Relativistic electrodynamics Lagrangian and Hamiltonian for particle accelerators
by Adrian Sfarti
International Journal of Nuclear Energy Science and Technology (IJNEST), Vol. 5, No. 3, 2010

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.

Online publication date: Wed, 02-Jun-2010

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