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1Matthias Liepe October 13, 2007
Matthias Matthias LiepeLiepeDepartment of Physics, CLASSEDepartment of Physics, CLASSE
Cornell UniversityCornell University
Operational Aspects of SC RF Cavities with Beam
2Matthias Liepe October 13, 2007
And there was beam…
• Two different points of view:– The SRF cavity view:• I could function so nicely if the beam wouldn't cause
such a mess…
– The beam view:• OK, gaining energy is nice, but why do these cavities
also have to disturb me so much?
3Matthias Liepe October 13, 2007
The Cavity and the Beam…Impact on the Beam:• Energy gain, energy
stability• Emittance growth– Short range wake fields– HOM fields, BBU– Transverse kick fields
• Cavity misalignment• Asymmetry from
couplers, …– RF focusing
• Beam loss due to RF trips
Impact on the SRF cavity:• Beam loading, field
perturbations, increased RF power
• Beam based field calibration
• HOM power handling and heating issues
• Beam induced trips• Cavity performance
with beam
4Matthias Liepe October 13, 2007
Let’s start “simple”: The Fundamental mode (passband) and the beam
• Accelerating field
• Beam induced fields: Single bunch and bunch train
• Beam loading and optimal loaded Q
• Beam induced field perturbations
• LLRF field control
• Beam based field calibration
5Matthias Liepe October 13, 2007
The mode we love so much: TM010
electric field magnetic field
⇒ acceleration
lowest frequency mode:
transverse magnetic
0 ⇒ monopole mode
z
6Matthias Liepe October 13, 2007
The Accelerating Mode in an Elliptical RF Cavity
electric field
for ILC cavities
magnetic field
7Matthias Liepe October 13, 2007
Multi-cell Cavities• N coupled cells ⇒ N TM010 modes = TM010 passband!
• Highest frequency mode (π-mode) is the accelerating mode
8Matthias Liepe October 13, 2007
The Accelerating Mode
t=0
t=T/2
t=T/4
electron bunch
9Matthias Liepe October 13, 2007
Accelerating Voltage Accelerating π-mode:
Accelerating voltage:
( )∫+
−==
2/
2/
/
chargegain energy maximum L
L
czizacc dzeEV ω
lengthcavity active
Vacc=accE
Accelerating field gradient:
10Matthias Liepe October 13, 2007
Coupling Strength: R/Q
Shunt-impedance: Quality factor:
( )dis
accsh P
VR
2
2
=dis
L PU
Qω=
( )U
V
Q
R
Q
R acc
L
sh
ω2
2
==
Note: Here I use the circuit definition of the shunt impedance. The so-called accelerator definition of it is a factor of 2 larger!
11Matthias Liepe October 13, 2007
Excitation of the Fundamental Mode
Two different sources excite the accelerating mode:
• RF Generator (power source)– RF power at the fundamental mode frequency is
coupled into the cavity via the input coupler
• Beam current– Bunches / bunch train excites the fundamental
mode
12Matthias Liepe October 13, 2007
Equivalent Circuit ModelThe full picture: generator - transmission line - coupler - cavity
coupler acts like a transformer:
V2 = N V1
I2 = 1/N I1
generator:2
02
1gg IZP =
cavity modeled as LCR circuit:
Note: R is the shut impedance,
not Rsurf!
