Speaker
Andrey A. Kulichenko
Description
See the full Abstract at http://ocs.ciemat.es/EPS2018ABS/pdf/P1.4013.pdf
SUPERDIFFUSIVE TRANSPORT IN PLASMA FOR A FINITE
VELOCITY OF CARRIERS: GENERAL SOLUTION AND THE
PROBLEM OF AUTOMODEL SOLUTIONS
A.A. Kulichenko1, A.B. Kukushkin1,2
1
National Research Center «Kurchatov Institute», Moscow, 123182, Russian Federation
2
National Research Nuclear University MEPhI, Moscow, 115409, Russian Federation
The analysis of the Green’s function of the non-stationary Biberman-Holstein equation for
radiative transfer in plasmas and gases has shown [1] that there is an approximate automodel
solution based on three scaling laws: for the propagation front and asymptotic solutions far
beyond and far ahead of the propagation front. All these scaling laws are determined
essentially by the long-free-path carriers (named Lévy flights). The validity of the suggested
automodel solution was proved by its comparison with analytical solutions in the 3D case of
the Biberman–Holstein equation of the resonance radiation transfer for various spectral line
shapes (Doppler, Lorentz, Voigt and Holtsmark) with complete redistribution over frequency
in the elementary act of the resonance scattering of the photon by an atom/ion. Scaling laws
of Biberman-Holstein equation Green’s function and the implications for algorithms of
numerical modeling of superdiffusive transport are considered in [2]. The results of accuracy
analysis of automodel solutions for Lévy flight-based transport, including the resonance
radiative transfer and a simple general model, are reported in [3].
Here, we generalize the method [1] of approximate automodel solutions of the 1D
transport equation with a model, power-law step-length probability distribution function
(PDF) to the case of a finite velocity of the carriers (e.g., photons in space plasmas). First, we
derive general solution. Further, the analytic results for the asymptotics far ahead and far
beyond the perturbation front are derived. And finally, an approximate automodel solution
based on the above asymptotics is suggested, and its accuracy is analyzed via comparison
with exact numerical solution. The method is of interest for a broad range of superdiffusive
transport problems in physics and beyond.
References
[1]. Kukushkin A.B. and Sdvizhenskii P.A., J. Phys. A: Math. Theor. 2016, 49, 255002.
[2]. Kukushkin A.B., Sdvizhenskii P.A., Voloshinov V.V., and Tarasov A.S., International Review of Atomic
and Molecular Physics, 2015, 6 (1), 31-41.
[3]. Kukushkin A.B. and Sdvizhenskii P.A., J. Phys. Conf. Series, 2017, 941, 012050.
