active control of lorentz-detuning and microphonics · - stiffness: depends on young’s modulus of...

Active Control of Lorentz-Detuning

M. Liepe, W.D. Möller, H.-B. Peters, S.N. Simrock

I Why?Lorentz-force detuning, microphonicsand power requirements

II How?The piezoelectric tuner: principle, layout, control, ...

III Can it work?Reliability: high dynamic operation, low temperature, radiation,Controllability: coupling to mechanical modes

IV First ResultsThe piezo as a sensor: microphonics, mechanical oscillations,The piezo as an active element: lorentz-detuning compensation

and Microphonics

I Why?

• Pulsed Operation of s.c. Cavities:

time [ms]

am

plitu

de

[a

.u]

0.50.0 1.0 1.5

gradient

time dependent detuning!

0

time dependent gradient+ inertial mass of cavity walls

⇓

∆f

TESLA: 950µs flat top5 to 10 Hz repetition rate

SNS: 1 ms flat top60 Hz (!) repetition rate

Lorentz-vibration model: differential equation for mode #k:

d2∆ f k

dt2

---------------ωk

Qk------

d∆ f k

dt------------- ωk

2∆ f k+ + KkEacc2= ∆f ∆

k∑ f k=

M. Liepe, April 2001

electromagnetic field exerts

deformation of cavity

resonance frequency shift∆f

⇓

⇓

Lorentz-forces

(detuning) ∆f f cav f gen–=

0 500 1000 1500 2000

−600

−500

−400

−300

−200

−100

0

100

200

time [usec]

de

tun

ing

[H

z]

cavity AC59 at 20, 25, 30 and 34 MV/m


• Lorentz-Force Detuning:

0 200 400 600 800 1000 1200−450

−400

−350

−300

−250

−200

−150

−100

−50

0

E2 [(MV/m)2] fr

eq

ue

ncy d

rift

du

rin

g F

T [

Hz]

frequency drift during 800 usec flat top

fit for Km

=−0.36

measured 20 MV/m

25 MV/m

30 MV/m

34 MV/m

TESLA 9-cell cavityFrequency drift during 800µs flat top

Frequency drift during 950µs flat top (TESLA 9-cell cavity):

∆ f FT 0.4 to 0.65( )–Hz

MV m2⁄

--------------------Eacc2≈


• The Problem:

detuning of cavity during 950µs FT:

TESLA 9-cell cavity:

K=0.4 ... 0.65 Hz/(MV/m)2

required power to keep the gradientand phase constant:

∆ f FT f cav f gen–= K– E2=

Pcomp

P ∆f 0=( )-------------------

14--- ∆f

f 1 2⁄----------

2E

4∝=

⇒ At high gradients significant additional power would be required to keep the gradient and phase constant!

⇒ Increase stiffness of the cavity oruse a fast piezo-tuner foractiveLorentz-force compensation.


• Simulation for 35 MV/m (TESLA800):

0 500 1000 1500 2000−5

0

5

10

15

20

25

30

35

40

time [µs]

grad

ient

[MV/

m] ,

pha

se [2

deg

] , d

etun

ing

[20

Hz]

0 500 1000 1500 2000−20

−10

0

10

20

30

40

time [µs]

grad

ient

[MV/

m] ,

pha

se [2

deg

] , d

etun

ing

[20

Hz]

0 500 1000 1500 20000

100

200

300

400

500

600

700

time [µs]

forw

ard

powe

r [kW

]

0 500 1000 1500 20000

100

200

300

400

500

600

700

time [µs]

forw

ard

powe

r [kW

]

TESLA 9-cell cavity with detuning:

time [µs] time [µs]

time [µs]time [µs]

TESLA 9-cell cavity with compensated detuning during flat top:

additional power

detuning

detuning

gradient

gradient

phase

phase

power

power

grad

ient

[ΜV

/m]

detu

ning

[20

Ηz]

- ph

ase

[2 de

g]

grad

ient

[ΜV

/m]

detu

ning

[20

Ηz]

- ph

ase

[2 de

g]

pow

er [k

W]

pow

er [k

W]

’distance from cavity’ [cm

]

time [µs]

amplitude [arb. units]

’distance from cavity’ [cm

]

time [µs]

amplitude [arb. units]

0 500 1000 1500 2000−5

0

5

10

15

20

25

30

35

40

time [µs]

grad

ient

[MV/

m] ,

pha

se [2

deg

] , d

etun

ing

[20

Hz]

0 500 1000 1500 2000−20

−10

0

10

20

30

40

time [µs]

grad

ient

[MV/

m] ,

pha

se [2

deg

] , d

etun

ing

[20

Hz]


am

plit

ud

e [

arb

. u

nits]

"dis

tanc

e fr

om c

avity

" [c

m]

"dis

tanc

e fr

om c

avity

" [c

m]


• Standing Waves in the Input Coupler / Waveguide:

gradient gradient

detuning

detuning

grad

ient

[ΜV

/m]

detu

ning

[20

Ηz]

- ph

ase

[2 de

g]

