DiffusiveShockAccelerationModels.jl

This package provides a number of efficiency models for Diffuse Shock Acceleration (DSA). It provides a number of functions to calculate what fraction of the energy dissipated at a shock is used to accelerate Cosmic Rays (CRs). If you use this implementation in a publication please cite Böss et. al. (2023).

Install

As usual with Julia just run

] add DiffusiveShockAccelerationModels

Mach number dendent efficiency models

Different authors found a number of models that describe the acceleration efficiency of CRs at shocks dependent on the sonic Mach number. Here we implemented the following DSA models:

Magnetic field angle dependent efficiency models

Another parameter in the acceleration efficiency is the shock obliquity. Here we used the results from Pais et. al. (2019) who fit a functional form to the data by Caprioli&Spitkovsky (2014).

Ions

Ions are found to be accelerated primarily at quasi-parallel shocks. We provide two helper functions for this.

Electrons

Electrons are found to be accelerated primarily at quasi-perpendicular shocks. We provide two helper functions for this.

Usage

To use for example the mach number dependent model by Kang & Ryu (2013), combined with the shock obliquity model by Pais et. al. (2019)

using DiffusiveShockAccelerationModels

ηM_model = KR13()  # Mach number dependent model
Mach = 5.0         # we assume a Mach 5 shock
θ_B  = 0.1π        # angle between shock normal and magnetic field vector
X_cr = 0.0         # X_cr = P_cr / P_th -> in this case no pre-existing CRs

# magnetic field angle dependent acc. efficiency
ηB   = ηB_acc_p(θ_B)  

# Mach number dependent acc. efficiency
ηM   = η_Ms(ηM_model, Mach, X_cr)

# total efficiency
η_tot = ηB * ηM