Fiber averaged dynamics associated with the Lorentz force equation

Abstract

It is shown that the Lorentz force equation is equivalent to the auto-parallel condition ${}^L{\nabla }_{\dot{x}}\dot{x}=0$ of a linear connection ${}^L\nabla$ defined on a convenient pull-back vector bundle. By using a geometric averaging method, an associated {\it averaged Lorentz connection} $⟨{}^L\nabla ⟩$ and the corresponding auto-parallel equation are obtained. After this, it is shown that in the ultra-relativistic limit and for narrow one-particle probability distribution functions, the auto-parallel curves of $⟨{}^L\nabla ⟩$ remain {\it nearby} close to the auto-parallel curves of ${}^L\nabla$. Applications of this result in beam dynamics and plasma physics are briefly described.

This version, except for very few typographical corrections and several changes in the bibliography, was published in Journal of Geometry and Physics

References in corpus (7)

• Fermat Principle in Finsler Spacetimes
• Asymptotic analysis of ultra-relativistic charge
• On a rigidity condition for Berwald Spaces
• Averaged Lorentz Dynamics and an application in Plasma Dynamics
• Fluid Models from Kinetic Models using a Geometric Averaging Procedure
• On the convex invariance in Finsler geometry
• Jacobi equations and particle accelerator beam dynamics

Cited by in corpus (6)

• On singular generalized Berwald spacetimes and the equivalence principle
• A second order differential equation for a point charged particle
• Averaged Lorentz Dynamics and an application in Plasma Dynamics
• Fluid Models from Kinetic Models using a Geometric Averaging Procedure
• Averaged dynamics of ultra-relativisitc charged particles beams
• Jacobi equations and particle accelerator beam dynamics