L-band (1.3 GHz) 5-Cell SW Cavity

High Power Test Results

Faya Wang, Chris Adolphsen

SLAC National Accelerator Laboratory

. . . . . . . . . . . . . . . . . . . . . .

L-band 5-Cell SW Cavity Introduction

A half-length (5-cell) prototype, SW cavity was built at SLAC

to verify that the ILC-required gradient (15 MV/m in 1.0 ms

pulses) can be achieved stably and without significant

detuning from the RF heat load (4 kW per cell).

Field Probe

Matching Cell (Driving Cell)

L-band 5-Cell SW Cavity Introduction

0 0.2 0.4 0.6 0.8 11280

1285

1290

1295

1300

1305

/

f n: M

Hz

0130 ,1 μs,8.1 ,29000 GHz,3.1 e0 .kQf

Gradient = 7.4 MV/m for 1 MW input rf power (verified in a beam test)

Field Profile J. wang

RF Conditioning Statistics Until Jan-4-2008

Pulse Width: us

Conditioning Time: hrs

100 160

200 20

400 70

1000 280

Total 530

(~5.5e6 pulses)

~Max unloaded Acc. Gradient: 15MV/m

~6167 Breakdown Events (1233 per cell)

5Hz repeating frequency

1Hz repeating frequency

0 100 200 300 400 500 6000

10

20

30

40

Time: hr

Bre

akdo

wn

rate

: 1/

hr

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

Time: hr

Hard breakdown rate percent

Soft breakdown rate percent

0 0.5 1 1.5 2 2.5 3 3.5 410

-4

10-3

10-2

10-1

100

Breakdown time interval: hr

Pos

sibi

lity

0~135hrs-5Hz

135~270hrs-5Hz270~405hrs-1Hz

405~528hrs-1Hz

BKD Characteristics with RF conditioning Time5Hz 1Hz

6

600 700 800 900 1000

0.8

1

1.2

1.4

1.6

1.8

2

Pulse Width: us

BK

D R

ate

: 1/h

r

RF repeat frequency 5 Hz, 5000Gauss, unloaded gradient: 13.5MV/m

Breakdown Rate Pulse Width And Gradient Dependence

2.5 2.55 2.6 2.65 2.7 2.75-5

-4

-3

-2

-1

0

1

2

Ln(E): E in MV/m

Bre

ak d

own

rate

: Ln

(B)

1/hr

Ln(B) = 20.7*Ln(E) - 55.9

data 1

linear

21~ G

5 Hz, 200 μs

7

Klystron

SW Cav

Coup

Reflect from cavity

Input to cavity

When breakdown occurs in the waveguide the klystron rf is shut off in few us.

The cavity still sees input power, which is just the emitted power from cavity that is reflected back to the cavity by the waveguide breakdown

By comparing reflected and input power waveform timing, one can determine the breakdown position

Breakdown in the Input Waveguide

230 235 240 245

-25

-20

-15

-10

-5

0

Time: us

Nor

mal

ized

pow

er:

dB

Input power to cavity

Reflect power from cavityStored energy Change

Klystron output

8

0 5 10 1555

60

65

70

75

80

85

90

Time: us

dB

m

Reflect after BKDProbe Singal after BKDInput Signal after BKDNormal reflectNormal probe

0 0.5 1 1.5 2 2.5 3 3.5 480

82

84

86

88

90

92

Time shift = 300ns

Sample Frequency: 100MHz

0 10 20 30 40 500

10

20

30

40

50

60

70

WG length from cavity: m

Per

cent

of

WG

BK

D e

vent

s

26 Events in WG Mar-13-2009~Mar-19-2009

Resolution: 1m

Cavity Coupled Resonator Equation

1

1

12

,1

,11

1

12

,1

,1

21,

2,1

22

2

ˆ1

ˆ12

1

2

ˆ

1

1

1

1ˆ1ˆ

nnn

nn

nn

nnn

nn

nn

nn

nn

n

nnnn

n

nnn

n

vQR

QR

k

kv

QR

QR

k

k

v

kkdt

vd

Qdt

vd

g

gR

vI

dt

dv

QR

QR

k

k

v

kdt

vd

Qdt

vd

ˆˆˆˆ

12

2

ˆ

1

11

ˆ1ˆ

1

12

12

212

2,1

2,1

12

2,1

1

1122

1

12

For a multi-cell cavity coupling from one end:

