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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 ?