Anomalous transport of cosmic ray electrons

Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time: 〈 ∆x 〉 ∝ t with 0 < α < 2 are modelled using the formalism of continuous time random walks. We compute particle propagators which have the required dependence on space and time and use these to find the spatial dependence of the synchrotron radiation emitted by a population of continuously injected electrons. As the electrons are transported away from the source they cool, and the synchrotron spectrum softens. Subdiffusive (α < 1) transport – corresponding to stochastic trapping, or restriction of the transport across the average direction of a stochastic magnetic field – produces a much slower rate of change of spectral index than does supra-diffusion (1 < α < 2) – which occurs when particles move almost without scattering, in a field containing large ordered regions. Application to the diffuse emission of the outer parts of the Coma cluster favours an interpretation in terms of supra-diffusion.