Space charge dominated envelope dynamics of asymmetric beams in RF photoinjectors

While it has been proposed for several years that strongly asymmetric ((σ_x≫σ_y)) beams can be employed in RF photoinjectors to obtain asymmetric emittances for linear collider applications, it is known that the emittances obtained directly from RF photocathode guns are not suitably small for this purpose. Because of this, simulation work has been performed in an attempt to apply the principle of emittance compensation to recover the small and asymmetric emittances after suitable focusing and acceleration of photoinjector beams. In order to guide this difficult three-dimensional analysis, we present an extension of a previous theoretical model of the emittance compensation process in axisymmetric photoinjectors. In the extended model, we first analyze the general quadrupolar oscillations in a symmetric accelerating system, and then proceed to examine a propagation mode under asymmetric focusing. This mode is a generalization of the previously analyzed axisymmetric invariant envelope, allowing an optimization of the compensation process. Design philosophies, including RF cavity considerations, are included in the discussion