Power Overhead Calculation For Lorentz Detuning Force

Rihua Zeng2012-Mar-20

Pre-detuning for reducing overhead

Overhead estimation for cavity with optimal Ql

Overhead calculation for cavity with non-optimal Ql• It makes calculation easier to discuss detuning according to the rate Δf/f1/2

• Below f1/2 , ( K~1.5 for high beta, K~2 for med beta), most cavity overhead is <7%.

• 25% or more are required for detuning > 2 f1/2 (K~3 for high beta, K~4 for med beta)

• Appropriate pre-detuning for both sync. phase and LFD is assumed

Overhead for Lorentz force detuning under Ql variations

Overhead for Lorentz force detuning in Spoke cavity

0 50 100 150 2000

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1000000Generator power (W)

Some measured data about LFD of spokes is 4~8 Hz/(MV/m)2.

Worse data in some individual measurement.

Overhead is relatively higher in the beginning section of spokes

Lorentz force detuning under mechanical resonance

Typical mechanical modes in superconducting cavity

1st and 2nd order equation simulation for LFD

Some measurement data by piezo sensor at FLASH

Conclusion

• The overhead could be reduced to a small value if the detuning is limited into half cavity bandwidth with lower LFD coefficient, optimal pre-detuning for LFD, and avoiding mechanical resonance.

• Overhead increases by the square of rate Δf/f1/2 . 25% or more are required for detuning Δf/f1/2 > 2 (K~3 for high beta, K~4 for med beta) , under optimal pre-detuning for LFD

• It seems non-significant overhead is required for Ql variations ±5%

• More overhead is required for some spoke cavities at the beginning of spoke section.

• Need to investigate more details for mechanical modes of cavities at ESS.