1

Simulation for power overhead

and cavity field estimation

Shin Michizono(KEK)

•Performance (rf power and max. cavity field)@35 MV/m 24 cav. operation@31.5 MV/m 24 cav. Operation@33.5 MV/m 26 cav. operation@31.5 MV/m 26 cav. operation

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Assumption•Number of cavities: 24(8-8-8) or 26(9-8-9)•Ql=~3.3e6 (optimum loaded Q depending on the set-cavity gradient and beam current)•Beam current=9.6 mA (corresponding to +1%)•Cavity gradient=35 MV/m ,31.5 MV/m 33.5MV/m, 31.5 MV/m•Microphonics 10Hz(rms)•FB gain=50

•Ql preciseness : 3%rms (Random selections at each simulation)•Waveguide coupling preciseness : 3%rms(0.2 dBrms) (random selections at each simulation)•Beam fluctuation (bunch by bunch) : 1%rms(But this does not affect rf power because this random current fluctuations can not be compensated by the FB.)•Lorentz force detuning reduction 97%

•Vector sum control

•Bottom up rf power calculation with variations of Ql/rf distribution/beam current.

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Procedure1. Set parameters:1-1.Number of cavities: 24 or 261-2.Cavity gradient:35 MV/m, 31.5 MV/m, 33.5 MV/m

2. Random selection of:2-1. loaded Q of 24 (or 26) cavities2-2. rf distribution ratio of 24 (or 26) cavities

3. Calculation start (24 or 26 cav. Vector sum)4. Calculation of rf power, cavity gradient distribution

The obtained rf power is the power required for the set cavity gradient (such as 35 MV/m).

5. Back to 1. and repeat 500 times

6. Statistical investigation of rf power and maximum cavity fields

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Cavity field variation(during rf pulse)

Pf [MW](sum of cavity inputs.)

Detuning during rf pulse(microphonics+Lorentz force)

Cavity phase variation(during rf pulse)

Ql variation 3%rms(random values)

Beam current fluctuation during rf pulse(but no extra rf power is necessary because FB can not suppress this fast random variation)

Example of simulation

Cavity #

Maximum cavity field(due to vector sum)

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Simulation4 kinds of simulations1. 24 cav. 35 MV/m2. 24 cav. 31.5 MV/m3. 26 cav. 33.5 MV/m4. 26 cav. 31.5 MV/mEach 500 simulation (~same order to linac rf units)

500 times

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Histograms of cavity power and maximum cavity gradient @24 cav. system

31.5 MV/m 24 cav.

35 MV/m 24 cav.

These value is the sum of the cavity input (w/o rf losses and so on.)

Maximum field gradient in 500 times simulation is >40 MV/m

Histogram of RF power Histogram of max. cavity field

38.8 MV/m: Mean value of max. cavity field with 500 times simulations

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Histograms of cavity power and maximum cavity gradient @26 cav. system

Maximum field gradient in 500 times simulation is >40 MV/m

Histogram of RF power Histogram of max. cavity field

33.5 MV/m 26 cav.

31.5 MV/m 26 cav.

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Summary

*I add 17%(12% (13%-1%parameter vatriation)+5% extra FB margin) in order to include waveguide loss etc.. FB margin of 5% is necessary for suppression of the perturbations. (We do not need this margin if we give up FB and operate only with FF.)

** mean value of the maximum gradient by 500 times simulations

*** maximum gradient in 500 times simulations

•>10 MW will be necessary for the FB with 26 cavities system at maximum field gradient operation (33.5 MV/m)

•In case of vector sum operation, some cavities with higher Ql or higher power rf input have 10%-20% higher rf fields.

cav.op. gradient

[MV/ m]

cavityinput[MW]

max. Pf[MW]*

ave. max.gradient**

[MV/ m]

max.gradient***

[MV/ m]24 31.5 7.83 9.16 35 38.124 35 8.71 10.19 38.8 42.326 31.5 8.48 9.92 35.1 39.226 33.5 9.03 10.57 37.3 40.5

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Histograms of cavity power and maximum cavity gradient @26 cav. System (33.5 MV/m)

Ql,distribution error 3%rms+ microphonics+LFD

11% higher (ave.) or 21% higher (max.) field

5.1% more power is necessary.

