Periodically-focused solutions to the nonlinear Vlasov-Maxwell equations for intense charged particle beams

An intense nonneutral ion beam propagates in the z-direction through a peri odic focusing quadrupole field with transverse focusing force, F-toc = -kap pa(q)(s)(x (e) over cap(x) - y (e) over cap(y)), on the beam ions. Here, th e oscillatory lattice coefficient satisfies kappa(q)(s + s) = kappa(q)(s), where S = const. is the axial periodicity length. The model employs the Vla sov-Maxwell equations to describe the nonlinear evolution of the distributi on function f(b)(x, y, x', y',s) and the normalized self-field potential ps i(x, y, s) in the transverse laboratory-frame phase space (x, y, x', y'). U sing a third-order Hamiltonian averaging technique, a canonical transformat ion is employed with an expanded generating function which transforms away the rapidly oscillating terms, and leads to a Hamiltonian in the 'slow' tra nsformed variables ((X) over tilde,(Y) over tilde,(X) over tilde',(Y) over tilde') with constant focusing coefficient kappa(fq) = const. (C) 1999 Else vier Science B.V. All rights reserved.