Adorable reversed field configuration with self-fields effect in a fel

Abstract

The dynamical behavior of relativistic electron governed by the combination of a realistic helical-wiggler free-electron laser (FEL) with a uniform axial guide magnetic field is investigated by the consideration of the effect of the relativistic electrons self-fields. The electron beam is assumed to have uniform density. In Raman regime, a three-dimensional Hamiltonian approach is derived in detail. The consideration of the additional scalar potential Φs represents the basic feature of the analysis. The approach recognized the two usual constants of motion: one concerns the total energy while the other is the canonical axial angular momentum \(\hat P_{z'}\). After some tedious algebra, the dynamical variables problems are solved analytically to study stable and unstable fixed point. The additional scalar potential Φs changes the nature of groups, in group II orbits reversed field configuration near \(\hat \rho _0 = 0\) converted to a simple group II. At the time of the variation of e the energetic interaction zones are discussed. The stability zones of fixed points that allow an excellent interaction between the electron and the existing fields are limited. To validate our model, we apply it to the well-known experience of Conde and Bekefi [Phys. Lett. 67, 3082 (1991)] and get some encouraging results.