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I investigate the effect of non-uniform magnetic fields in the extendedstructures of radio galaxies on the observed synchrotron and inverse-Comptonemission. On the assumption of an isotropic field, with a given power spectrumand a Gaussian distribution of the Cartesian components of the magnetic fieldstrength, I derive a simple integral that can be used numerically to calculatethe synchrotron emissivity from any electron population. In the case ofpower-law spectra, I show that it is possible to estimate the differencebetween the synchrotron emissivity from a region with such a field and thatfrom the commonly assumed arrangement where $B$ is constant everywhere, thoughfully tangled, and that this difference is small, though it increases if theelectron energy density scales with the field. An aged electron spectrum insuch a field produces a characteristic curved synchrotron spectrum whichdiffers significantly from the classical Jaffe-Perola spectrum, and I discusssome effects that this might have on standard spectral age fitting. Finally, Ishow that inverse-Compton scattering of the cosmic microwave background is onlymoderately affected by such a field structure, with the effects becoming moreimportant if the electrons follow the field. Magnetic-field estimates in theliterature from combined synchrotron and inverse-Compton modelling will givereasonable estimates of the mean magnetic field energy density if the field isnon-uniform but isotropic.

Synchrotron and inverse-Compton emission from radio galaxies with non-uniform magnetic field and electron distributions