-


• CW Operation of s.c. Cavities:- Microphonics: modulation of resonance frequency by external

mechanical disturbances- thin wall-thickness and small bandwidth of superconducting cavities

⇒ sensitive to microphonics

detuning of cavity due to microphonics ⇒ additional power required to keep

the gradient and phase constant:

for matched QL:

Pcomp

P ∆f 0=( )-------------------

14--- ∆f

f 1 2⁄----------

2=

QL

Vacc

R Q⁄( )I beam------------------------------=

⇒ At high QL (i.e. low beam current)

to keep the gradient and phase constant!significant additional power would be required


• Example: TESLA 9-cell Cavity at 10 MV/m

106

107

108

0

5

10

15

20

25

Ql

po

we

r [k

W]

0 Hz 10 Hz20 Hz30 Hz40 Hz50 Hz

106

107

108

0

5

10

15

20

25

Ql

po

we

r [k

W]

0 Hz 10 Hz20 Hz30 Hz40 Hz50 Hz

beam current: 1mA beam current: 0.1mA

⇒ At low beam currents microphonics should be low!Use a fast tuner to compensate external

mechanical disturbances.


⇒ fast frequency tuner based on piezotranslators!II How?

• Principle:

piezoHe-tank

He-tankbellow

bellow


• Proof of Principle Setup of a fast Piezo-Tuner:

Piezo-Actuator:

Umax=150Vl = 39 mm

∆l≈ 4 to 5µm at 2K∆fmax, static≈ 500Hz

He-tank

piezo

tuning mechanism

+ cavity


• Fundamentals of Piezo-Actuators:

multilayer design

+

electric dipoles:anisotropic crystal structureafter poling

randomly orientatedWeiss domains(group of parallelorientated dipoles)

before poling:

poling (electric field applied to the piezo):electric dipoles align, material expands along the field axis

after poling:remanent polarization

When an electric voltageis applied, the Weissdomains increasestheir alignment andthe material expands.


• New Piezo-Holder for two Stacks

preload

piezostack piezostackplace for 2nd

with Lever Motion Amplifier:


• Prototype Tuner for TESLA

tuning

cavity withHe-tank

mechanical tuner(dog bone design)

possible positionfor piezos?

⇒ under study


• Piezostacks:

- maximum stroke at room temperature: ≈ 0.1% of stack lengthwithout external forces

- maximum stroke at 2K: ≈ 10 to 15% of stroke at room temp.

- stiffness: depends on Young’s Modulus of the ceramic(≈ 25% that of steel), the cross section and the length of the ceramic(plus a number of nonlinear parameters)

- maximum force generation:high pushing forces < stiffness * max. stroke,but reduction in displacement!

- preload: zero point is offset, but piezostack will not lose any travel

- mechanical damage: piezo ceramics cannot withstand high pulling forcesor shear forces

- electrical behavior: capacitor (first order estimation)

- heat generation: loss factor in the order of 1 to 2% (at room temp.)


• Control Principle: Lorentz-Force Compensation

⇒ Adaptive feedforward control:

system model

optimizecontrol table

piezo

rf pulsecavity

detuning


• Control Principle: Compensation of Microphonics

system model piezo

cavity

detuning

calculatecontrol signal

⇒ A simple proportional feedback control can not be used!(mechanical resonances)


III Can it work?

The piezo-actuator has to work reliable at

• high dynamic operation: TESLA: 3⋅109 rf-pulses in 10 years of operation (10 Hz)

SNS: 2⋅1010 rf-pulses in 10 years of operation (60 Hz)

• at 2K: only a fewµm travel ⇒ low mechanical stress

• in radiational environment: up to some MGray / 10 years


• High Dynamic Operation of a Piezo:Statement by PIEZOMECHANIK:

“This operation mode is characterized by the high acceleration forces act-ing in the piezostack or ring. One popular application in the near future willbe thepiezo triggered Diesel fuel injection, where the control valve ispiezoactuated in theµs-range with maximum stroke.

In the early days of this application, a typical failure mechanism was thegeneration of cracks inside the ceramic, which was the starting point forelectrical break down and short-circuiting of the stacks. ...

An essential contribution to the stack’s reliability under dynamic cycling isthesufficiently high preloading of stacks in the range of 50% to 100% ofthe specified maximum loads.

PIEZOMECHANIK’s actuator are well-known for their excellent stability

under high dynamic operation showing aperformance of more than 1010

cycles. ...”


• Piezo used for Diesel Fuel Injection:

U = -60 to 160 Vsize: 30 x 7 x 7 mm

∆l ≈ 40 µm at room temp.


• Sensitivity of a Piezostack to Radiation:

Component Damage and utility

piezo-electricalcrystal

magneticmaterialsinorganicmaterials

resistors

capacitors

electron tubes

transducers

organicisolation

semiconductors

γ-radiation [gray] 1 102 104 106 1010 1012108

From Cern Report: 75-18

TESLA:Radiation limit:average 10 Gray/h(2K heat load 0.1W/m)i.e. < 2 MGray / 20 years

> 100 MGray

Damageincipient to mildmild to moderatemoderate to severe

Utilitynearly always usableoften satisfactorylimited use


• Controllability:

for a linear system:ideal system: same coupling to all modes:

real system:

⇒ K is invertible, if all rows are≠ 0, i.e. if thepiezo is coupling to all modes (and if all rows and columns are different).

