ORBITAL RESONANCES AND CHAOS IN A COMBINED RF TRAP

The rf combined trap for confining a non-neutral plasma by a combinati on of rf fields and a uniform magnetic field is introduced. The partic le motion is studied in such a trap in which the rf fields are given b y the TM011 mode. The aim is to determine limits on a focus at the cen ter for low angular momentum particles. Such a focus allows densities in excess of the local Brillouin limit, The motion is described in ter ms of an effective potential consisting of the ponderomotive potential V-pon(r,z) plus a radial potential m Omega(c)(2)r(2)/8 due to the mag netic field B-z plus a centrifugal potential p(theta)(2)/2mr(2). Near the origin r = 0, z = 0, the equations reduce to a pair of Mathieu equ ations for the r and z motions, For certain parameters the system is q uasispherically symmetric, i.e. the effective ponderomotive frequencie s Omega(r), Omega(z) in r and z are equal. In this case the Brillouin limit for a uniform density plasma is shown to equal the usual cylindr ical limit, Numerical integration of the ponderomotive equations is sh own for parameters near those giving quasispherical symmetry, There is resonance for Omega(r)/Omega(z) = 1, giving in = 2, n = 2 islands. Th e islands limit the size of the focus at the origin, even for p(theta) = 0. For particles with large effective energy E-eff, there can also be chess, depending on the elongation L/a of the rf cavity. It is foun d that the deleterious effect of islands and chaos on the focus is min imized by having the elongation L/a close to unity and having particle s trapped deeply in the ponderomotive well. (C) 1997 American Institut e of Physics.