beam current
13Matthias Liepe October 13, 2007
Simplified Circuit Model
transformed external load:
02ZNZext =
fictitious generator current:
gg NII /2~ =
⇒ Use this model to simulate cavity filling, RF field control, beam loading, …
14Matthias Liepe October 13, 2007
More Figures of Merit…
Resonance frequency: LCf 12 00 ≈= πω
Intrinsic quality factor:L
R
P
UQ
wall 00 ω
ω ==
External quality factor:L
Z
P
UQ ext
extext
0ωω ==
Loaded quality factor: ⎥⎦
⎤⎢⎣
⎡+
==ext
ext
totalL ZR
RZ
LP
UQ
0
1
ωω
Bandwidth of mode:LQ2/02/1 ωω =
Cavity detuning:driveωωω −=Δ 0
15Matthias Liepe October 13, 2007
Beam induced voltage (beam starts at t = 0):
( )( ) titibL
bbee
i
IQQ
R
tV ωωω
ωω 1
1
2)(
2/1
2/1 Δ−−−Δ−=
Generator and Beam Induced VoltageGenerator induced voltage (for constant generator power):
( )( ) titigL
ggee
i
PQQ
R
tVωωω
ωω 1
1
8
)(
2/1
2/1 Δ−−−Δ−=
16Matthias Liepe October 13, 2007
Example: FLASH
time
gene
rato
r po
wer
The generator and the beam induced voltage compensate each other if QL is properly adjusted.
17Matthias Liepe October 13, 2007
Complex Phasor Diagram
Vb
Vb
Vg
V
( ) bacc VVV φcosˆRe ==
angle tuningtan2/1
1 =⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ=Ψ −
ωω
18Matthias Liepe October 13, 2007
Single Bunch• So far: treated beam as an AC current
• Reality: bunches!
• Accelerating mode voltage induced by a single bunch:
• On average, bunch “sees” half of its own induced field:
(fundamental theorem of beam loading)
bunchbunch qQ
RV 0ω=Δ
bunchbacc VVV2
1cosˆ −= φ
19Matthias Liepe October 13, 2007
Bunch Train• Need to sum individual bunch induced
voltages:
⇒ Substructure!
⇒ Envelope given by previous equation
time [μs]
beam
indu
ced
volta
ge [k
V] Example: For
first 10 bunches
[ ]...1 222/12/1 +++= ΔΔ−Δ−ΔΔ−Δ− bbbb TiTTiTbunchtrain eeeeVV ωωωω
20Matthias Liepe October 13, 2007
Steady State • Sum of beam induced and generator induced
voltage is not constant, but shows saw-like shape!
time [μs]
volta
ge [M
V]
21Matthias Liepe October 13, 2007
But there are N TM010 modes in a N-cell Cavity…
Both, the generator and the beam will not only excite the accelerating TM010 mode, but with small amplitudes also all other TM010 modes:
Example: TTF 2x7-cell superstructure
22Matthias Liepe October 13, 2007
field amplitude total accelerating voltage
time [μs] time [μs]
sum over all cells!
cell #13
cell #1
Note:
- Energy transport from one cell to another requires excitation of more than one mode!
Resulting Bunch to Bunch Energy
Fluctuation
23Matthias Liepe October 13, 2007
RF Power Requirements with Beam
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛+Δ+⎟⎟
⎠
⎞⎜⎜⎝
⎛+=
2
2/1
22
sin2cos218
bacc
bextb
acc
bext
ext
accg V
IQ
Q
R
V
IQ
Q
R
RV
P ϕω
ωϕ
bb
accopt
IQ
R
VQ
ϕcos2 ⎟⎟⎠
⎞⎜⎜⎝
⎛=
The RF power required to maintain an accelerating voltage Vacc is given by:
From this one can calculate, that the minimum RF power is required if:
beam phase
optimal loaded Q:
optimal cavity detuning: bacc
bopt V
I
Q
R ϕωω sin0−=Δ
All power is transferred to the beam (no reflected power)
24Matthias Liepe October 13, 2007
Example 1: Cornell ERL 2-cell Cavity (on-crest acceleration):
1 2 3 4 5 6 7 8 9 10x 104
0
50
100
150
200
250
1 MV, 100 mA0.8 MV, 100 mA
1.2 MV, 100 mA
optimal QL
Req
uire
d po
wer
[kW
]
QL
25Matthias Liepe October 13, 2007
Example 2: Cornell ERL Main Linac
ERL: ⇒ No effective beam loading in main linac!(accelerated and decelerated beam compensate each other)
ff
Qopt Δ= 0
21
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ+=2
2/1
21
8 ff
QQrV
P
L
g
106
107
108
1090
5
10
15
20
loaded QRF
dri
ve p
ow
er [
kW]
Δf=0 Hz10 Hz20 Hz30 Hz40 Hz
26Matthias Liepe October 13, 2007
ERL Cavity Operation at QL=108
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
time [sec]
klys
tron
pow
er [k
W] 5.5 mA
4 mA2.5 mA0 mA
Power for cavity operation at 12.3 MV/m at the JLAB FEL:
27Matthias Liepe October 13, 2007
Beam induced Field PerturbationsFrom• Beam current modulations• Bunch to bunch charge fluctuations• Return phase fluctuation of the decelerated beam
in and ERL• Potential instabilities in storage rings (coupling of
energy and path length)• Pulsed beam transients (FLASH, ILC, SNS)• Excitation of other passband modes⇒ Beam energy fluctuation!
