Power Overhead Calculation For Lorentz Detuning Force
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Power Overhead Calculation For Lorentz Detuning Force
Rihua Zeng2012-Mar-20
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Pre-detuning for reducing overhead
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Overhead estimation for cavity with optimal Ql
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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
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Overhead for Lorentz force detuning under Ql variations
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Overhead for Lorentz force detuning in Spoke cavity
0 50 100 150 2000
100000
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600000
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800000
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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
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Lorentz force detuning under mechanical resonance
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Typical mechanical modes in superconducting cavity
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1st and 2nd order equation simulation for LFD
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Some measurement data by piezo sensor at FLASH
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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.