# CRPropa 3.1—a low energy extension based on stochastic differential equations

## Abstract

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ{sub ∥} and perpendicular κ{sub ⊥} diffusion coefficients. This dependency is systematically examined as well the influencemore »

- Authors:

- Theoretische Physik IV: Plasma-Astroteilchenphysik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44801 Bochum (Germany)
- Theoretische Physik IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44801 Bochum (Germany)
- II Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)

- Publication Date:

- OSTI Identifier:
- 22676142

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 06; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; ALGORITHMS; ANISOTROPY; COMPUTERIZED SIMULATION; COSMIC RADIATION; COSMIC RAY PROPAGATION; DENSITY; DIFFUSION; ENERGY SPECTRA; EQUATIONS OF MOTION; GALAXIES; INTERACTIONS; MAGNETIC FIELDS; MATHEMATICAL SOLUTIONS; STOCHASTIC PROCESSES; TRANSPORT THEORY

### Citation Formats

```
Merten, Lukas, Tjus, Julia Becker, Eichmann, Björn, Fichtner, Horst, and Sigl, Günter, E-mail: lukas.merten@rub.de, E-mail: julia.tjus@rub.de, E-mail: hf@tp4.rub.de, E-mail: eiche@tp4.rub.de, E-mail: guenter.sigl@desy.de.
```*CRPropa 3.1—a low energy extension based on stochastic differential equations*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/06/046.

```
Merten, Lukas, Tjus, Julia Becker, Eichmann, Björn, Fichtner, Horst, & Sigl, Günter, E-mail: lukas.merten@rub.de, E-mail: julia.tjus@rub.de, E-mail: hf@tp4.rub.de, E-mail: eiche@tp4.rub.de, E-mail: guenter.sigl@desy.de.
```*CRPropa 3.1—a low energy extension based on stochastic differential equations*. United States. doi:10.1088/1475-7516/2017/06/046.

```
Merten, Lukas, Tjus, Julia Becker, Eichmann, Björn, Fichtner, Horst, and Sigl, Günter, E-mail: lukas.merten@rub.de, E-mail: julia.tjus@rub.de, E-mail: hf@tp4.rub.de, E-mail: eiche@tp4.rub.de, E-mail: guenter.sigl@desy.de. Thu .
"CRPropa 3.1—a low energy extension based on stochastic differential equations". United States.
doi:10.1088/1475-7516/2017/06/046.
```

```
@article{osti_22676142,
```

title = {CRPropa 3.1—a low energy extension based on stochastic differential equations},

author = {Merten, Lukas and Tjus, Julia Becker and Eichmann, Björn and Fichtner, Horst and Sigl, Günter, E-mail: lukas.merten@rub.de, E-mail: julia.tjus@rub.de, E-mail: hf@tp4.rub.de, E-mail: eiche@tp4.rub.de, E-mail: guenter.sigl@desy.de},

abstractNote = {The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ{sub ∥} and perpendicular κ{sub ⊥} diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.},

doi = {10.1088/1475-7516/2017/06/046},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 06,

volume = 2017,

place = {United States},

year = {Thu Jun 01 00:00:00 EDT 2017},

month = {Thu Jun 01 00:00:00 EDT 2017}

}