A Paul trap configuration to simulate intense non-neutral beam propagationover large distances through a periodic focusing quadrupole magnetic field

This paper considers an intense non-neutral charged particle beam propagati ng in the z-direction through a periodic focusing quadrupole magnetic field with transverse focusing force, -kappa(q)(s)[x (e) over cap(x)-y (e) over cap(y)], on the beam particles. Here, s = beta(b)ct is the axial coordinate , (gamma(b) - 1)m(b)c(2) is the directed axial kinetic energy of the beam p articles, q(b) and m(b) are the charge and rest mass, respectively, of a be am particle, and the oscillatory lattice coefficient satisfies kappa(q)(s S) = kappa(q)(s), where S is the axial periodicity length of the focusing field. The particle motion in the beam frame is assumed to be nonrelativist ic, and the Vlasov-Maxwell equations are employed to describe the nonlinear evolution of the distribution function f(b)(x,y,x',y',s) and the (normaliz ed) self-field potential psi(x,y,s) = q(b)phi(x,y,s)/gamma(b)(3)m(b)beta(b) (2)c(2) in the transverse laboratory-frame phase space (x,y,x('),y(')), ass uming a thin beam with characteristic radius r(b) much less than S. It is s hown that collective processes and the nonlinear transverse beam dynamics c an be simulated in a compact Paul trap configuration in which a long non-ne utral plasma column (L much greater than r(p)) is confined axially by appli ed dc voltages (V) over cap = const on end cylinders at z = +/- L, and tran sverse confinement in the x-y plane is provided by segmented cylindrical el ectrodes (at radius r(w)) with applied oscillatory voltages +/- V-0(t) over 90 degrees segments. Here, V-0(t + T) = V-0(t), where T = const is the osc illation period, and the oscillatory quadrupole focusing force on a particl e with charge q and mass m near the cylinder axis is -m kappa(q)(t)[x (e) o ver cap(x)-y (e) over cap(y)], where kappa(q)(t)equivalent to 8qV(0)(t)/pi mr(w)(2). (C) 2000 American Institute of Physics. [S1070-664X(00)01103-4].