Stability of ripple-assisted neutral beam injection against loss-cone modes

Aspects of the stability of the toroidal field ripple-assisted neutral beam injection scheme proposed by Jassby and Goldston are considered. It is found that beams sufficiently peaked in perpendicular energy are unstable to the generation of loss-cone modes - specifically, lower hybrid waves propagating nearly perpendicular to the magnetic field and driven unstable by the perpendicular velocity space anisotropy-free energy. In the infinite-medium theory, the beam density threshold is intolerably small. However, radial convection of energy provides an important additional source of damping. The resulting threshold may be tolerable if the beam temperature is sufficiently high. Even if the linear stability condition is violated, it is shown that quasilinear diffusion will produce broadening quite rapidly (several e-foldings), with small saturated field amplitudes.