Electromagnetic field of a charge moving in a cold magnetized plasma

The present paper addresses the electromagnetic field generated by a point charge or a small charged particle bunch moving with constant velocity in a cold magnetized plasma, along the external magnetic field. Attention is focused on the case of ultrarelativistic motion. The field surrounding the point charge is investigated both analytically and numerically. In the analytical study, we obtain rigorous decomposition of the field into quasistatic and wave components. Beating behavior in the far-field zone and harmonic behavior in the vicinity of the charge trajectory are found using suitable approximate approaches. The transverse component of the electric field exhibits a strong (inversely proportional) singularity on the charge trajectory, while the longitudinal components of both the electric and magnetic fields exhibit a weaker (logarithmic) singularity. An efficient numerical approach is developed to calculate the field for arbitrary parameters. An efficient algorithm for calculating the fields of small bunches with different forms is also presented, using a thin charged disk and a charged cylinder as representative examples..