Particle Beam Stability in the Hollow Plasma Channel Wake Field Accelerator

The electromagnetic wake field response of a hollow plasma channel to a driver (laser or charged particle beam) of arbitrary velocity is derived. The dispersion and loss factors of excited fundamental and higher order azimuthal modes are computed. Growth rates for beam breakup instabilities are calculated and beam transport is studied. External focusing is shown to provide a method of controlling transverse instabilities. For parameters of interest for high gradient plasma-based accelerators, it is shown that the most severe limitation to the interaction length of a single accelerator stage based on the hollow plasma channel structure is the transverse instability of the particle beam.