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The evolution of the non-thermal emission emitted by pulsar wind nebulae isgenerally calculated using spatially-independent particle transport models.Although useful, these models implicitly assume that the source of non-thermalparticles is located uniformly throughout the system, contrary to the nature ofpulsar wind nebulae where the source is located at the centre of the system.Additionally, it is not possible to take into account the spatial properties ofthe magnetic field and flow velocity, or the effects of diffusion and gradientand curvature drifts in these models. In this paper we present an extension tothe current nebula models by including a spatial dependence in our numericalsolutions of a Fokker-Planck particle transport equation. These solutions alsoshow the effect that the magnetic field structure has on the evolution of theparticle spectrum. Although applied within the context of pulsar wind nebulae,the presented solutions are equally valid for any similar central source systemsuch as globular clusters.

Spatial Development of Energetic Particle Spectra in Pulsar Wind Nebulae