If not, place second piezo at aappropriate place.

∆f ω1( )…

∆f ωN( )

K

Vpiezo ω1( )…

Vpiezo ωN( )

=

∆f ω1( )…

∆f ωN( )

K11 … K1N

… … …KN1 … KNN

Vpiezo ω1( )…

Vpiezo ωN( )

=


IV First Results

• used piezo as asensor:⇒ measure piezo-voltage⇒ oscillations (rf-pulses, microphonics)

• tested piezo as anactive element:⇒ apply voltage to piezo⇒ damping / excitation of oscillations⇒ Lorentz-force compensation


• The Piezo as Sensor:

0 0.02 0.04 0.06 0.08 0.1

−0.4

−0.2

0

0.2

0.4

0.6

time [s]

−(pie

zo−v

oltag

e) [

V]

The cavity oscillates between the RF-pulses.

RF-pulse with Lorentz-force detuning

TESLA 9-cell Cavity at 30 MV/m with 10 Hz repetition rate:

- vo

ltage

[V

]mechanical oscillations due to Lorentz-force detuning:


0 0.05 0.1 0.15 0.2 0.25 0.3

−0.6

−0.4

−0.2

0

0.2

0.4

The oscillation is highly repetitive from pulse to pulse.⇒ Same initial detuning at the beginning of the RF pulses!

RF-pulse

TESLA 9-cell Cavity at 30 MV/m with 10 Hz repetition rate:

time [s]

- vo

ltage

[V

]


• Spectrum of the mechanical Oscillations

0 200 400 600 800 100010

−1

100

101

102

mechanical resonances of the cavity

frequency [Hz]

ampl

itude

[arb

. uni

t] due to the RF Pulses (Example):

He-system

pumps


• Frequency Spectrum of Oscillation for 2 Cavities (30MV/m 2Hz)

100 200 300 400 500 6000

1

2

3

4

5

6

7

frequency [Hz]

ampl

itude

[arb

. uni

ts]


• Comparison between the Piezo Signal and the Phase-Variation

0 0.05 0.1 0.15 0.2 0.25−0.5

0

0.5

time [s]

due to Microphonics (Example):

⇒ Clear correlation!⇒ Oscillation can be damped by a piezo-tuner.

phas

e [d

eg]

-6⋅V

piez

o [V

]

cw-operation, open loop


• Microphonics Spectrum:

0 0.05 0.1 0.15 0.2 0.25 0.3−40

−30

−20

−10

0

10

20

30

40

time [s]

detuni

ng [Hz

]de

tuni

ng [H

z]

time [s]

cw-operation of 9-cell cavity

0 200 400 600 800 10000

2

4

6

8

10

12

frequency [Hz]

am

plit

ud

e [

Hz]

pumps,He-system

mechanical resonance

⇒ Only a few frequencies!

0 200 400 600 800 10000

0.005

0.01

0.015

0.02

0.025

frequencypiezo

[Hz]

ampl

itude

[arb

. uni

ts]


• Piezo as an active Element: Excitation of mechanical Modes

2 dominating groups ofmechanical modes


−200

−100

0

100

200

300

400de

tuni

ng [H

z]

0 500 1000 1500 2000time [µs]

fill time 900 µs constant gradient

without compensation

with compensation

“beam on”- time

TTF 9-cell cavity operated in pulsed mode at 23.5 MV/m (TESLA500)• Piezo as an active Element: Lorentz-Detuning Compensation


0 500 1000 1500 2000−5

0

5

10

15

20

25

30

35

40

time [µs]

grad

ient

[MV/

m] ,

pha

se [2

deg

] , d

etun

ing

[20

Hz]

0 500 1000 1500 20000

100

200

300

400

500

600

700

time [µs]

forw

ard

powe

r [kW

]


detuning

gradient

phase

power

grad

ient

[ΜV

/m]

detu

ning

[20

Ηz]

phas

e [2

deg]

pow

er [k

W]

• Lorentz-Detuning Compensation:

−200

−100

0

100

200

300

400

detu

ning

[Hz]

0 500 1000 1500 2000time [µs]

fill time 900 µs constant gradient

without compensation

with compensation

“beam on”- time

Simulation:

Measurement:


• Future Plans:

Proof of Principle: Active Lorentz-Detuning Compensation

Investigatemechanical oscil-lations of cavitiesin detail:

measurements,FE-models.

Design, built andtest a prototypepiezo-tuner.

Develop feedfor-ward control.

Test reliability:

Long term oper-ation at 2K andradiation hard-ness of differenttypes of piezoac-tuators.

Reliable, well understood piezoelectric tuner.

workstarted

active control of lorentz-detuning and microphonics · - stiffness: depends on young’s modulus of...

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