28Matthias Liepe October 13, 2007
Example 1: Bunch Charge Fluctuations
29Matthias Liepe October 13, 2007
Example 2: Beam Transients
30Matthias Liepe October 13, 2007
Example 3: Excitation of Passband Modes (I)
Example: TTF/Flash 9-cell cavity[a
rb. u
nits
]
31Matthias Liepe October 13, 2007
Example 3: Excitation of Passband Modes (II)
Example: TTF 9-cell cavity with 1 MHz beam
M. Ferrario et al.
bunchbunch bunch
32Matthias Liepe October 13, 2007
Example 4: ERL with Return Phase Error
y = 0.031x2 + 0.0635x + 0.2767
y = -0.0041x2 + 0.0664x + 0.2829
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5Beam Current (mA)
RF
Pow
er (
kW)
Tuners ONTuners OFFPoly. (Tuners OFF)Poly. (Tuners ON)
. Cavity tuners need to adjust the cavity detuning to its optimal value to compensate for the reactive loading
Tom Powers, Chris Tennant; TJNAF FEL
IaccIdec Inet
33Matthias Liepe October 13, 2007
Field Stability Requirements• Different accelerators have different
requirements for field stability!
• approximate RMS requirements:– 1% for amplitude and 1 deg for phase (storage
rings, SNS)
– 0.1% for amplitude and 0.1 deg for phase (linear collider, …)
– down to 0.01% for amplitude and 0.01 deg for phase (XFEL, ERL light sources)
34Matthias Liepe October 13, 2007
LLRF Field Control: Concept
• Measure cavity RF field.
• Derive new klystron drive signal to stabilize the cavity RF field.
• Derive new frequency control signal.
Frequency tuner
35Matthias Liepe October 13, 2007
LLRF Control: A complex System
Many connected subsystems…
36Matthias Liepe October 13, 2007
LLRF Hardware
Virtex II FPGADSP
37Matthias Liepe October 13, 2007
Perturbation Compensation: Feedback and Feedforward
• Active Control of Perturbations– Feedforward: (fixed or adaptive)
– Feedback:• Measured cavity field• Klystron output• Cavity detuning• Beam energy• Bunch length
• Klystron drive• Frequency tuner drive
• Vibration signals• Beam current• HV PS ripple
• Klystron drive• Frequency tuner drive
38Matthias Liepe October 13, 2007
Achieved Energy Stability: TTF/FLASH
39Matthias Liepe October 13, 2007
Achieved Energy Stability: TTF/FLASH
40Matthias Liepe October 13, 2007
Adaptive Feedforward (SNS, FLASH)
• Adaptively adjusted forward power to compensate beam transients in pulsed mode operation
41Matthias Liepe October 13, 2007
ERL high QL Cavity Test OperationWith feedback: Very good field stability with 5 mA ERL
beam:
0 0.2 0.4 0.6 0.8 112.1
12.2
12.3
12.4
time [sec]acce
lera
tin
g f
ield
[M
V/m
]
0 0.2 0.4 0.6 0.8 19
9.5
10
10.5
11
ph
ase
[deg
]
time [sec]
σA/A ≈ 1·10 - 4
σϕ ≈ 0.02 deg
0 0.2 0.4 0.6 0.8 1
-100
0
100
phas
e [d
eg]
time [sec]
0 0.2 0.4 0.6 0.8 10
5
10ac
cele
ratin
g fie
ld
[MV
/m]
time [sec]
Without feedback:
42Matthias Liepe October 13, 2007
Beam Based Calibration
43Matthias Liepe October 13, 2007
Setting the RF Phase at SNS (I)
44Matthias Liepe October 13, 2007
Setting the RF Phase at SNS (II)
45Matthias Liepe October 13, 2007
Setting the RF Phase at SNS (III)
46Matthias Liepe October 13, 2007
Field Calibration based on Single Bunch Transients
P. PAWLIK, M. GRECKI, S. SIMROCK
47Matthias Liepe October 13, 2007
More cavity eigenmodes: Higher-Order-Modes
• Beam excitation
• HOM heating issues
• Beam based HOM damping measurements
• HOM based BPM
48Matthias Liepe October 13, 2007
Higher-Order-Mode Excitation
time
The bunched beam excites higher-order-modes (HOMs) in the cavity.
