On the optimal conditions for alpha-channelling

We investigate the simplest model of alpha channelling, in which high-frequency electrostatic wave interacts with fusion alpha particles and the effect of low-frequency waves is modeled by an outward flux of particles at the threshold energy E w for wave-particle interaction. The associated Fokker-Planck equation is then solved analytically in the limit of large wave-induced diffusion with absorbing boundary conditions at the outer edge. The power flowing from alpha particles to the wave is explicitly computed and its dependence on the outward flux at E w and on the spatial extent of the high-frequency wave is determined. The best option for alpha channelling is realized when the outward flux equals the flux of pure wave-induced diffusion, in which case the whole perpendicular energy of alpha particles can be extracted. On the contrary, if the outward flux is negligible, no more than ∼ of alpha particle energy can be channelled to the wave for an extended source, which raises up to ∼ for a localized source.