A periodically-switched ODE model for N-bunch beamloading in a storage ring

Abstract

A new baseband formulation of the coupled cavity/longitudinal-bunch ODEs is derived. Assuming linearity, a model of the form x/spl dot/(t)=A(t)x(t)+B(t)u(t) arises, where A(t) and B(t) are piecewise constant, and periodic with the revolution period T/sub 0/. Such models, known in the control community as (periodic) switched systems, have known (in)stability criteria and control theoretic properties, which can be useful in the analysis and control of multiple bunch beamloading.