Title: Relativistic electrodynamics Lagrangian and Hamiltonian for particle accelerators

Authors: Adrian Sfarti

Addresses: CS Department, UC Berkeley, 387 Soda Hall Berkeley, CA 94720-1776, USA

Abstract: A Lagrangian L of a dynamical system is a function that summarises the dynamics of the system (Goldstein et al., 2002). If the Lagrangian of a system is known, then the equations of motion of the system may be obtained by its direct substitution into the Euler-Lagrange equation. One important advantage of the Lagrange formulation of dynamical systems is that the formulation is not tied to any particular coordinate system – rather, any convenient set of variables may be used to describe the system. Finding the Lagrangian for a system is a mix of science and art. In the following paper we will demonstrate how to find it for the case of relativistic electrodynamics as a direct application for particle accelerators. We will show how we can start from the expression of the Lagrangian in classical electrodynamics in finding its expression for relativistic cases.

Keywords: Lagrangian; Hamiltonian; relativistic electrodynamics; particle accelerators.

DOI: 10.1504/IJNEST.2010.033474

International Journal of Nuclear Energy Science and Technology, 2010 Vol.5 No.3, pp.189 - 194

Available online: 02 Jun 2010 *

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