix injection time
- generate random pulses
- find the minimal energy spread
- adjust delay step
Monte Carlo Tdelays(i,Tstep)
pi(t) = p(t,Tswitch(i))
εi = spread (Vloaded ( tb(n),Tinj ))
i < NshotsYesi = i + 1
No
i = 0Tstep = C / f buncher
Tswitch(i) = Tswitch + Tdelays(i)
min(εi) < ε
No
Tswitch = Tswitch(imin)ε = εimin
Yes
ε < ε1 :-)
Tinj = [0,Tinj max ]Tswitch = Tnominal
ε = ε0
Yes
No
PETS: Single Bunch Response
0 5 10 15 20 25
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time, ns
Vol
tage
, a.u
.
*Alessandro Cappelletti, Igor Syratchev
0 5 10 15 20 250
10
20
30
40
50
60
70
80
90
Optimized Pulse Shape for theSimplified PETS Bunch Response
0 50 100 150 200 250 300 350-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time, ns
Vol
tage
, a.u
.
PETS PulsePerfect PulsePulse Difference
0 50 100 150 200 250 300 350-10
-8
-6
-4
-2
0
2
4
6
8 x 10-4
Bunch Number
Vol
tage
Spr
ead,
%
Bunch Voltage Spread
Voltage Spread ≈ 0.08 %
Note: factor 3 better than using the reference
pulse method!
Optimized Pulse Shape for the Full Bunch Response in PETS
0 5 10 15 20 250
10
20
30
40
50
60
70
80
90
0 50 100 150 200 250 300 350 400-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time, ns
Vol
tage
, a.u
.
PETS PulsePerfect PulsePulse Difference
0 50 100 150 200 250 300 350-10
-8
-6
-4
-2
0
2
4
6 x 10-4
Bunch Number
Vol
tage
Spr
ead,
%
Bunch Voltage Spread
Energy Spread ≈ 0.08 %
Possible CTF3 ExperimentCTF3 CLIC
Delay loop x2 x2
Combiner Ring #1 x3 x4
Combiner Ring #2 x4 -
Bunch Frequency 1.5 GHz 2 GHz
Number of Bunches 1-226 312
Bunch Charge Total charge of 12 nC 0.6 nC
Energy 177 MeV 2.424 GeV
Energy spread 2% (from CALIFES) 1.3% (at linac injection)
PETS length 1 m 0.213 m
Remark: number of AS in CLIC >> number of AS in TBTS, so energy spread from CALIFES seems to be too high for now to see the influence of the pulse shape optimization, however we can try not to increase the one
Conclusions1. Beam loading model based on the plane wave approach seems to be a
reasonable one
2. Two developed methods of the pulse shape optimization are presented. It is demonstrated that the direct method gives better results and within the acceptable level of 10-4
3. Pulse shape optimization which takes into account reflections in the tail of the PETS bunch response gives the same level of the energy spread
4. Final value of the energy spread depends on many parameters and also on the optimization algorithm
Further steps
1. Moving to the TD26 (CLIC baseline) accelerating structure
2. Possible different optimization techniques usage, i.e. genetic algorithm in the case if the energy spread is not within the acceptable level
3. CTF3 experiment for the beam loading compensation
Thank You for the Attention!