Coupled resonator equation for middle cells:

With βe, generator resistor Rg could be expressed as

N

nqn

q

eg

V

VRR

1

2

21

2 L n -1 R n -1 C n -1 2 L n -1

k n -1 , n k n , n + 1

2 L n R n C n 2 L n 2 L n + 1 R n + 1 C n + 1 2 L n + 1

V n -1 V n V n + 1

(a )

k 1 , 2

I g R g 2 L 1 R 1 C 1 2 L 1 2 L 2

e

Z cav

V cav ,I cav

(b )

qnV (n=1…N) is n-th the cell voltage in q-th mode

Cavity Static and Transient Study

4

5

Static Response

qcave

qcave

gcav

gcav

RZ

RZ

RZ

RZ

0

0

21

21

i

i

e

e

Circuit model

The circuit model matches the static characteristics of the cavity!

Cavity Reflection Measurement & Prediction

Cavity Static and Transient Study

Transient Response

0 2 4 6 8 10 12

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time: t/ 0

Driving Cell

Cell 2

Cell 3

Cell 4

Cell 5

f=0

f=20kHz

f=40kHz

f=60kHz

Simulated field amplitudes in the cavity cells for different drive frequencies but the same input power.

Rel

ativ

e C

ell F

ield

Am

plitu

de If the drive frequency

differs from the

nominal frequency,

other cavity modes

will be excited when

the drive power is

turned off

0 0.2 0.4 0.6 0.8 1-10

-8

-6

-4

-2

0

Time: t/0

Sto

red

En

erg

y D

eca

y: d

B

Test at -20kHzTest at -100kHzSimulate at -20kHzSimulator at -20kHz

Cavity Static and Transient Study

Transient Response

Mode beating after rf power turned off

0 5 10 15 20 25-40

-35

-30

-25

-20

-15

-10

-5

0

Time (us)

dB

Normal Refl PwrNormal FieldBredkwon Refl PwrBreakdown FieldInput Pwr

Cavity Breakdown Localization β = 1

Typical Breakdown waveforms from the 5cell cavity, sampled at 100MHz.

RF isolated by the plasma in the downstream end of

the cavity

Plasma clears out, trapped rf now discharges

Waveform at the end of pulse

Typical Breakdown Waveform

0 5 10 15 20-40

-35

-30

-25

-20

-15

-10

-5

0

Time: us

Po

we

r: d

B

reference Refreference OutBkd refBkd out

Cavity completely isolated (Q ~ Qo)

Plasma cleared!

Cavity Breakdown Localization

B re akdo wn

D r iving C e ll

R e f le c te d P o we r S to re d E ne rgy D am ping

e e

p ic k-up1 s t Ir is 2 n d Ir is 3 r d Ir is 4 th Ir is

Plasma

The plasma block the coupling. Cavity isolated to two parts.

Both parts will see the natural modes beating after rf shutoff

Direction coupler

Cavity Breakdown Localization

0 5 10 15-30

-25

-20

-15

-10

-5

0

Freq: MHz

Am

plitu

de:

dB

FFT on stored energy no iris blocked

FFT on stored energy with 1st iris blocked

FFT on stored energy with 2nd iris blocked FFT on stored energy with 3rd iris blocked

FFT on stored energy with 4th iris blocked

Assume zero coupling at different irises and compute the FFT of the simulated field decay.

The distinct mode beating spectra differentiate the breakdown locations

Cavity Breakdown Localization

0 5 10 15 20 25-40

-35

-30

-25

-20

-15

-10

-5

0

Time: us

Po

we

r: d

B

Normal Reflected Power

Normal Stored Energy DecayReflected Power at Breakdown

Stored Energy Decay at Breakdown FFT Results

The dashed lines are the expected mode beating frequencies with the 1st iris blocked

0 5 10 15 20-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Beating Frequency: MHz

Am

plit

ud

e: d

B

Cavity Breakdown Localization

0 5 10 15 20 25-40

-35

-30

-25

-20

-15

-10

-5

0

Time: us

Po

we

r: d

B

Normal Reflected Power

Normal Stored Energy DecayReflected Power at Breakdown

Stored Energy Decay at Breakdown FFT Results

The dashed lines are expected mode beating frequencies without breakdown

5 10 15 20-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Beating Frequency: MHz

Am

plit

ud

e: d

B

5 10 15 20-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Beating Frequency: MHz

Am

plit

ud

e: d

B

Cavity Breakdown Localization

0 5 10 15 20 25-40

-35

-30

-25

-20

-15

-10

-5

0

Time: us

Po

we

r: d

B

Normal Reflected PowerNormal Stored Energy DecayReflected Power at BreakdownStored Energy Decay at Breakdown

Example of Breakdown at 2nd iris.

