Numerical studies of orbits in a 3-D magnetic cusp geometry

Summary form only given. The magnetic confinement concept known as the Polywell/sup TM/ makes use of the field created by three pairs of Helmholtz coils situated on the opposing faces of a cube. Near the origin, the rectangular components of the vector potential is given by A/sub x//spl sim/y/sup 3/ z/spl sim/z/sup 3/ y, plus cyclic permutations. The field configuration has six face cusps and eight corner cusps through which charged particles preferentially escape. Confinement properties of the configuration can be studied by numerical solution of the equation of motion. However, the orbits have to be followed for very long times, and this presents difficulties as the system exhibits chaos in the sense of sensitive dependence on initial conditions. We have studied a number of numerical methods for solving the equations of motion and found that the simplectic algorithms, which apply to Hamiltonian systems, allow the orbits to be followed for the longest time when the same time-steps are used. The Lyapounov exponents are computed as an attempt to understand the origin of the chaotic dynamics.