TITLE:
Relativistic Corrections to the Maxwellian Distribution for Astrophysical and Fusion Plasmas
AUTHORS:
Amaury de Kertanguy
KEYWORDS:
Maxwell-Jüttner Distribution, Relativity Modification to Maxwell Law, Lorentz Factor, Linear Stark Effect, Plasma Physics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.8,
August
24,
2023
ABSTRACT: We present calculations and improvement inspired by the work of Lorenzo Zaninetti, published in 2020, it concerns a problem whose origin dates back 1911 with so called Maxwell-Jüttner distribution these lies on the Lorentz factor , with . This work uses powerful modern software for a reconstruction of Zaninetti work, which computes with special functions, these are included in the Mathematica software, as by instance Bessel and Meijer G-functions ready to manipulate. A progress is made, it is possible to perform an integral that is not computed in Zaninetti paper. This author connects the correct relativistic probability law: the Maxwell-Jüttner to the synchrotron emissivity with a magnetic B field, this work generalize these results, using the linear Stark effect and deals with an electric field E.