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Fusion yield: Guderley model and Tsallis statistics

Published online by Cambridge University Press:  04 October 2010

H. J. HAUBOLD  and
D. KUMAR
H. J. HAUBOLD
Affiliation:
Office for Outer Space Affairs, United Nations, Vienna International Centre, P.O. Box 500, A-1400 Vienna, Austria (hans.haubold@unoosa.org) Centre for Mathematical Sciences, Pala Campus, Arunapuram P.O., Pala, Kerala 686 574, India
D. KUMAR
Affiliation:
Centre for Mathematical Sciences, Pala Campus, Arunapuram P.O., Pala, Kerala 686 574, India
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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 in 2005 (A pathway to matrix-variate gamma and normal densities. Linear Algebr. Appl.396, 317–328). The extended thermonuclear reaction rate is obtained in the 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 (Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave. Plasma Phys.23, 399–411). An interpretation for the pathway parameter is also given.

Type
Papers
Information
Journal of Plasma Physics , Volume 77 , Issue 1 , February 2011 , pp. 1 - 14
Copyright
Copyright © Cambridge University Press 2010

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