Galactic Cosmic Rays

Propagation of Galactic cosmic rays can be done with the single-particle approach (solving the equation of motion) or with an ensemble averaged ansatz (solving the transport equation for a particle distribution). The latter one is explained in section “Diffusion of Cosmic Rays”. The single-particle approach is demonstrated in the following example.

Galactic trajectories
- 3D trajectory plot

Diffusion of Cosmic Rays

Diffusion of cosmic rays can be modeled in an ensemble averaged way using transport equations. In CRPropa this is done based on stochastic differential equations (SDEs) which are mathematically equivalent to the more familar transport equations.

The first notebooks give an overview how to set up a simulation using a user-defined diffusion coefficient.

Advection and Adiabatic Energy Changes

Advection in non-divergence-free velocity fields causes adiabatic energy changes, which can be modeled following the next examples.

Adiabatic Cooling
- Example

Diffusive Shock Acceleration

Diffusive shock acceleration or first order Fermi acceleration can be modeled in the diffusive picture as an interplay between diffusion, advection and adiabatic cooling. Simple shock configurations are shown in the following example notebook.

Diffusive Shock Acceleration (DSA)

Momentum Diffusion

Momentum diffusion or second order Fermi acceleration is explained in the following example notebook.

Momentum Diffusion
- Functionality to run the simulation and analyse the data
  - Slow time evolution setup
  - Fast time evolution setup

Example of diffusion in the Milky way

Example for Galactic Propagation

Gas Densities

The last two examples show how to use the gas density fields. They can be used to, e.g., model the CR source distribution and will later be used as target fields for hadron-hadron interation.