A wide class of non-stationary superdiffusive transport on a uniform background with a powerlaw decay, at large distances, of the step-length probability distribution function (PDF) is shown to possess an automodel solution. The solution for Green function is constructed using the scaling laws for the propagation front (relevant-to-superdiffusion average displacement) and asymptotic solutions far beyond and far in advance of the propagation front. These scaling laws are determined essentially by the long-free-path carriers (Lévy flights). The validity of the suggested automodel solution is proved by its comparison with numerical solutions in the one-dimensional (1D) case of the transport equation with a simple long-tailed PDF with various power-law exponents and in the 3D case of the Biberman-Holstein equation of the resonance radiation transfer for various (Doppler, Lorentz, Voight and Holtsmark) spectral line shapes.

i) The problem: to measure T e as high as 40 keV using Thomson Scattering in the reactor core both for Maxwellian and non-Maxwellian case of electron velocity distribution function especially in the case of unknown system spectral responsivity. (ii) The suggested solutions:to use IR probing laser 1320 nm additionally to convenient NIR laser 1064 nm to improve measurement accuracy for T e~ 40keV;to use specific algorithm for TS data processing in case of non-Maxwellian eVDF; to use multi-laser approach, that suggests plasma probing with 3 lasers -946 nm/1064 nm/1320 nm simultaneously in the case of unknown system spectral sensitivity.(iii) Next steps -test multi-laser approach and designed data procession technique in real experiment on existing fusion device.

Abstract:The accuracy of approximate automodel solutions for the Green's function of the Biberman-Holstein equation for the Stark broadening of spectral lines is analyzed using the distributed computing. The high accuracy of automodel solutions in a wide range of parameters of the problem is shown.

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