Electron Dynamics in Presence of Static Helical Magnet Inside Circular Waveguide

The dynamics of an electron in the fields associated with a TE electromagnetic wave propagating inside a circular waveguide is analytically studied. The motion of this electron along the axis of the waveguide is investigated in the existence of a helical magnet (in which the field is perpendicular to the axis of the waveguide and rotating as a function of position along the magnet). It is shown that it can be accelerated due to its interaction with polarized fields of microwave radiation propagating along the waveguide. The fields for the lowest order
$\hbox{TE}_{11}$
modes and the deflection angle of electron trajectory, due to these fields, are obtained. Also, an expression of the acceleration gradient of the electron and its energy gain are evaluated for different intensities and frequencies of the microwave.