The Effect of Diffusion on the Particle Spectra in Pulsar Wind Nebulae

A possible way to calculate particle spectra as a function of position in pulsar wind nebulae is to solve a Fokker-Planck transport equation. This paper presents numerical solutions to the transport equation with the processes of convection, diffusion, adiabatic losses, and synchrotron radiation included. In the first part of the paper the steady-state version of the transport equation is solved as a function of position and energy. This is done to distinguish the various effects of the aforementioned processes on the solutions to the transport equation. The second part of the paper deals with a time-dependent solution to the transport equation, specifically taking into account the effect of a moving outer boundary. The paper highlights the fact that diffusion can play a significant role in reducing the amount of synchrotron losses, leading to a modification in the expected particle spectra. These modified spectra can explain the change in the photon index of the synchrotron emission as a function of position. The solutions presented in this paper are not limited to pulsar wind nebulae, but can be applied to any similar central source system, e.g. globular clusters

Drift and Forbush decreases

Evidence is presented that the drift effect on the modulation of galactic cosmic rays can be seen on Forbush decreases observed by the Deep River and Hermanus neutron monitors

Proton Modulation Near Solar Minimum Periods in Consecutive Solar Cycles

Observations or the Pioneer/Voyager missions during 1985/1986/1987, together with observations at Earth in 1976/1977 and 1987, are compared with predictions of a steady-state modulation model. The qualitative features of the modulation are well understood, but to get quantitative agreement with observations, drastic modifications have to be made to the Parker spiral magnetic field above the solar poles

Cosmic Ray Perpendicular Diffusion Coefficient and Drift Velocity Calculated from Pioneer/Voyager Observations

The radial and latitudinal gradients measured by the Pioneer 10 and Voyager 1 and 2 spacecraft, reported by Cummings and Stone (1990), provide a unique opportunity to calculate the cosmic ray perpendicular diffusion coefficient and drift velocity

Notes on drift theory

It is shown that there is a simpler way to derive the average guiding center drift of a distribution of particles than via the so-called single particle analysis. Based on this derivation it is shown that the entire drift formalism can be considerably simplified, and that results for low order anisotropies are more generally valid than is usually appreciated. This drift analysis leads to a natural alternative derivation of the drift velocity along a neutral sheet