The Doppler Effect in a Warm Uniaxial Plasma

In this paper we consider the character of the radiation emittedby a radiator moving with uniform velocity through a warm, uniaxialplasma. It is shown that the dispersive and anisotropic natureof the plasma plays an important role in determining both theDoppler shift in frequency and the power spectrum of the radiation.The power spectrum and the Doppler relation between the frequencyand the direction of the emitted radiation are calculated when(a) the motion is parallel to the magnetic field, and (b) themotion is perpendicular to the magnetic field. It is shown thatthe Doppler shift and the power spectrum are substantially differentin these two cases. The formulae for the {caron}erenkov radiationemitted by a moving charged particle may be obtained from thosefor Doppler radiation. In the last section we show that a particlemoving parallel to the axis of symmetry excites a power spectrumwhich is linear with frequency, whereas a particle moving perpendicularto that axis excites a power spectrum that is sharply peakednear the plasma frequency.