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sLHC
SPL
LLRF simulations
Feasibility and constraints for operation with more
than one cavity per klystron
Power overhead
Wolfgang Hofle
Acknowledgements and Participation:
S. Chel, G. Devanz, M. Desmons, O. Piquet (CEA Saclay)
M. Hernandez Flano, J. Lollierou, D. Valuch (FB section)
O. Brunner, E. Ciapala, F. Gerigk, J.Tuckmantel
This project has received funding from the European Community's Seventh Framework Programe
(FP7/2007-2013) under the Grant Agreement no212114
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
1/23
sLHC
Outline
SPL parameters
Optimization of Qext
Delay and Power budget
Lorentz Force detuning
Layouts (1 cavity / 2 cavities per klystron) and
perturbations to be considered in the simulations
First simulation results for one high energy RF station (O. Piquet & M. Hernandez)
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
2/23
sLHC
SPL parameters
SPL cavities and frequency:
704.4 MHz, cooling @ 2K He-II
Low energy part :
b=0.65, 5–cell cavities, 6 cavities/cryostat,
60 cavities, R/Q = 320 Wlinac
1 klystron / cavity  likely baseline
High energy part:
b=1, 5-cell cavities, 8 cavities/cryostat,
160 for 4 GeV (200 for 5 GeV) cavities, R/Q = 525 Wlinac
One 1.x MW klystron for 2 cacvities (LPSPL)
One 1.x MW klystron for 1 cavity (HPSPL)
One ~5.5MW klystron per 4 cavities (previous)
SPL requirement:
Stability:
for b=1  25 MV/m
0.5% and 0.5 degrees for Vacc during beam pulse
LPSPL:
HPSPL:
2 Hz
50 Hz
4 GeV
5 GeV
1.2 ms beam pulse
0.4 ms / 1.2 ms beam pulse
20 mA beam current (DC)
40 mA beam current (DC)
Cavity loaded Q ~ 106
HPSLP: ppm change of beam pulse length ??
Fixed coupler position optimized for 40 mA operation, will give reflection @ 20 mA
fs=15 degrees
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
3/23
sLHC
Principle of pulsed operation
SPL (with beam)
beam arrival, jump of set-point gradient, start of flat top
(transient)
Vcav/V0
determined by QL and Pg
excess power (reactive beam loading and non-optimal QL)
2
excess power Lorentz Force detuning (no piezo)
modulator droop
1
beam pulse
RF pulse (If) [idealized]
time
closure of FB loops
(transient)
tF only determined by QL
tinj
W. Hofle @ 3rd SPL
collaboration Meeting
cavity voltage
determined by QL and Pg
November 12, 2009
5/23
sLHC
Parameters for 40 mA operation,
optimized coupling for zero reflected power during beam pulse
frequency:
accelerating gradient of b=1 cavities:
length of cavity L=b5l/2:
cavity accelerating voltage for b=1
synchronous phase angle fs
704.4 MHz
25 MV/m
1.06 m
26.5 MV
15 degrees
power delivered to beam
Pb  I b Vacc  cos s  1.0239 MW
zero refl. power during beam pulse
Qext  QL 
Vacc
 1.3064 106
( R / Q) I b cos s



filling of cavity
V (t )  2V0 1  e t / 2t F  2V0 1  e t /t V
filling time
t V  2t F 
 0.5903 ms
0
tinj  t V ln 2  t F ln 4  0.4092 ms
beam injected at
forward power for filling
1.0239 MW
Vacc  V0  Vfwd
W. Hofle @ 3rd SPL
collaboration Meeting
2QL

November 12, 2009
Pfwd
2
Vfwd

( R / Q)QL
6/23
sLHC
Parameters for 20 mA operation,
optimized coupling for zero reflected power during beam pulse
frequency:
accelerating gradient of b=1 cavities:
length of cavity L=b5l/2:
cavity accelerating voltage for b=1
synchronous phase angle fs
704.4 MHz
25 MV/m
1.06 m
26.5 MV
15 degrees
power delivered to beam
Pb  I b Vacc  cos s  512 kW
zero reflected power during beam pulse
Qext  QL 
Vacc
 2.6128 106
( R / Q) I b cos s



filling of cavity
V (t )  2V0 1  e t / 2t F  2V0 1  e t /t V
filling time
t V  2t F 
2QL
 1.1806 ms
0
tinj  t V ln 2  t F ln 4  0.8184 ms
beam injected at
forward power for filling
512 kW
Pfwd
W. Hofle @ 3rd SPL
collaboration Meeting

