Introduction “ Two modes ” model Method of the calculation for the transient response

SCRF Meeting @FNAL 21-25/Apr/2008SCRF Meeting @FNAL 21-25/Apr/2008 11

Measurement & Calculation of the Lorentz Measurement & Calculation of the Lorentz DetuningDetuning

for the transient response of the resonant for the transient response of the resonant cavitycavity

Measurement & Calculation of the Lorentz Measurement & Calculation of the Lorentz DetuningDetuning

for the transient response of the resonant for the transient response of the resonant cavitycavity

Introduction “Two modes” model Method of the calculation for the transient response Case of Flat-top Comparison between experiment and calculation Next Measurement Plan Summary

Y. Yamamoto, H. Hatori, H. Hayano, E. Kako, S. Noguchi, M. Sato, T. Shishido, K. Watanabe(KEK), H. Hara, K. Sennyu(MHI)

04/21/2304/21/23 TESLA Technology Collaboration MeetingTESLA Technology Collaboration Meeting 22

Improvement in the KEK TESLA-like Cavities

Stiffness of Cavity Fixing Support 80 kN/mm 13 kN/mmLorentz Detuning -480 Hz -1050 Hz (31.5 MV/m)

TTF Cavity

Thick Titanium Baseplate,Thick Nb Beam Tube & Thick Nb End-cell

KEK TESLA-like Cavity

Cell Taper13 deg. → 10 deg.

Beam Tube78 → 84

Input Port40 →

KEK TESLA-like Cavity TTF CavityＦｚ

Ｆｒ


IntroductionIntroductionIntroductionIntroductionThe shape of the resonant cavity is generally deformed by the Lorentz force.

The frequency of the cavity is changed according to the square of the field strength.

The cavity is detuned, and the field may not be constant during the flat-top of the pulse.

It is necessary to compensate or lower the detuning by the Lorentz force.

The methods to do it are following…(1) Using Piezo(2) Setting the initial offset of the frequency to the cavity(3) Increasing the mechanical strength of the cavity

STF base-line cavity is mechanically stronger than TESLA’s one!


Fast mode

Slow mode

Mechanical Oscillation (Two Modes Model)Mechanical Oscillation (Two Modes Model)

Time1.5 msec.

Oscillation Amplitude (Xk)

Eacc

Stationary Amplitude

Offset Compensation

Piezo Compensation

Very roughly speaking, the fast mode is mainly contributed to the Lorentz Detuning before 500μsec and the slow mode after 500 μsec.

The behavior of the filling is considered not to be different between on resonance and the slight detuning.


Two Modes ModelTwo Modes ModelTwo Modes ModelTwo Modes ModelIn this model, the Lorentz detuning is generated by two modes.One is the “fast mode” and the other is “slow”.

fast mode(linear)

slow mode(sine)

500μsec5msec(=200Hz)

300Hz90HzIn the simulation

From the mechanical calculation

slow mode fast mode

Actually, so many modes exist in 9-cell cavity!But, these modes are mainly effective.


U(t)V(t)ωV(t)dt

d

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ω)

Q

Qj(1V(t)

dt

d 2o

L

o

o

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(exp)(exp)~~

(~~

tT

jT

tVVVV

FFdod

Cavity Voltage EquationCavity Voltage Equation

Equi-angular Spiral

If the factor in each term is constant in time, this equation can be solved analytically.But, if not so…

From J.

Slater


Voltage SolutionVoltage SolutionVoltage SolutionVoltage Solution

11,

1,

11

1,1,

expcos~

tanexpexp1~

tanexpexp~

tanexpexp~~~~

nnng

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jV

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tj

T

tV

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1μsec

Generally normalized by 1

Within the very short period (Δt), the following equation is filled and solved analytically.


Used numerical valuesfilling time : Tf = 2QL/ω0

f0 = 1300.25MHzQL = 1.15x106 (from horizontal test for STF B.L. #3

cavity)Δt = 1μsec (sufficiently short)Δf = sine + linear (t<500μsec)

→ sine (t>500μsec)

Expressions and values for the Expressions and values for the calculationcalculationExpressions and values for the Expressions and values for the calculationcalculation

11,

1,

11

1,1,

expcos~

tanexpexp1~

tanexpexp~

tanexpexp~~~~

nnng

Fn

Fng

Fn

Fn

Fn

Fngnngn

jV

T

tj

T

tV

T

tj

T

tV

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tVVVV

tanΨ=-2QLΔf/f0

Used expressions

After 500µsec, the fast mode disappears, because the damping is very fast.


Example of Flat-top Example of Flat-top calculationcalculationExample of Flat-top Example of Flat-top calculationcalculation

Input data (frequency)

Input data (degree)

Output data (VC)

Output data (ΨCavity)

tanΨ=-2QLΔf/f0

fast mode + slow mode

slow mode (sine)

After 500µsec, the fast mode disappears.


Case of Flat-top (offset Case of Flat-top (offset +160Hz)+160Hz)Case of Flat-top (offset Case of Flat-top (offset +160Hz)+160Hz)


One pulse during High-Power Test (+160Hz One pulse during High-Power Test (+160Hz Offset)Offset)One pulse during High-Power Test (+160Hz One pulse during High-Power Test (+160Hz Offset)Offset)


Comparison between experiment and calculation Comparison between experiment and calculation ①①Comparison between experiment and calculation Comparison between experiment and calculation ①①

No offset +160Hz offset

Before 500µsec, the response speed of the phase detector is probably significant.After that, it is consistent between the experiment and the calculation.

