Propagation through Turbulent Magnetic Fields

We have examined the propagation of cosmic rays through turbulent magnetic fields as described by Lee and Clay (1995) and Clay (2000). We used a random magnetic field with a turbulent Kolmogorov spectrum and a maximum scale size of 100pc. We wished to determine how far cosmic ray particles would propagate in such a field before their flux was significantly reduced by scattering. One might expect that the attenuation length would be related, in an order of magnitude way, to the gyroradius of particles in a simple field which had the strength of the random field under consideration. In propagating particles through a slab containing such a modelled field, it was found that the number passing completely through a certain thickness of slab reduces exponentially to e^-1 over approximately six gyroradii. In other words, a diffusive propagation model would require containment dimensions greater than or of the order of 5 to 10 gyroradii in order that the diffusive process would operate without significant particle loss from the sides of the container. With a field strength of G, this distance would be several kiloparsecs at an energy of

eV (0.7kpc gyroradius for protons).

If one asks what thickness is required to obtain a particular magnitude of anisotropy, our modelling can be extended to observe how many particles pass the observer and then how many return, based on the distance of the observer to the far limit of the slab which acts as a sink. In this case, for a 10% anisotropy, the distance to the limit of the slab is required to be 1-2 gyroradii, in broad agreement with the argument discussed above.

© Copyright Astronomical Society of Australia 1997