Vacc  V0  Vfwd
November 12, 2009
V02

( R / Q)QL
7/23
sLHC
Forward power for reactive beam
loading compensation
1
2
Preactive BL comp  Qext ( R / Q) I b  sin s
4
optimized cases (40 mA , 20 mA)
Qext I b  const  1.3064 106  40 mA  52256 A
Preactive BL comp  4.5944 MV  I b
for fs= 15 degrees
9.2 kW for 20 mA
18.4 kW for 40 mA
W. Hofle @ 3rd SPL
collaboration Meeting
must be added to power budget during beam pulse
or corrected by detuning; then situation for
charging is no longer optimal and would require
more power to follow the ideal case or more time:
solution half detuning ?
November 12, 2009
8/23
sLHC
Parameters for 20 mA operation, with optimized coupling for zero
reflected power during 40 mA beam pulse (1)
frequency:
accelerating gradient of b=1 cavities:
length of cavity L=b5l/2:
cavity accelerating voltage for b=1
synchronous phase angle fs
704.4 MHz
25 MV/m
1.06 m
26.5 MV
15 degrees
power delivered to beam
Pb  I b Vacc  cos s  512 kW
chosen (optimal value for 40 mA)
Qext  QL  1.3064 106
Vacc
1
 I b cos s  19.3 mA
( R / Q) Qext
reflected current in steady state with beam
Ir 
reflected power in steady state with beam
1
2
Prefl  ( R / Q)  Qext  I r  64 kW
4
forward current in steady state with beam
If 
forward power in steady state
1
2
Pfwd  ( R / Q)  Qext  I f  576 kW
4
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
Vacc
1
 I b cos s  58.0 mA
( R / Q) Qext
9/23
sLHC
Parameters for 20 mA operation, with optimized coupling for zero
reflected power during 40 mA beam pulse (2)
1) choice: keep forward power constant at arrival of beam: 576 kW, i.e. fill with higher power
2) choice: during filling use 512 kW
filling time fixed by coupling and not affected by available power
1) 512 kW
V  Vfwd  Vrefl  2 Pfwd QL ( R / Q)  37.48 MV  2V0


V (t )  2V0 1  et / 2t F  V0
2 1  2e
tinj / 2t F
2
 2.456 t F,40 mA,opt  0.7249 ms
2 1
compared to 40 mA opt. tinj  2t F, 40mA,opt ln 2  1.386  t F,40 mA,opt  0.4092 ms
tinj  2t F,40 mA,opt ln
20 mA opt. tinj  2t F,20mA,opt ln 2  1.386 t F,20 mA,opt  0.8184 ms
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
10/23
sLHC
Parameters for 20 mA operation, with optimized coupling for zero
reflected power during 40 mA beam pulse (3)
2) 576 kW V  Vfwd  Vrefl  2 Pfwd QL ( R / Q)  49.73 MV  1.5 V0