bunch
bunch
bunch
49Matthias Liepe October 13, 2007
Higher-Order-Mode Excitation
bunch
•Short range wake-field: Fields inside the bunch and just behind it
•Long range wakes (Higher-Order-Modes)•Monopole modes: RF heating and longitudinal emittance dilution
•Dipole modes: transverse emittance dilution and beam break-up
50Matthias Liepe October 13, 2007
HOM Excitation by a Single BunchThe HOM power excited by a single bunch depends on:
• the HOMs of the cavity (cavity shape),
• the bunch charge (PHOM∝q2),
• the bunch length (i.e. the spectrum of a bunch).
0 20 40 60 80 1000
20
40
60
80
100
HOM frequency [GHz]% o
f H
OM
po
wer
loss
ab
ove
f HO
M
Example:
σbunch = 0.6 mm⇒ Short bunches can excite very high frequency modes!
51Matthias Liepe October 13, 2007
HOM Excitation by a Bunch Train
The excited HOM power of a bunch train depends on:
the HOM excitation by the individual bunches,
the beam harmonic frequencies and the HOM frequencies (resonant excitation is possible!),
the bunch charge and the beam current
and the external quality factor, Qext of the modes.
52Matthias Liepe October 13, 2007
Average Monopole Power
• Bunch excites EM cavity eigenmodes (Higher-Order Modes)
• Single bunch losses determine the averagemonopole HOM power per cavity.
bunch
-5 -4 -3 -2 -1 0 1 2 3 4 5-30
-20
-10
0
S [mm]wak
e p
ote
nti
al W
[V
/pC
]
bunch
sdsswsqsWs
′′−′= ∫∞−
)()()(
beambunchIQkP |||| =
0 50 100 150 200 25010 -6
10 -4
10 -2
10 0
frequency [GHz]
no
rmal
ized
inte
gra
l o
f lo
sses
600 μm
Loss Factor:
∫∞
∞−= dssWsqk )()(||
53Matthias Liepe October 13, 2007
Resonance Monopole Mode Excitation
If a monopole mode is excited on resonance, the loss for this mode can be very high:
22 beamQIQ
RP ⎟⎟
⎠
⎞⎜⎜⎝
⎛= Need strong HOM damping!
⇒ Example: To stay below 200 W with I=200 200 W with I=200 mAmA: • achieve (R/Q)Q < 2500 (R/Q)Q < 2500 ΩΩ, • or avoid resonant excitation of the mode.
Resonant MonopoleMonopole ModeMode Excitation if fHOM=N⋅fbunch
54Matthias Liepe October 13, 2007
Example: ERL Main Linac Cavity• No high Q monopole modes near first beam
harmonics (2.6 GHz, 5.2 GHz)
2400 2600 2800
102
104
106
Q
frequency [MHz]5000 5200
102
104
106
Q
frequency [MHz]
55Matthias Liepe October 13, 2007
Example: HOM Power Heating• Example: Shielded bellows at KEK-B:– Comb-type RF shield developed to replace RF
fingers.
