Velocity inversion of a relativistic electron incident by a vortex beam in a magnetic field

A method is proposed to invert the velocity of a relativistic electron incident by a vector Bessel vortex beam in a magnetic field by analyzing the spectra of the backward scattered echoes. The scattering power and spectra are investigated based on the vector plane wave angular spectrum theory and the Thomson scattering theory. The results indicate that the high velocity of an electron causes the distribution of the scattered power on the x o y plane to shift in the direction of the velocity. Additionally, the spectra of the scattered echoes display periodic bimodality due to the cyclotron motion of the electrons. The velocity of a relativistic electron parallel to the applied magnetic field can be obtained from the spectrum of the scattered echoes and the parameters of the vortex beam. The conclusions suggest that both the magnitude and the direction of the velocity of a relativistic electron can be determined using a set of orthogonal magnetic fields. This work is significant for studying the scattering of vortex beams by plasmas and developing diagnostic techniques of plasmas.