operational aspects of sc rf cavities with beam · two different sources excite the accelerating...

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


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?


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


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


The mode we love so much: TM010

electric field magnetic field

⇒ acceleration

lowest frequency mode:

transverse magnetic

0 ⇒ monopole mode

z


The Accelerating Mode in an Elliptical RF Cavity

electric field

for ILC cavities

magnetic field


Multi-cell Cavities• N coupled cells ⇒ N TM010 modes = TM010 passband!

• Highest frequency mode (π-mode) is the accelerating mode


The Accelerating Mode

t=0

t=T/2

t=T/4

electron bunch


Accelerating Voltage Accelerating π-mode:

Accelerating voltage:

( )∫+

−==

2/

2/

/

chargegain energy maximum L

L

czizacc dzeEV ω

lengthcavity active

Vacc=accE

Accelerating field gradient:


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!


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


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


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, …


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


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−=


Example: FLASH

time

gene

rato

r po

wer

The generator and the beam induced voltage compensate each other if QL is properly adjusted.


Complex Phasor Diagram

Vb

Vb

Vg

V

( ) bacc VVV φcosˆRe ==

angle tuningtan2/1

1 =⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ=Ψ −

ωω


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


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


Steady State • Sum of beam induced and generator induced

voltage is not constant, but shows saw-like shape!

time [μs]

volta

ge [M

V]


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


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


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

QQ

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)


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


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


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:


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!


Example 1: Bunch Charge Fluctuations


Example 2: Beam Transients


Example 3: Excitation of Passband Modes (I)

Example: TTF/Flash 9-cell cavity[a

rb. u

nits

]


Example 3: Excitation of Passband Modes (II)

Example: TTF 9-cell cavity with 1 MHz beam

M. Ferrario et al.

bunchbunch bunch


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


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)


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


LLRF Control: A complex System

Many connected subsystems…


LLRF Hardware

Virtex II FPGADSP


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


Achieved Energy Stability: TTF/FLASH


Adaptive Feedforward (SNS, FLASH)

• Adaptively adjusted forward power to compensate beam transients in pulsed mode operation


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:


Beam Based Calibration


Setting the RF Phase at SNS (I)


Setting the RF Phase at SNS (II)


Setting the RF Phase at SNS (III)


Field Calibration based on Single Bunch Transients

P. PAWLIK, M. GRECKI, S. SIMROCK


More cavity eigenmodes: Higher-Order-Modes

• Beam excitation

• HOM heating issues

• Beam based HOM damping measurements

• HOM based BPM


Higher-Order-Mode Excitation

time

The bunched beam excites higher-order-modes (HOMs) in the cavity.

bunch

bunch

bunch


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


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!


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.


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 )()(||


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


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]


Example: HOM Power Heating• Example: Shielded bellows at KEK-B:– Comb-type RF shield developed to replace RF

fingers.


Absorbing High Frequency HOM Power


Example: HOM Heating at SNS

Beam pipe temperature increases by beam induced heating


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!


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,


Cavity Performance and Performance Degradations

- Some Examples -


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

– …


Example 1: FLASH Linac


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”!


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


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


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

]


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


Example 2: SNSDesigned to operate at 2.1 K

(superfluid helium)

Return end can

Helium vessels

Space frame

Supply end can

Fundamental power couplers


Cavity Limitations at SNS (I)


Cavity Limitations at SNS (II)


SNS: HOM Loop-Coupler Problems


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


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)


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


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


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


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


CEBAF: Type of Cavity Performance Limitation


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.


Emittance Dilution caused by SRF Cavities

- Some Examples -


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∝


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


Example 3: Cavity Misalignment• Cavity and cryomodule offset and tilt cause

emittance growth


Example 4: BBU from high Q HOM

• Insufficiently damped dipole modes can cause emittance growth and even beam break-up


Conclusion

SRF Cavity and Beam

What would be one without the other?

If we do it right, they both can be happy…

operational aspects of sc rf cavities with beam · two different sources excite the accelerating...

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