Cascaded integrator comb filters with smoothly varying coefficients for reduced delay in synchrotron feedback loops

The Rapid Cycling Synchrotron (RCS) of the J-PARC complex in Tokai, Japan, is designed to accelerate a high intensity proton beam from 181 MeV, and later 400 MeV to 3 GeV in 20 ms within the 40 ms machine cycle. The beam power up to 1 MW demands a stable beam control to avoid excessive losses and activation of the accelerator chain. The fully digital control system is based on quadrature modulation and demodulation. In the amplitude control loops standard FIR filters separate the harmonics (h=2) and (h=4) after down conversion. For the phase loops at (h=2) and (h=4), intended to damp synchrotron oscillations, the delay in a FIR filter would limit the loop stability. Cascaded integrator comb filters, also called CIC filters, provide a shorter delay because they filter the longitudinal beam signal only where it is necessary. The notches are located at multiples of the revolution frequency of the proton beam. For fixed frequency accelerator applications, digital comb filters with fixed clock frequency are widely used to improve loop stability. For variable frequency accelerator applications, as in a proton synchrotron, where the frequency swing is larger than the notch width, usually the clock frequency of the comb filter is variable and chosen to be an integer multiple of the particle revolution frequency. At J-PARC RCS, the clock frequency has to be fixed. Tracking the frequency would require a variable noninteger number of filter taps. Here we present a filter, based on the weighted output of 2 CIC filters with variable length, and one tap difference. The filter function looks like a CIC with smoothly varying coefficients, where the notches follow the revolution frequency of the proton beam. The delay of this filter is approximately half of the corresponding FIR filter, so that the phase loops have a higher stability margin.