56Matthias Liepe October 13, 2007
Absorbing High Frequency HOM Power
57Matthias Liepe October 13, 2007
Example: HOM Heating at SNS
Beam pipe temperature increases by beam induced heating
58Matthias Liepe October 13, 2007
Beam Based HOM Damping Measurements
• The beam can be used to excite HOMs on purpose to search for weakly damped / trapped HOMs. TTF/Flash results with current modulated beam
reveled several weakly damped modes.
Some of them where initially not predicted by numerical
HOM calculations!
59Matthias Liepe October 13, 2007
Cavity HOMs can be used as a BPMAngular scan resolutionand accuracy < 50 µrad
Relative position resolution~ 4 µm
(cf. M. Ross and J. Frisch).-1 0 1 2 3
Transverse beam offset [mm]
HO
M a
mp
litu
de
[ar
b. u
nit
s]
courtesy N. Baboi,
60Matthias Liepe October 13, 2007
Cavity Performance and Performance Degradations
- Some Examples -
61Matthias Liepe October 13, 2007
Linac Cavity Performance
• SRF cavity performance can change over time:– “Dust” can propagate through beam pipe into
cavity (beam fields)
– Field emitter can turn on suddenly
– Special events (vacuum leaks…)
– Collective effects
– …
62Matthias Liepe October 13, 2007
Example 1: FLASH Linac
63Matthias Liepe October 13, 2007
Experience from FLASH• Recent measurements show that there is basically
no degradation in gradient vs. time.• Never had vacuum failures or dirt/dust
contaminating the cavities. Also no problems after conditioning etc.
• Conditioned state is preserved also after some time of operation and after some time off.
• So far, there was no need to replace modules due to degradation or failure (but destroyed tuning motors)
⇒ Whole machine is assembled “dust free”!
64Matthias Liepe October 13, 2007
FLASH: Vector Sum Control!
• Need to adjust power distribution according to cavity performance, or weakest cavity will limit all other cavities!!
ACC 6 ACC 5 ACC 4 ACC 3 ACC 2 ACC 1 RF-Gun
Kly 3 (5 MW)
Kly 4 (10 MW)
Kly 5 (5 MW)
Kly 2 (5 MW)
new, XFEL-type RF power distribution
65Matthias Liepe October 13, 2007
FLASH Operation
limited at 33.0 MV/m321 ... 4
limited at 22.0 MV/m215, 6
limited at 26.0 MV/m—251 … 8ACC5
limited at 27.0 MV/m
XFEL type
RF power
distribution267, 8
ACC6
limited at 23.5 MV/m—231 … 8ACC4
limited at 25.5 MV/m—251 ... 8ACC3
quench2186
quench3162
quench1211
limited at 24 .. 25 MV/m—233, 4, 5, 7, 8
ACC2
too high FE3147
—205, 6, 8
capture section, lower gradient—131, 2, 3, 4
ACC1
commentattenuator [dB]
Eacc [MV/m]cavitymodule
66Matthias Liepe October 13, 2007
FLASH Operation
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 80
5
10
15
20
25
30
cavitymodule ACC1 ACC2 ACC3 ACC4 ACC5 ACC6
Eac
c [M
V/m
]
67Matthias Liepe October 13, 2007
FLASH: Module Operation vs. Temperature
Module 6 at CMTBMeas. Qo/Eacc average gradient 10Hz 500/800us
1.0E+10
1.5E+10
2.0E+10
2.5E+10
3.0E+10
0 5 10 15 20 25 30Eacc [MV/m]
Q0
2K 19-Dec-062K 21-Feb-072K 28-Feb-07 FB/piezo1.8K 1-Mar-071.55K 1-Mar-072K 9-Mar-071,8K 9-mar-071,59K 9-mar-07
1.6K
1.8K
2K
68Matthias Liepe October 13, 2007
Example 2: SNSDesigned to operate at 2.1 K
(superfluid helium)
Return end can
Helium vessels
Space frame
Supply end can
Fundamental power couplers
69Matthias Liepe October 13, 2007
Cavity Limitations at SNS (I)
70Matthias Liepe October 13, 2007
Cavity Limitations at SNS (II)
71Matthias Liepe October 13, 2007