1
t / 2t
3
 e in j F
V (t )  V0 1  e t / 2t F  V0
3
2
tinj  2t F,40 mA,opt ln 3  2.198 t F,40 mA,opt  0.648 ms
compared to 40 mA opt.
tinj  2t F, 40mA,opt ln 2  1.386 t F,40 mA,opt  0.4092 ms
20 mA opt. tinj  2t F,20mA,opt ln 2  1.386 t F,20 mA,opt  0.8184 ms
Qext  QL  1.3064 10
tinj  0.648 ms
0.576 MW, 2 cavities  1.152 MW
6
tinj  0.4092 ms
1.024 MW, 1 cavity
 1.024 MW
12.5 % more power required for two cavities / klystron due to non optimal Qext
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
11/23
Waveguide group delay
sLHC
The maximum frequency range in which a rectangular wave guide
supports the propagation of only one mode is one octave
To obtain this maximum frequency range the width of the wave guide has to be
at least a factor 2 of its height
The propagation constant is
f 
2  f
b ( ) 
1   c 
c
 f 
2
WR975,
SPL 704.4 MHz
1.96
The group delay is
tg 
L/c
f 
1   c 
 f 
2
cut-off in MHz
group delay (rel to free space)
group delay (rel to WR-975)
rel cross section
cross section for 200 waveguides
(full height, in m**2), net
W. Hofle @ 3rd SPL
collaboration Meeting
WR1150, SPL 704.4 MHz
1.46
WR-975 WR-1150 LHC (WR-2300)
605
513
257
1.96
1.46
1.3
1
0.74
0.66
1
1.18
2.36
6.16
7.27
15.54
LHC, 400 MHz
1.30
multiply by a factor 3-5 for required
space
November 12, 2009
12/23
sLHC
Group delay budget (tentative)
klystron:
80 m waveguides (WR-1150)
80 m cabling (0.9 velocity factor)
driver amplifier
waveguide components (circulator etc.)
local cabling (LLRF to klystrons etc.)
LLRF latency
total:
250 ns ?
360 ns (WR-1150)
270 ns
40 ns
40 ns ?
50 ns
250 ns ?
1260 ns
part related to 80 m distance
(surface to underground)
630 ns (50 %)
savings 60 m  15 m
(2nd tunnel)
510 ns (40 %)
80 m seems ok (feedback does not need high bandwidth)
unknown, details to be studied: beam transients, chopping, HV ripple
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
13/23
sLHC
Waveguide attenuation
From the attenuation point of view it is also better to stay away from the
cut-off frequency, i.e. f/fc > 1.5
WR975,
SPL 704.4 MHz
~5.4 mdB/m
WR1150, SPL 704.4 MHz
~4 mdB/m
Fundamental mode in full-height rectangular waveguide (Al 37.7x106 1/Wm)
AL alloys, Al Mg Si 0.5  35 % to 45 % higher losses !
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
14/23
sLHC
Power budget (very tentative)
power minimum two cavities / klystron
reactive beam loading reserve
detuning res. (Lorentz Force + micr.ph.)
transients for loops
variation in QL
variation in cavity parameters
beam current fluctuations
power at cavity input:
1152 kW
20 kW
20 kW ?
50 kW
15 kW ?
15 kW ?
40 kW ?
1302 kW ?
from klystron:
end of life klystron reserve
unusable (last 3%)
waveguide losses
circulator losses
reserve for imperfect matching
ripple and noise due to HV
100%
0%
3%
7% (more ?)
3%
0% ?
3% ?
1532/1152 = 1.33
 85%
klystron peak (saturated) power: 1532 kW  no reserve for unforeseen items
How much we need to stay away from klystron saturation – depends on klystron
characteristics
Need simulations to better quantify these needs (see presentation by M. Hernandez)
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
15/23
sLHC
Lorentz Force Detuning (1)
Magnet field component of cavity field and image current result in a force (Lorentz force) that
deforms the cavity shape and consequently changes its tune
The ensemble of the cavity mounted in its tuner frame and He vessel in the cryostat is a complex
mechanical object with many mechanical modes of oscillation, usually with frequencies as low as
100 Hz to 200 Hz for the lowest longitudinal mode of oscillation.
Tune change due to mechanical mode of oscillation:
d m m dm
2
2  Vcav 


