compensation of transient beam-loading in clic main linac

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!