Unified nonlinear orbit dynamics of an equilibrium electron in a helical wiggler with a positive or reversed axial-guide magnetic field at magnetoresonance.

Abstract

Nonlinear orbit dynamics are investigated analytically for a single relativistic electron in an ideal helical wiggler with a positive or reversed axial-guide magnetic field at magnetoresonance. An algebraic equation is derived for determining the maximum perpendicular velocity. The upper limit for a transverse electron orbit excursion is found to be proportional to ${\mathrm{\ensuremath{\varepsilon}}}^{1/3}$ and \ensuremath{\varepsilon} for the positive and reversed guide field, respectively, where \ensuremath{\varepsilon} is the ratio of the wiggler field to the guide field. The analytical results are in agreement with numerical calculations.