 m m  2 k mm 
2
dt
Qm dt
 Lacc 
2
For a single short pulse or very low repetition rate, 1st order
system (symplification), sum of collective effect of all modes
2
H ( s) 
K0
,
t Ls 1
Typical values K0  1...  2 Hz /( MV / m)2
t L  5 ms... 10 ms
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
16/23
sLHC
Lorentz Force Detuning (2)
slope determined
by time constant of model
stop of RF pulse
25
90
80
70
60
15
dflor (Hz)
cavity voltage amplitude (MV)
20
10
50
40
30
20
5
10
0
0
1
2
3
time (ms)
4
5
6
0
0
1
2
3
time (ms)
4
5
6
time offset 1 ms, i.e. 01 ms on left hand side graph
detuning negative !
This case (O. Piquet, CEA Saclay, simulation)
K0  1 Hz /( MV / m)
2
t L  10 ms
H ( s) 
K0
,
t Ls 1
considerable spread from cavity to cavity to be expected !
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
17/23
sLHC
Many possible Layouts,
final for high energy part of HPSPL ?
1 klystron per cavity: individual control possible without RF vector modulator
Disadvantage: Many klystrons required
Advantage: Easiest for control, considered adopted solution for low energy part
In this case and all following cases we assume individual Lorentz-force detuning
compensation with a fixed pulse on the piezo or an adaptive feedforward (pulse-to-pulse)
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
18/23
sLHC
Many possible Layouts,
initial for high energy part of LPSPL ?
optional
RF vector modulator
Vector
modulator
Vector
modulator
Klystron
Feedback
Vector
SUM
This case was analysed, see O. Piquet, CEA Saclay, simulation, LLRF09 workshop
and presentation by M. Hernandez Flano
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
19/23
sLHC
Two cavities per klystron
high energy part of LPSPL
350
25
Vcav1
Vcav2
300
cavity voltage amplitude (MV)
20
dflor (Hz)
250
200
150
100
Vcav1
Vcav2
15
10
5
50
0
0
1
2
3
time (ms)
4
5
0
6
0
1
2
3
time (ms)
4
5
6
46.4
23.3
Vcav1
Vcav2
vector sum
46.3
Vector Sum amplitude (MV)
cavity voltage amplitude (MV)
23.2
23.1
23
22.9
46.2
46.1
46
45.9
45.8
22.8
45.7
1
1.2
1.4
1.6
1.8
2
time (ms)
2.2
2.4
2.6
2.8
1.4
1.6
1.8
2
time (ms)
2.2
10% variation in
Lorentz Force detuning
KL,1=-2.0 Hz/(MV/m)2
KL,2=-2.2 Hz/(MV/m)2
PI FB controller
5 ms delay in FB loop
loop closed at start
of beam pulse
2.4
O. Piquet, CEA Saclay, simulation, LLRF09 workshop
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
20/23
sLHC
Two cavities per klystron
high energy part of LPSPL
200
Vcav1
Vcav2
150
1.5
cavity voltage phase (deg)
100
cavity voltage phase (deg)
Vcav1
Vcav2
2
50
0
-50
1
0.5
0
-0.5
-100
-1
-150
-1.5
-200
0
1
2
3
time (ms)
4
5
6
1
1.5
2
2.5
time (ms)
2
vector sum
phase
Vector Sum phase (deg)
1.5
1
0.5
Typical results needing
refinement, but showing
that delay is not (so) crucial
0
-0.5
1.2
1.4
1.6
1.8
2
time (ms)
2.2
2.4
O. Piquet, CEA Saclay, simulation, LLRF09 workshop
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
21/23
sLHC
Power overhead due to field stabilization,
perturbations
Lorentz force detuning (cavity is not on tune during entire beam pulse)
Micro-phonics (cavity tune oscillating due to external perturbations)
Ripple+droop from high voltage leading to a modulation of the klystron phase
Transients at loop closure (and opening)
Transients at beam arrival (and beam out), effect of chopping of beam
Feedforward can be used, pulse to pulse, but many perturbations will have
varying or non-correlated parts from pulse-to-pulse
A low group delay in the loop is desirable in order to be able to keep cavity
voltage in phase and amplitude within specs in presence of non-repetitive
perturbations, simulations needed to show limits as function of group delay
Simulations continue to justify a reasonable overhead in installed RF power
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
22/23
sLHC
Conclusions
SPL parameters reviewed
Optimization of Qext very important,
should settle to a nominal QL and error bars for simulation
Delay and Power budget, power more critical, ~12 ms delay ok
Lorentz Force detuning and its compensation crucial, need more input from tests for
modeling and realistic assumptions of residual detuning not compensated by piezos
Layouts and perturbations to be considered in the simulations
First simulation results for one high energy RF station (O. Piquet & M. Hernandez)
Future: continue simulations towards a string of cavities and move to low energy part,
include b change along accelerator, model klystron, circulator …
W. Hofle @ 3rd SPL
collaboration Meeting
November 12, 2009
23/23