Cerenkov Radiation in a Plasma

Abstract

This paper treats Cerenkov radiation produced by a charged particle or beam moving in a plasma along an arbitrary direction with respect to the magnetic field. The expressions for the Cerenkov condition and the radiation output are obtained for the cases of a charged particle or beam moving both along and perpendicular to the magnetic field. The frequency ranges of the radiation for two type of waves, i.e. the ordinary and extraordinary waves, are determined by using the Cerenkov condition.For the case of a charged particle of beam moving in a plasma along the magnetic field, the extraordinary waves can be emitted, for a certain range of β=v/c, in the range of frequencies lower as wellas higher than the plasma frequency, and then the regions for the ordinary, and extraordinary waves can overlap. Under the non-relativistic condition (β<<1), the total power radiated by a charged particle or a bunched beam is, respectively, as follows : [dW/dt] _??_β_??_0μ0q2v/16π (2ω2p+ω2c) or[W] _??_β_??_0μ0I2/8·ω3/ω2C, ωp≤ω<√ω2p+ω2c, where μ0 is the permeability in vacuum, ωp and ωc are the plasma and cyclotron angular frequencies, q and v are the charge and velocity of a particle, and I is the beam current. The power output for the extraordinary waves is evaluated numerically. The result shows that Cerenkov radiation occurs with considerably high power at comparatively small magnetic field strengths and also under non-relativistic conditions.For the case of a charged particle or beam moving perpendicular to the magnetic field, the ordinary waves are emitted in the range of frequencies higher as well as lower than the plasma frequency, while the extra-ordinary waves are emitted in the range of frequencies higher than the plasma frequency. The maximum frequency emitted for both types of waves never exceed the frequency defined by ω=√ω2p+ω2c·In the non-relativistic case (β<<1) only the ordinary waves are emitted under the following coherence condition : [cos2θ0 (φ)] β_??_0=1-ω2 (ω2p+ω2c-ω2) /ω2pω2csin2φ, φ≠0, and the frequency ranges are separated into two regions. The radiation pattern is more complicated as compared with the case of a particle or beam moving along the magnetic field; instead of circular cones, we have two non-circular Cerenkov cones for the ordinary and extraordinary waves, with the radiation intensity varying on different generatrices of these conical surfaces.