Spectrum of particles radiating in cylindrical and filament magnetic fields

Particle trajectories, and the energy distribution and frequency spectrum for an initially power-law distribution of particle energies, are calculated for particles radiating in cylindrical and filament magnetic fields. If there is a continuous supply of particles to the fields, the spectrum develops two 'breaks'. For the filament field the spectral index changes from - alpha at low frequencies to - alpha - 0.875 at high frequencies. There is also a cutoff to the spectrum. The results are applied to Cas A and the Crab Nebula. 9 references