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 B^sol(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 f_b,(x, v, 0), using the method of characteristics. It is shown that the Vlasov equation possesses a class of exact, dynamically evolving solutions f_b(W_⊥, W _z), where W^⊥ and W_z 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 f_b,(W_⊥, W_z).