Riemann-Lagrange Geometric Dynamics for the Multi-Time Magnetized Non-Viscous Plasma

TL;DR

This paper develops a Riemann-Lagrange geometric framework on 1-jet spaces to model multi-time relativistic magnetized non-viscous plasma, deriving conservation laws, continuity equations, and stream sheet PDEs.

Contribution

It introduces a novel geometrical model for multi-time plasma using Riemann-Lagrange methods, including new conservation laws and PDE formulations.

Findings

Derived conservation laws for multi-time plasma

Formulated continuity equations for plasma dynamics

Established PDEs for stream sheets in the geometric model

Abstract

In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum distinguished (d-) tensor. In that arena, we give the conservation laws and the continuity equations for multi-time plasma. The partial differential equations of the stream sheets (the equivalent of stream lines in the classical semi-Riemannian geometrical approach of plasma) for multi-time plasma are also written.