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

This paper considers an intense non-neutral charged particle beam propagating in the z-direction through a periodic focusing quadrupole magnetic field with transverse focusing force, $−κq(s)[xêx−yêy],$ on the beam particles. Here, $s=βbct$ is the axial coordinate, $(γb−1)mbc2$ is the directed axial kinetic energy of the beam particles, $qb$ and $mb$ are the charge and rest mass, respectively, of a beam particle, and the oscillatory lattice coefficient satisfies $κq(s+S)=κq(s),$ where S is the axial periodicity length of the focusing field. The particle motion in the beam frame is assumed to be nonrelativistic, and the Vlasov-Maxwell equations are employed to describe the nonlinear evolution of the distribution function $fb(x,y,x′,y′,s)$ and the (normalized) self-field potential $ψ(x,y,s)=qbφ(x,y,s)/γb3mbβb2c2$ in the transverse laboratory-frame phase space $(x,y,x′,y′),$ assuming a thin beam with characteristic radius $rb≪S.$ It is shown that collective processes and the nonlinear transverse beam dynamics can be simulated in a compact Paul trap configuration in which a long non-neutral plasma column $(L≫rp)$ is confined axially by applied dc voltages $V̂=const$ on end cylinders at $z=±L,$ and transverse confinement in the $x−y$ plane is provided by segmented cylindrical electrodes (at radius $rw)$ with applied oscillatory voltages $±V0(t)$ over $90°$ segments. Here, $V0(t+T)=V0(t),$ where $T=const$ is the oscillation period, and the oscillatory quadrupole focusing force on a particle with charge q and mass m near the cylinder axis is $−mκq(t)[xêx−yêy],$ where $κq(t)≡8qV0(t)/πmrw2.$