On the anisotropic velocity distribution of fast ions in NBI-heated toroidal plasmas

A method to calculate the flux-surface-averaged anisotropy (the second Legendre order) in the slowing down velocity distribution of the fast ions generated by tangentially injected neutral beams is shown. This component is required for (1) perpendicular and parallel currents in MHD equilibrium calculations including the fast ions\u27 pressure, (2) the anisotropic heating analyses on the thermalized target plasma species, and (3) the classical and the Pfirsch-Schlüter radial transport of both the thermalized target plasma species and the fast ions themselves. For including the parallel guiding center motion effect in non-symmetric toroidal configurations such as stellarators and heliotrons, the adjoint equation and the eigenfunctions are applied. In contrast to the previously investigated configuration dependence of the first Legendre order as the momentum input to the target plasma species, a quite different dependence of the second Legendre order on the magnetic field strength modulation B(θ,ζ) on the magnetic flux-surfaces is found. Even in a low energy range of the slowing down velocity distribution, the deviation (reduction) of the anisotropy from a result neglecting the orbit effect is proportional to 1− ⟨B⟩/Bmax