Maximal entropy distribution functions from generalized R\'enyi entropy

TL;DR

This paper introduces a new class of reference distribution functions derived from maximizing generalized Rènyi entropy, providing explicit algebraic decay solutions for approximating Fokker-Planck equations in tokamak plasma dynamics.

Contribution

It presents a novel derivation of distribution functions using generalized Rènyi entropy maximization with scale-invariant constraints, extending previous exponential tail models.

Findings

Derived explicit algebraic decay distribution functions

Generalized Rènyi entropy maximization under scale-invariant restrictions

Applicable to numerical solutions of Fokker-Planck equations in plasma physics

Abstract

New class of reference distribution functions for numerical approximation of the solution of the Fokker-Planck equations associated to the charged particle dynamics in tokamak are studied. The reference distribution functions are obtained by maximization of the generalized Renyi entropy under scale-invariant restrictions. Explicit analytic form, with algebraic decay, that is a generalization of the previous distribution with exponential tails was derived.