  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 $H_0+H_1$, motion in the \emph{unperturbed} Hamiltonian
$H_0$ 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
expression for a transit-time correction factor, exponentially decreasing with
increasing frequency. The theory is illustrated using the geometry of a typical
laboratory experiment.
