Cosmic Ray Transport

From the vast field of cosmic ray related research my main interest is in the study of Galactic propagation and on modelling cosmic ray sources. The latter of these topics is discussed here, while their propagation is discussed here.
The study of cosmic ray propagation or cosmic ray transport concerns the motion of the energetic particles in interstellar space, between their acceleration in the cosmic ray sources and their arrival at Earth.
This motion can be described on different levels of complexity. The most general description considers the motion of the individual particles. After such a cosmic ray particle leaves some cosmic ray source with high energy it propagates through interstellar space, where it interacts with the interstellar medium (ISM). This interaction determines the motion in space and the energy loss of such a particle.
The relevant energy loss processes of a cosmic ray electron include synchrotron, inverse compton and bremsstrahlung losses. Cosmic ray nucleons suffer much weaker energy losses and are mainly affected by Coulomb and ionisation losses.
The motion of a cosmic ray particle in space is mostly determined by its interaction with the interstellar magnetic field. Being chared particles, cosmic rays gyrate about magnetic field lines. Therefore, they are also affected by convective motions of the plasma in the ISM. More importantly cosmic rays frequently scatter off irregularities in the interstellar magnetic field.
This shows that the motion of a cosmic ray particle in the ISM is a random motion requiring a very large number of such particles in a corresponding model. Consequently, mainy studies, including ours, rather use a statistical description of the cosmic ray transport process, where it was found that on average their spatial can be described by a diffusion process. The resulting transport equation for a distribution function of cosmic rays reads:
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My personal interst is in the solution of this transport equation with numerical means. While a analytical solution of this equation is also possible with sufficiently simplified transport parameters, only a numerical solution allows to take the complexity of the interstellar medium into account. Also most numerical models particularly for Galactic cosmic ray transport apply a variety of simplifications like the assumption of axial symmetry. Therefore, our current studies investigate the effect of a more realistic description of the cosmic ray transport parameters on the cosmic ray transport. Our corresponding simulations apply the Picard code to solve the cosmic ray tranport equation.