Kinetic description of neutralized drift compression and transverse focusing of intense ion charge bunches

A kinetic model based on the Vlasov equation is used to describe the axial drift compression and transverse focusing of an intense ion charge bunch propagating along the axis of a solenoidal focusing field Bˢᵒˡ(x). The space charge and current of the ion charge bunch are assumed to be completely neutralized by the electrons provided by a dense background plasma. In the absence of self-field forces, the Vlasov equation is solved exactly for general initial distribution function fb(x,v,0), using the method of characteristics. It is shown that the Vlasov equation possesses a class of exact, dynamically evolving solutions fb(W_⊥,Wz), where W_⊥ and Wz are transverse and longitudinal constants of the motion. Detailed dynamical properties of the charge bunch are calculated during axial compression and transverse focusing for several choices of distribution function fb(W_⊥,Wz).