Higher-Order Modes and Beam-Loading Compensation in

CLIC Main Linac

Oleksiy KononenkoBE/RF, CERN

CLIC RF Structure Development Meeting, March 14, 2012

2

Outline

• Motivation• Beam-loading compensation scheme• Frequency Domain: HFSS/ACE3P benchmark• Time Domain: HFSS/ACE3P/gdfidl benchmark• Effect of the higher-order modes to the

compensation scheme• Conclusion

3

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%

CLIC Drive Beam Generation Complex

*CLIC-Note-764

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Energy Spread Minimization SchemeUnloaded 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

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Beam-Loading Compensation

Main results are published: O. Kononenko, A. Grudiev, Transient beam-loading model and compensation in Compact Linear Collider main linac, Physical Review, Special Topics on Accelerators and Beams, 2011, Vol. 14, Issue 11, 10 pages, http://prst-ab.aps.org/abstract/PRSTAB/v14/i11/e111001

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HFSS Simulation Setup Model:

- 90 deg of the structure- copper outer walls

H-plane

Port 2

Port 1

H-plane

Simulation profile: - second order basis functions

- curvilinear elements enabled- 0.001 s-parameters accuracy

leads to ~300K tet10 mesh

8

HFSS Port and Plane Wave Excitations

Thanks to Valery Dolgashev from SLAC for the idea to use the plain wave source

9

s3p Simulation Setup Model:

- 90 deg of the structure- copper outer walls

H-plane

Port 2

Port 1

H-plane

Simulation profile: - second order basis functions

- curvilinear elements enabled- 2M tet10 mesh

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Reflection Coefficient s11

11.99 11.991 11.992 11.993 11.994 11.995 11.996 11.997 11.998 11.999 12-65

-60

-55

-50

-45

-40

-35

-30

-25

-20

Frequency, GHz

Re

fle

cti

on

, d

B

s3pHFSS

11

Complex Magnitude Ez, f=11.994GHz

0 50 100 150 200 250 3000

5

10

15

20

25

30

35

40

45

z, mm

|Ez|

, k

V/m

s3pHFSS|s3p-HFSS|

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Ez(z) in a Complex Plane, f=11.994GHz

-50 -40 -30 -20 -10 0 10 20 30-40

-30

-20

-10

0

10

20

30

40

Re(Ez), kV/m

Im(E

z), k

V/m

HFSSs3p

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s3p/HFSS Benchmark SummaryTD26 RF Design

Remarks s3p HFSSf, GHz 11.994

Filling time, ns 67.3393 66.98

Q-factor, Cu 5682.5388 5657

S12, dB -3.8784 -3.8750

S11, dB -60.7318 -58.2715

Voltage, V (Pin=4W) 7022.376 7040

There is a very good agreement between the HFSS and s3p results

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t3p Simulation Setup Model:

- 90 deg of the structure- bunch sigma = 1mm- ABC/WG condition: couplers, beam-pipe, damping waveguides- PEC/copper outer walls

Simulation profile: - second order basis functions

- curvilinear elements enabled- 2, 3, 6, 12M tet10 meshes

H-plane

H-plane

Beam

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Bunch Passage through TD26

DC trail which is caused by the numerical errors can be observed, 2M mesh has been used

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ACE3P Wake Convergence Study

0 10 20 30 40 50 60 70 800

20

40

60

80

100

120

140

Time, ns

Lo

ng

itu

din

al

Wa

ke

, V

/pc

2M_p1_1ps12M_p2_1ps_IMP2M_p2_1ps6M_p1_1ps12M_p1_1ps

Different wake length is simulated because of the limited computer resources. Maximum 6hours x 2400 CPU per one run

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gdfidl Simulation Setup Model:

- 90 deg of the structure- bunch sigma = 1mm- PEC outer walls

Simulation profile: - mesh planes fixed to the irises, thanks to Vasim - 100, 50 um uniform cubic meshes, 50x50x25um mesh

Model:- 90 deg of the structure- bunch sigma = 1mm- PML condition: couplers, beam-pipe, damping waveguides- PEC outer walls

H-plane

H-plane

Beam

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gdfidl Convergence upon the Mesh Size

0 10 20 30 40 50 60 70 80 90 100-20

0

20

40

60

80

100

120

140

160

Time, ns

Wa

ke

, V

/pc

25um50um100um

Convergence is observed while wake rises at the tail for some reason

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12 14 16 18 20 22 24 2610

-6

10-4

10-2

100

102

Frequency, GHz

Imp

ed

an

ce

, V

/A

HFSSACE3Pgdfidl

Beam Coupling Impedance HFSS/ACE3P/gdfidl

Strange ACE3P Resonances

Monopole band

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Lowest Monopole Band ImpedanceHFSS/ACE3P/gdfidl

24 24.5 25 25.5-0.04

-0.02

0

0.02

0.04

0.06

0.08

Frequency, GHz

Lo

ng

itu

din

al

Imp

ed

an

ce

, V

/A

HFSSACE3Pgdfidl

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Fundamental Mode ImpedanceHFSS/ACE3P/gdfidl

11.5 11.6 11.7 11.8 11.9 12 12.1 12.2 12.3 12.4 12.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Frequency, GHz

Lo

ng

itu

din

al

Imp

ed

an

ce

, V

/A

HFSSACE3Pgdfidl

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HFSS/ACE3P/gdfidl Wakes

0 10 20 30 40 50 60 70 80-50

0

50

100

150

200

Time, ns

Lo

ng

itu

din

al

Wa

ke

, V

/pc

HFSS, copper wallsACE3P, PEC wallsgdfidl, PEC walls

HFSS and gdfidl are ok at the beginning, while ACE3P/gdfidl are ok after that because of the PEC boundary condition (copper in HFSS), also no ACE3P/HFSS wake rise is observed in the tail

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-10 0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140

160

Time [ns]

Wa

ke

Po

ten

tia

l [V

/pC

]

30 GHz0.6 GHz1 GHz

HFSS wake shape vs BW

This wake (wake function) for the delta function bunch is used for the compensation scheme, since bunch length in CLIC is only 44um.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

50

100

150

Time [ns]

Wa

ke

Po

ten

tia

l [V

/pC

]

30 GHz0.6 GHz1 GHz

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Energy Spread vs BW

0 50 100 150 200 250 300 350-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

Bunch Number

10

0*

E /

<E

> [

%]

0.6 GHz1 GHz30 GHz

Fixed optimized buncher delays and injection time for 1 GHz BW

BW, GHz ΔE/E,%

0.6 0.0257

1.0 0.0253

30 0.028

Bunch Number

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Conclusions

• Good agreement between ACE3P and HFSS in frequency domain

• Some difference has been observed between HFSS/ACE3P/gdfidl in time domain

• HOM’s taken into account don’t affect the developed beam-loading compensation scheme on the level of 0.03%

• Beam-loading compensation scheme should work

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Acknoledgement

I would like to thank my supervisor Alexej Grudiev, all of the members of the CERN CLIC RF team, SLAC ACD group.

Thank you!