Energy and Momentum in Electromagnetic Wiggler Free-Electron Laser with A Guide Magnetic Field

The relation between energy E and both parallel and perpendicular components of canonical momentum for a system consisting of a large amplitude electromagnetic wiggler FEL in the presence of a constant axial guide magnetic field is investigated. Analysis of this model at fixed points which represent steady state conditions show that this system consists of two branches: one is the stable branch, which is necessary for efficient FEL operation. The other is an unstable branch, which put limitations on efficient FEL outputs. Deep analysis of energy E as a function of momentum components in addition to the study of the relation between the components of momentum clarifies the situation of energy at equilibrium. Moreover, the relation between the relativistic factor γ and the momentum components selects stable orbits for this system.