For the three-body Coulomb problem a hyperspherical parametrisation of independent variables is given on a five-dimensional sphere S5 with a hyperradius RH, the first linear invariant of the inertia tensor. The hyperspherical adiabatic basis is defined as a complete set of eigenfunctions and eigenvalues of the Hamiltonian on the sphere S5 for every fixed value of the slow variable RH. The partial wave analysis in the total momentum J representation allows the authors to separate three Euler angles and to reduce the hyperspherical problem on S5 to a system of (J+1) two-dimensional problems. Classification is given of the hyperspherical adiabatic basis for small and large values of the hyperradius RH. The logarithmic Fock singularity at the point of triple collision (RH=0) is explicitly shown. The approach is assigned to computing the cross sections of mesic atomic processes in the muon catalysis problem.
The problems related to the spectral line-shape formation in the scrape of layer (SOL) in fusion reactor plasma for typical observation chords are considered. The SOL plasma is characterized by the relatively low electron density (10 12-10 13 cm −3) and high temperature (from 10 eV up to 1 keV). The main effects responsible for the line-shape formation in the SOL are Doppler and Zeeman effects. The main problem is a correct modeling of the neutral atom velocity distribution function (VDF). The VDF is determined by a number of atomic processes, namely: molecular dissociation, ionization and charge exchange of neutral atoms on plasma ions, electron excitation accompanied by the charge exchange from atomic excited states, and atom reflection from the wall. All the processes take place step by step during atom motion from the wall to the plasma core. In practice, the largest contribution to the neutral atom radiation emission comes from a thin layer near the wall with typical size 10-20 cm, which is small as compared with the minor radius of modern devices including international test experimental reactor ITER (radius 2 m). The important problem is a strongly non-uniform distribution of plasma parameters (electron and ion densities and temperatures). The distributions vary for different observation chords and ITER operation regimes. In the present report, most attention is paid to the problem of the VDF calculations. The most correct method for solving the problem is an application of
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