Electron orbits in combined electromagnetic wiggler and axial guide magnetic fields

Abstract

The single-particle orbits due to a large amplitude, backward propagating electromagnetic wave and an axial guide magnetic field are derived, and the stability of the orbits are discussed. The large amplitude electromagnetic wave acts like a magnetostatic wiggler in a free-electron laser. Two classes of orbit are found corresponding to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Omega_{0} &lt; \gamma(\omega_{w} + k_{w}\upsilon_{\parallel})</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Omega_{0} &gt; \gamma(\omega_{w} + K_{w}\upsilon_{\parallel})</tex> , where Ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> is the electron cyclotron frequency, ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</inf> and k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</inf> are the frequency and wave vector of the electromagnetic wave, γ is the relativistic factor, and υ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∥</inf> is the axial electron velocity. However, unlike the case of a magnetostatic wiggler, both classes of orbit are shown to be stable.