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

Abstract

Particle motion in a cylindrical multiple-cusp magnetic field configuration is shown to be highly (though not completely) chaotic, as expected by analogy with the Sinai billiard. This provides a collisionless, linear mechanism for phase randomization during monochromatic wave heating. A general quasilinear theory of collisionless energy diffusion is developed for particles with a Hamiltonian of the form H0+H1, motion in the unperturbed Hamiltonian H0 being assumed chaotic, while the perturbation H1 can be coherent (i.e., not stochastic). For the multicusp geometry, two heating mechanisms are identified—cyclotron resonance heating of particles temporarily mirrortrapped in the cusps, and nonresonant heating of nonadiabatically reflected particles (the majority). An analytically solvable model leads to an expression for a transit-time correction factor, exponentially decreasing with increasing frequency. The theory is illustrated using the geometry of a typical laboratory experiment.