Radiation from charged particles in weakly inhomogeneous magnetic fields

Abstract

The spectral distribution of radiation emitted by a charged particle moving nonrelativistically in a prescribed electromagnetic field, consisting of a strong uniform magnetic induction on which is superimposed a weak inhomogeneity, is determined. The calculation is confined to trajectories characterized by small Larmor radii, and to the azimuthal average of the full angular distribution of the radiation, the azimuthal angle being measured in a co-ordinate system for which the uniform component of the field defines the polar axis. If the particle gyrates for a time long compared to the gyro-period, the spectrum separates into several independent lines. Quantitative expressions for the distribution of energy within each line are presented, and then evaluated for selected inhomogeneities. Qualitatively, it is found that inhomogeneities (i) may distort the distribution of energy within the spectral line at the gyro-frequency by broadening, displacing, destroying the symmetry of, and/or splitting that line, and (ii) may also generate spectral lines at aipproximate harmonics of the gyro-frequency. These harmonics are second order in the inhomogeneity, are of successively higher order in the Larmor radius, involve successively higher-order spatial derivatives of the inhomogeneities, may occur at frequencies whose ratios are not precisely ratios of integers, and may be split into two or more closely spaced components.