The dashed lines are the expected mode beating frequencies with the 2nd iris blocked

0 5 10 15 20 25-40

-35

-30

-25

-20

-15

-10

-5

0

Time: us

Po

we

r: d

B

Normal Reflected PowerNormal Stored Energy DecayReflected Power at BreakdownStored Energy Decay at Breakdown

5 10 15 20-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Beating Frequency: MHz

Am

plit

ud

e: d

B

Cavity Breakdown LocalizationExample of Breakdown at 3rd iris.

The dashed lines are the expected mode beating frequencies with the 3rd iris blocked

Cavity Breakdown Localization

Example of Breakdown at 4th iris.

0 5 10 15 20 25-40

-30

-20

-10

0

Time: us

Pow

er:

dB

reference Ref

reference Out

Bkd ref

Bkd out

No Beating in the Stored Energy Decay !

0 5 10 15 20-1

-0.5

0

0.5

1

1.5

2

2.5

Beating Frequency: MHz

Am

plit

ud

e; d

B

0 5 10 15 20 25-40

-30

-20

-10

0

Time: us

Pow

er:

dB

reference Ref

reference Out

Bkd ref

Bkd out

5 10 15 20

-4

-3

-2

-1

0

Freq: MHz

Am

p: d

B

Cavity Field

Reflect

Beating Freq. from 5 cell natural modes.

Cavity Breakdown Localization

Breakdown between the directional coupler and cavity !

D riving C e l l

p ic k-up

1 s t Ir is 2 n d Ir is 3 r d Ir is 4 th Ir isB re akdwo n

More Complex Cavity Breakdown Simulation

D riving C e l l

p ic k-up

1 s t Ir is 2 n d Ir is 3 r d Ir is 4 th Ir isB re akdwo n

When first did the above analysis, the simulations with k = 0 for the breakdown iris did not match well the fast decay of the rf energy in the upstream, non-isolated part of the cavity.

Have recently modified the model, letting k of the breakdown iris and Qo of the upstream cell to vary to try to better match this behavior and that of the isolated part.

Q_u

0 5 10 15 20-50

-40

-30

-20

-10

0

10

Time: us

Po

we

r: d

B

Normal refl pwrNormal fieldBreakdown refl pwrBreakdown fieldSimulated refl pwrSimulated field

Cavity Breakdown Simulation – Iris 1 Breakdown

k_bkd/k_nor Q_d_nor/Q_d_bkd Q_u_nor/Q_u_bkd0.2 1 4

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 2 4 6 8 10 12-40

-30

-20

-10

0

Time (us)

Po

we

r: d

B

Cavity Breakdown Simulation – Iris 1 Breakdown

k_bkd/k_nor Q_d_nor/Q_d_bkd Q_u_nor/Q_u_bkd0.15~0.25 1 1

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

0 5 10 15 20-40

-30

-20

-10

0

Time: us

Po

we

r: d

B

Cavity Breakdown Simulation – Iris 2 Breakdown

k_bkd/k_nor Q_d_nor/Q_d_bkd Q_u_nor/Q_u_bkd0.05~0.2 1 1.5~8

0 2 4 6 8 10-40

-35

-30

-25

-20

-15

-10

-5

0

0 2 4 6 8 10-40

-35

-30

-25

-20

-15

-10

-5

0

Time: us

Po

we

r: d

B

Field Pickup Refl. Pwr

Cavity Breakdown Simulation – Iris 4 Breakdown

k_bkd/k_nor Q_d_nor/Q_d_bkd Q_u_nor/Q_u_bkd0.1 1 25

Summary: L-band 5-cell SW Cavity

1. Breakdown locations can be determined from the FFT

signature of the decay fields

2. By varying the breakdown iris coupling and the upstream

cell Q in the cavity circuit model, can match reasonably

well the decay field patterns (through the simulations

show more pronounced mode beating).

3. Why does the breakdown plasma stay for so long (many

us) after the drive rf is shut-off and not cause large rf

losses ?