Power Overhead Calculation For Lorentz Detuning Force

1. Power Overhead Calculation For Lorentz Detuning Force Rihua Zeng 2012-Mar-20

2. Pre-detuning for reducing overhead

3. Overhead estimation for cavity with optimal Ql

4. 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

5. Overhead for Lorentz force detuning under Ql variations

6. Overhead for Lorentz force detuning in Spoke cavity 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

7. Lorentz force detuning under mechanical resonance

8. Typical mechanical modes in superconducting cavity

9. 1st and 2nd order equation simulation for LFD

10. Some measurement data by piezo sensor at FLASH

11. 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.