Only Ql variation

5% higher (ave.) or 10% higher (max.) field by 3%(rms) loaded Q distribution

4.4% more power is necessary.

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Histograms of cavity power and maximum cavity gradient @26 cav. System (33.5 MV/m)

Ql and rf distribution error 3%rms11% higher (ave.) or 23% higher (max.) field.

4.3% more power is necessary.

Only LFD+microphonics variation

0.6% higher (ave.) or 1% higher (max.) field　->negligible smallBut 2.9% more power is necessary.

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Ql error v.s. max. cavity gradient in case of the 2 cavities

100

100.5

101

101.5

102

102.5

103

103.5

104

104.5

0 2 4 6 8 10 12

Ql error [%]

cavi

ty fi

eld

[%]

Only Ql variation

FB gain=50 and 5 deg.off-crest beam-> -0.1 deg=5 deg/50(This can be compensated with proper FF.)

10% error in loaded Q induces 4% higher cavity field

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Rf distribution error v.s. max. cavity gradient in case of the 2 cavities

Only rf distribution variation

100

101

102

103

104

105

106

107

108

109

0 5 10 15distribution error [%]

cavi

ty fi

eld

[%]

10% error in rf distribution induces 8.5% higher cavity field

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Summary (2)

* I add 17%(12% (13%-1%parameter vatriation)+5% extra FB margin) in order to include waveguide loss etc.. FB margin of 5% is necessary for suppression of the perturbations. (We do not need this margin if we give up FB and operate only with FF.)** mean value of the maximum gradient by 500 times simulations*** maximum gradient in 500 times simulations

•Each components of the power loss are calculated.–Parameter variation (Ql+rf distribution): ~4%

•3% rms loaded Q and rf distribution control requires 4% additional power.–Detuning (Lorentz force detuning + microphonics): ~3%–Total (detuning, parameter variation, beam current): ~5%

•Higher gradient during vector sum will become another problem.

<In order to flatten the cavity fields, careful loaded Q control and rf distribution control are necessary.>

cav.op. gradient

[MV/ m]

cavityinput[MW]

additionalratio [%]

max. Pf[MW]*

ave. max.gradient**

[MV/ m]

max.gradient***

[MV/ m]comment

26 33.5 9.03 5.1% 10.57 37.3 40.5 Ql,rf dist, LFD+micro.26 33.5 8.97 4.4% 10.49 35 36.9 Ql26 33.5 8.96 4.3% 10.48 37.3 41.3 Ql+rf distr.26 33.5 8.84 2.9% 10.34 33.7 33.8 LFD+microphonics

(9.03/8.59-1)*100 (8.59 MW: ideal cavity input)

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Summary (3)

I include in the simulation1.10 Hz microphonics2. 3% Lorentz force detuning3. +1% beam current4. Loaded Q variation 3% rms5. Rf distribution variation 3% rms

The results show1. 1% power loss by 1% beam2. 3% detuning effects (p.10,p.13)3. 4% due to parameter change (p.9,

p.10,p.13)

Voltage

loss

Power

loss

Available Power

(MW), when no

derating of klys

is considered

Power Source and High Level RF Loss Factors

Maximum Klystron Output Power 0.0% 10.00De- rating of klystron for end of life time 0.0% 10.00

Modulator Ripple Spec = 1% (Often worse) 1% 2.5% 9.75Waveguide and circulator losses 8.0% 8.97 Power loss due to cavity gradient variation 2.3% 8.76Parameter variation 0.0% 0.0% 8.76Total HLRF Loss and Available Power 12% 8.76

Low Level RF Loss Factors

Peak power headroom 2.5% 5.0% 8.33Dynamic Headroom 0.0% 0.0%Beam current fluctuations of 1%pk 1.0%Detuning errors of 30 Hz 0.5% 3.0%parameter variation 4.0%Klystron drive noise sidebands 1.0% 0.0% 0.00Total LLRF Loss (linear sum) andAvailable PowerTotal LLRF (square sum) andAvailable Power 5.1% 5.12%

9-8-9 Configuration Case

Power (kW) Required for 9.5ma @ 33.5 MV/ m 0.330344Power (MW) for 26 cavities 8.59Excess Power Headroom (when linearsum of LLRF losses assumed) (0.70)

8.83/ 9.03

Michizono (20061124)

Agree well with the total rf overhead.