“Two modes model” is valid!

500µsec 500µsec

1500µsec

Preliminary


+300Hz offset -160Hz offset

Comparison between experiment and calculation Comparison between experiment and calculation ②②Comparison between experiment and calculation Comparison between experiment and calculation ②②

“Two modes model” is valid!

500µsec500µsec

Preliminary


For the real operation (with Piezo), For the real operation (with Piezo), the calculation is modified for a few the calculation is modified for a few

parameters.parameters.

For the real operation (with Piezo), For the real operation (with Piezo), the calculation is modified for a few the calculation is modified for a few

parameters.parameters.

Eacc = 18.5 → 35MV/mQL = 1.15x106 → 3x106

Sorry! There is not the experimental data around 35MV/m.The result around 30MV/m will be obtained in STF-Phase 1.0 on June or July.


Example of Piezo Compensation (#1)Example of Piezo Compensation (#1)Example of Piezo Compensation (#1)Example of Piezo Compensation (#1)


Criteria of Piezo parameters (#1)Criteria of Piezo parameters (#1)Criteria of Piezo parameters (#1)Criteria of Piezo parameters (#1)

300Hz/μm for Δfcavity


Example of Piezo Compensation (#2)Example of Piezo Compensation (#2)Example of Piezo Compensation (#2)Example of Piezo Compensation (#2)


Criteria of Piezo parameters (#2)Criteria of Piezo parameters (#2)Criteria of Piezo parameters (#2)Criteria of Piezo parameters (#2)


Next Measurement PlanNext Measurement PlanNext Measurement PlanNext Measurement Plan Comparing between Two types of Piezo actuator

High voltage type– 2μm/1000V@2K

Low voltage type– 2μm/150V@2K

Measurement of the Lorentz detuning around 30MV/mSTF #2 B.L. cavity achieved 29.4MV/m in the V.T.

Measurement of the detuning angle during the RF decayThis was already demonstrated in the horizontal test of LL cavity.

Checking the response of the phase detector




Suggestion to the compensation Suggestion to the compensation method for the Lorentz Detuningmethod for the Lorentz DetuningSuggestion to the compensation Suggestion to the compensation method for the Lorentz Detuningmethod for the Lorentz Detuning

Put the initial offset for the cavity frequencyDuring the filling time, the cavity frequency is gradually decreased by

the Lorentz detuning.

Work piezo with the small oscillationAvoid to break out the Piezo by the large oscillationLonger lifetime of Piezo

Increase the mechanical strength of the cavity It is difficult to deform the cavity.


SummarySummarySummarySummary “Two modes model” is valid for the transient response of

the cavity in the horizontal test at STF Phase-0.5.

It is effective to increase the mechanical strength ofthe cavity for the reduction of the Lorentz detuning.

It is similarly effective to set the initial offset tothe cavity frequency around the high field.

In STF Phase-1.0, we will compare betweenthe experimental data around 30MV/m and the simulation.

We will re-examine “two modes model” for more optimization.

Backup SlidesBackup SlidesBackup SlidesBackup Slides



k

kkk

k

k

kk

kk

kk

m

Fx

td

xd

Qtd

xd

FFtsxtsx

2

2

2

;,,

Mechanical Detuning Equation

It is expected that there are two modes from the calculation of the mechanical oscillation.One is the fast mode and the other is slow.


Two Dominant Mechanical ModesTwo Dominant Mechanical Modes

~ +

~ ２５00Hz

~200Hz

Need Stiff Cavity

Need Stiff Jacket-Tuner

2-nd order mode(Fast mode)

Fundamental mode(Slow mode)

F

F


Case of Flat-top ① (no Case of Flat-top ① (no offset)offset)Case of Flat-top ① (no Case of Flat-top ① (no offset)offset)

Phaser diagram


Case of Flat-top ③ (offset Case of Flat-top ③ (offset +300Hz)+300Hz)Case of Flat-top ③ (offset Case of Flat-top ③ (offset +300Hz)+300Hz)


Case of Flat-top ④ (offset -Case of Flat-top ④ (offset -160Hz)160Hz)Case of Flat-top ④ (offset -Case of Flat-top ④ (offset -160Hz)160Hz)


One pulse during High-Power Test (No One pulse during High-Power Test (No Offset)Offset)One pulse during High-Power Test (No One pulse during High-Power Test (No Offset)Offset)

This pulse is used for the comparison later.

5˚

18.5MV/m

Ψcavity

Pkly

Vcavity

PRef


One pulse during High-Power Test (+300Hz One pulse during High-Power Test (+300Hz Offset)Offset)One pulse during High-Power Test (+300Hz One pulse during High-Power Test (+300Hz Offset)Offset)


One pulse during High-Power Test (-160Hz One pulse during High-Power Test (-160Hz Offset)Offset)One pulse during High-Power Test (-160Hz One pulse during High-Power Test (-160Hz Offset)Offset)

Documents

Introduction “ Two modes ” model Method of the calculation for the transient response