A test particle approach in the stochastic stability analysis of charged particle beams

The stochastic stability of a charged particle beam propagating in a randomly unhomogeneous medium is analyzed using an internal test particle approach. The effect of the random medium is included by adding a stochastic fluctuating term in the neutralization factors. The effects of weakly colored noise and of fluctuations called telegraphic noise, i.e. two valued Markov process, are studied. The exact solution of the telegraphist noise is compared with the approximate solution corresponding to the weakly colored noise, which was obtained using the Stratonovich approach, by means of an expansion technique. It is concluded that the beam is always probabilistically unstable, whenever the power spectral density of the fluctuations contains a component at the frequency of the radial oscillations of the test particles.