Compensation of Transient Beam-Loading in CLIC Main Linac

Oleksiy Kononenko, Alexej Grudiev

IWLC, October 20, 2010

Contents

• Motivation• Calculation of unloaded/loaded voltages • Optimization of the pulse shape• Spread minimization for BNS damping and

transient in the subharmonic buncher• Effects of the charge jitters in drive and main

beams• Conclusions

Motivation: CLIC Performance Issue

*CLIC-Note-764, private conversations with Daniel Schulte (CERN)

In order to have luminosity loss less than 1%, the RMS bunch-to-bunch relative energy spread must be below 0.03%

Beam Loading: Steady State

0 0.05 0.1 0.15 0.2 0.250

2

4

6

8

10

12

14x 10

7

z, m

G, V

/m

Gloaded

Gunloaded

Gbeam

20

*Beam loading for arbitrary traveling wave accelerating structure. A. Lunin, V. Yakovlev

Energy Spread Minimization Scheme

Klystron (reference) pulse

Unloaded Voltage in AS- fix phase switch times in buncher- generate corresponding drive beam profile- take into account PETS (+PETS on/off) bunch response- calculate unloaded voltage

Loaded Voltage in AS - calculate AS bunch response - calculate total beam loading voltage- add to unloaded voltage

Energy Spread Minimizationvarying buncher delays

Electric Field Distribution for Port and Plane Wave Excitations

Considering T24 CLIC main accelerator structure

Accelerating Voltage for the Port excitation and Beam Impedance

Eportz (z,f) → [ exp ( ± i *z *ω/c ) ] → [ ∫ dz ] → VU (f)

Epwz(z,f) → [ exp ( ± i *z *ω/c ) ] → [ ∫ dz ] → V (f) → [IHFSS = 2*π*r * E0 / Z0] → Z(f)

11.7 11.8 11.9 12 12.1 12.2 12.3

0.5

1

1.5

2x 106

f, GHz

Imp

edan

ce, V

/A Vo

ltage, V

abs ( Vacc

)

abs ( Zpw

)

1

2

3

4x104

Envelopes of the Time Response for the Port Excitation and Wake Potential

0 50 100 150

20

40

60

80

Time, nsWak

e P

ote

nti

al, V

/pC

Vo

ltage, V

abs ( r )abs (W)

8x103

6

4

2

CLIC 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 Linac

Optimizing injection time one canoptimize the energy spread down to the level of 6% only

0 100 200 300 400

0.5

1

1.5

2

2.5

3x 107

Time, ns

Vo

ltag

e, V

abs(Vunloaded

)

abs(Vbeam

)

abs(Vloaded

)

Schematic Pulse Shape for CLIC

Time

Pu

lse

Am

plit

ud

e

CLIC Pulse Main BeamA

Ar

6*TRF

trise

tfilling t

beamtrise

0 Tinj

tfilling

Optimization AlgorithmBrief Description:

1. Fix injection time

2. Generate delays

3. Find the minimal energy spread and optimal delays

4. Repeat 2. starting from the optimal delays

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

Energy Spread Calculation

r(t)

pCLIC(t)

Vbeam(t)

Vunloaded

Energy Spread Optimization Utility

Optimized Pulse Shape

Corresponding switch delays in buncher

0 5 10 15 20 25

20

40

60

80

100

Switch Number

Del

ay, n

s

0 50 100 150 200 250 300

-1

-0.5

0

0.5

1

Time, [ns]

Am

plitu

de,

a.u.

Optimized Energy Spread along the Main Beam

0 50 100 150 200 250 300-0.1

-0.05

0

0.05

0.1

Bunch Number

E

/<E

>, %

E / <E>

-0.03

0.03

E / <E>

RMS bunch-to-bunch relative energy spread is around 0.03%

Model Improvements

1. For BNS damping it is necessary to inject bunches a bit (10 - 30 deg) off-crest

2. Take into account transient in the subharmonic buncher during DB phase switch

Energy Spread Dependence on the Injection Phase

0 5 10 15 20 25 30 35 400.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Injection Phase, deg

En

erg

y S

pre

ad, %

Optimized Injection Time

Optimized Delays

CLIC constraint

Optimal Switch Delays for the Different Injection Phases

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

Switch Number

Sw

itch

Del

ays,

bu

nch

es

0 deg12 deg24 deg36 deg

Transient in the Subharmonic Buncher During DB Phase Switch

8.3 16.6 24.9 33.2 41.5 49.8 58.1 66.4 74.7

0

0.2

0.4

0.6

0.8

1

1.2

Time, ns

Ch

arg

e, a

.u.

odd bucketseven buckets

Energy Spread Dependence on the Buncher Switch Time

0 5 10 15 20 25 300.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

Switch Time, ns

En

erg

y S

pre

ad in

Mai

n B

eam

, %

Optimized Spread

Optimized Injection Time

Currently in CTF3

Optimal Switch Delays for the Different Buncher Switch Times

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

Switch Number

Sw

itch

Del

ay, b

un

ches

4 ns

12 ns

20 ns

24 ns

Study of the Charge JitterInfluence on the Energy Spread

1. Gaussian drive/main beams charge distribution with relative rms spread of 0.1%

2. “White noise” jitter of the charge along the drive/main beams

Drive Beam Charge Spread Effect

Constraint of 0.1% charge spread in drive beam (D. Schulte, CERN) is ok for the energy spread minimization

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

0.15

0.2

0.25

Relative RMS Charge Spread in Drive Beam, %

Rel

ativ

e R

MS

En

erg

y S

pre

ad in

Mai

n B

eam

, %

Minimum Spread

Maximum Spread

Mean Spread

CLIC constraint

Main Beam Charge Spread Effect

Constraint of 0.1% charge spread in main beam (D. Schulte, CERN) is ok for the energy spread minimization

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

Relative RMS Charge Spread in Main Beam, %

Rel

ativ

e R

MS

En

erg

y S

pre

ad in

Mai

n B

eam

, %

Minimum SpreadMaximum SpreadMean Spread

CLIC constraint

Conclusions1. Developed pulse shape optimization method allows to reach acceptable

level of 0.03% in the main beam energy spread

2. Performing optimization for the different possible buncher switching times and injection phases the same CLIC acceptable level of energy spread is reached

3. Randomly distributed along the bunch train 0.1% rms spread charge jitters in drive and/or main beams don’t increase the final energy spread in the main beam

Thank You for the Attention!