SNS: HOM Loop-Coupler Problems
72Matthias Liepe October 13, 2007
SNS: Operating Temperature (I)
0
2
4
6
8
10
12
14
16
8 10 12 14 16 18 20 22 24 26
Eacc (MV/m)
Num
ber
of C
aviti
es
2 K Open loop from 75 cavities tested in 2005
4 K Open loop from 79 cavities tested in 2005
73Matthias Liepe October 13, 2007
SNS: Operating Temperature (II)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
2 2.5 3 3.5 4 4.5
Operating Temperature (K)
No
rmal
ized
Op
erat
ing
Co
st
Duty=1 %
Duty=8 %
Duty=5 %
Duty=3 %
For SNS, operation at 4.2 K is overall more economical up to about ½ of the design beam power (if achieved by reducing repetition rate to 30 Hz)
74Matthias Liepe October 13, 2007
Example 3: KEK-B, Long Term Cavity Operation (I)
(1) maximum accelerating voltage
• All cavities can provide Vc >2 MV after 7 years operation.• Vc of D11C degraded after the vacuum trouble. • Vc of D11B degraded after changing the coupling of the input coupler.
T. Furuya, S. Mitsunobu
75Matthias Liepe October 13, 2007
Example 3: KEK-B, Long Term Cavity Operation (II)
• Unloaded Q at 2MV (8MV/m) has gradually degraded to 3-5x108.• Huge amount of out gas from the ferrite dampers has degraded the
cavity performance?• Baking may recover the performance, but we have to consider the
risk of vacuum leak at the indium seals.• The Q at the operating voltage (1.4MV) still keeps Q >1x109.
(2) Intrinsic Q T. Furuya, S. Mitsunobu
76Matthias Liepe October 13, 2007
KEK-B: Beam Aborts
• The cause of every beam abort is analyzed immediately.• Caused by beam loss (60%), RF (28%), or others (12%).• Average number of beam aborts in two rings caused by any
RF reasons is about once or twice /day.
H. Ikeda
Beam Loss
others
Caused by RF
77Matthias Liepe October 13, 2007
Example 4: CEBAF• See changes in cavity performance vs. time
• Not all of these changes are correlated to external disturbances (warm up, ..)!
Trip rate
1995 vs. 2003before
after
78Matthias Liepe October 13, 2007
CEBAF: Type of Cavity Performance Limitation
79Matthias Liepe October 13, 2007
CEBAF Downtime (1999)
Other than the arc trips, the SRF system directly contributed 48 minutes (less than 0.1%) of the 1620 hours of unscheduled downtime.
80Matthias Liepe October 13, 2007
Emittance Dilution caused by SRF Cavities
- Some Examples -
81Matthias Liepe October 13, 2007
Example 1: Transverse BBU in ERLs
• In an ERL a feedback system formed between cavities and the beam is closed. ⇒ Instability at sufficient high currents (BBU threshold)!
Cavity with dipole higher-order mode
• Simple model for instability beam current:
strong HOM damping (Q Q ≈≈ 101044 to 10to 1055 )!For IBBU > 100 mA, need
QQRIBBU )/(
ω∝
82Matthias Liepe October 13, 2007
Example 2: Coupler Kicks• Input couplers cause transverse, time
dependent kick fields on axis, and thereby emittance growth.
• Solutions– Optimize distance coupler – first cell
– Symmetry
– Compensating stub
83Matthias Liepe October 13, 2007
Example 3: Cavity Misalignment• Cavity and cryomodule offset and tilt cause
emittance growth
84Matthias Liepe October 13, 2007
Example 4: BBU from high Q HOM
• Insufficiently damped dipole modes can cause emittance growth and even beam break-up
85Matthias Liepe October 13, 2007
Conclusion
SRF Cavity and Beam
What would be one without the other?
If we do it right, they both can be happy…