Dynamic Lorenz detuning

1
Dynamic Lorenz detuning

• Gennady Romanov
• May 2, 2007

2

• Sources of perturbations in pulsed SC proton
  linac
• Lorenz force detuning. The pressure exerted by
  the RF fields on the cavity walls induces cavity
  deformation and then resonant frequency shift.
• Beam loading. Beam loading changes are generated
  by beam current fluctuations and any bunch
  oscillations induced by energy or phase offset of
  the incoming beam.
• Microphonics. The vibrations result generally
  from external excitations, such as cryogenic
  pressure oscillations, bubbles in the liquid
  helium or vacuum pumps.

3
LFD for SSR is new problem

• Assume for SSR
• Only one mechanical mode does matter
• Its frequency is much higher than 10 Hz
• The mode is well dumped between pulses
• Its dynamic Lorenz force parameter is equal
• to static one KLFD ? 4 Hz/(MV/m)2
• Then dynamic Lorenz detuning can be described
• by first order ODE.

I hope we are here
- detuning
- mechanical time constant
Lorenz force detuning during rectangular pulse
of accelerating field under assumed conditions.
4
Along with other parameters the mechanical time
constant ?m determines maximum of Lorenz force
detuning and weather the detuning decays
completely or not at the instance of a new RF
pulse.
?m1 ms
?m0.4 ms
?m0.2 ms
5
SSR1 filling time is ? 1.5 ms and Eacc 10 MV/m.
Let the generator frequency follow the cavity
frequency and assume mechanical time constant
1 ms. Then the dynamic detuning would look as
shown.
6
This preliminary estimation indicates that we can
pre-detune the cavity in order to relax the
feedback requirements (cavity bandwidth is ? 700
Hz)

• Conclusion
• We need to perform modal analyses of SSR and
  prepare mechanical parameter measurements during
  high power test. It would be also useful for
  mechanical mode excitation analyses
  (microphonics).
• We need to develop a model and simulate filling
  and flat top operation with fixed klystron
  frequency to define the feedback requirements.