Kernels of the Direct Collision Integral of the Nonlinear Boltzmann Equation


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Abstract

This paper reviews the properties of kernels of the direct collision integral describing the escape of particles from an element of the phase volume due to collisions, as well as properties of kernels of the integral operators arising in expansion of the direct collision integral in spherical harmonics. It is shown that, for isotropic scattering cross sections depending on the relative velocity by a power law, these kernels can be obtained in an analytical form. Since the analytical expressions for the kernels with large indices become too cumbersome, their asymptotics are found.

About the authors

L. A. Bakaleinikov

Ioffe Institute

Author for correspondence.
Email: bakal.ammp@mail.ioffe.ru
Russian Federation, St. Petersburg, 194021

E. A. Tropp

Ioffe Institute

Email: bakal.ammp@mail.ioffe.ru
Russian Federation, St. Petersburg, 194021

E. Yu. Flegontova

Ioffe Institute

Email: bakal.ammp@mail.ioffe.ru
Russian Federation, St. Petersburg, 194021

I. A. Ender

St. Petersburg State University

Email: bakal.ammp@mail.ioffe.ru
Russian Federation, St. Petersburg, 199034

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