Fiber averaged dynamics associated with the Lorentz force equation

JOURNAL OF GEOMETRY AND PHYSICS

卷:86

Article

Torrome, Ricardo Gallego^1,2 

[1] Univ Lancaster, Dept Phys, Lancaster LA1 4YB, England

[2] Cockcroft Inst, Warrington, Cheshire, England

关键词: Lorentz force equation;    Averaging methods;    Particle dynamics;   

DOI  :  10.1016/j.geomphys.2014.07.013

来源: Elsevier

【 摘 要 】

It is shown that the Lorentz force equation is equivalent to the auto-parallel condition (L)del((x)over dot)(x)over dot = 0 of a linear connection (L)del defined on a convenient pull-back vector bundle. By using a geometric averaging method, an associated averaged Lorentz connection <(L)del > 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)del > remain nearby close to the auto-parallel curves of (L)del. Applications of this result in beam dynamics and plasma physics are briefly described. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free