Quasilinear theory of collisionless Fermi acceleration in a multicusp magnetic confinement geometry

Particle motion in a cylindrical multiple-cusp magnetic field configuration is shown to be highly (though not completely) chaotic, as expected by anal ogy with the Sinai billiard. This provides a collisionless, linear mechanis m for phase randomization during monochromatic wave heating. A general quas ilinear theory of collisionless energy diffusion is developed for particles with a Hamiltonian of the form H-0 + H-1, motion in the unperturbed Hamilt onian H-0 being assumed chaotic, while the perturbation H-1 can be coherent (i.e., not stochastic). For the multicusp geometry, two heating mechanisms are identified-cyclotron resonance heating of particles temporarily mirror trapped in the cusps, and nonresonant heating of nonadiabatically reflected particles (the majority). An analytically solvable model leads to an expre ssion for a transit-time correction factor, exponentially decreasing with i ncreasing frequency. The theory is illustrated using the geometry of a typi cal laboratory experiment. [S1063-651X(99)10311-8].