Abstract
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' 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.
Highlights
In both present experiment devices for the fusion interest and future burning core plasmas in reactors the fast ions play roles as sources of particle, momentum, and energy for thermal particles
After the development of the charge exchange recombination spectroscopy,[1,2] determination of the velocity distribution of the thermalized ions (H,D,T,He,C, etc.) including this momentum input has been regarded as an important physics issue.[2]
When this type of source term is included in the RHS of Eq(21), the solving procedure will be analogous to the vda · ∇s in the viscosity and the P-S parts in Eqs.(25) and (27), and analogous velocity distribution components will be generated there
Summary
In both present experiment devices for the fusion interest and future burning core plasmas in reactors the fast ions play roles as sources of particle, momentum, and energy for thermal particles. The purpose of this study is to show a method to calculate the flux-surface-averaged anisotropy in the f f (x, v, ξ) of the NB-produced fast ions for these applications This velocity distribution in non-symmetric toroidal configurations will have a complicated phase space structure because the non-uniform magnetic field strength B · ∇B= 0 in the 3D real space makes three types of phase space regions, i.e., circulating, toroidally trapped, and ripple-trapped regions corresponding to different drift orbits. We shall adopt the adjoint equation method that was previously used by Taguchi for calculating the fast ions’ parallel particle flux Bnf u∥f ,20 since our purpose is not in the f f (x, v, λ) itself but in some surface∫ 3 averaged contributions of the velocity space integrals d v of this function Even though this adjoint equation is defined for the full phase space regions (x, v), we need its solution only at a specific pitch-angle range where the fast ion source exists.
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