Fusion yield: Guderley model and Tsallis statistics

TL;DR

This paper extends the thermonuclear reaction rate integral using the pathway model and Tsallis statistics, providing a closed-form solution and applying it to fusion plasma models to compare with standard yields.

Contribution

It introduces a generalized reaction rate integral using the pathway model and Tsallis statistics, offering a new analytical approach for fusion energy calculations.

Findings

Derived a closed-form reaction rate integral with Meijer's G-function.

Applied the model to fusion plasma shock waves for energy evaluation.

Compared new results with classical fusion yield models.

Abstract

The reaction rate probability integral is extended from Maxwell-Boltzmann approach to a more general approach by using the pathway model introduced by Mathai [Mathai A.M.:2005, A pathway to matrix-variate gamma and normal densities, Linear Algebra and Its Applications}, 396, 317-328]. The extended thermonuclear reaction rate is obtained in closed form via a Meijer's G-function and the so obtained G-function is represented as a solution of a homogeneous linear differential equation. A physical model for the hydrodynamical process in a fusion plasma compressed and laser-driven spherical shock wave is used for evaluating the fusion energy integral by integrating the extended thermonuclear reaction rate integral over the temperature. The result obtained is compared with the standard fusion yield obtained by Haubold and John in 1981.[Haubold, H.J. and John, R.W.:1981, Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave, Plasma Physics, 23, 399-411]. An interpretation for the pathway parameter is also given.