This is the homepage for the Chalmers Plasma Theory group's numerical tools for simulating runaway electrons. Our research has led to the development of a number of numerical tools that can be used to study runaway electrons, mainly in tokamak plasmas but some also in other plasmas where such particles are present. The tools have been used in several scientific studies which have been published in peer-reviewed journals such as Physical Review Letters, Nuclear Fusion and Physics of Plasmas, among many others.

Numeric tools


NOn-linear Relativistic Solver for Electrons
Matlab GitHub Documentation

  • Solves the spatially homogeneous kinetic equation with non-linear Fokker-Planck operator
  • Synchrotron losses
  • Self-consistent electric field evolution
  • Written in object-oriented Matlab

non-linear fokker-planck, synchrotron, self-consistent electric field, matlab


Synchrotron-detecting Orbit Following Toolkit
C++ GitHub Documentation

  • Computes detected synchrotron and bremsstrahlung
  • Simulates image, spectrum, Stokes parameters and more
  • Works in arbitrary tokamak magnetic field geometry

synchrotron, bremsstrahlung, image, spectrum, polarization


COllisional Distributions of Electrons

  • Solves the spatially homogeneous linear Fokker-Planck equation
  • Avalanche source, self-consistent electric field, partial screening of ions and more
  • Synchrotron and bremsstrahlung losses

linear fokker-planck, avalanche, synchrotron, bremsstrahlung, partial screening, matlab


COllisional Distributions of IONs
Matlab GitHub

  • Solves spatially homogeneous linear Fokker-Planck equation for ions

linear fokker-planck, runaway ions, matlab


SYnchrotron spectra from RUnaway Particles

  • Calculates emitted synchrotron spectrum
  • For single-particle or (CODE) distributions of electrons

Note: This code has been superseded by SOFT.

synchrotron spectrum, CODE distribution function, matlab


Radial evolution of runaway beam

  • 1D model for runaway current and electric field evolution
  • Simulates impurity injection
  • Includes ohmic heating, line radiation, bremsstrahlung, rate equations for ionizations and collisional energy exchange

radial, electric field, diffusion, magnetic field perturbations


In addition to the complete codes presented above, we have also written a number of scripts which runaway electron physicists may find useful. The scripts are provided under open source licenses, free-of-charge, for your convenience.

Name Language Description
Eceff MATLAB A script to calculate the effective critical electric field for runaway generation in the presence of partially ionized impurities.


The tools on this page are developed by the Plasma Theory group at Chalmers University of Technology, Sweden, together with a number of collaborators at other institutes and universities.

Development team
For emails, add the following: Chalmers =, IPP Garching =
Name Email Institution
Dr. Ola Embréus embreus Chalmers
Prof. Tünde Fülöp tunde Chalmers
Linnea Hesslow hesslow Chalmers
Mathias Hoppe hoppe Chalmers
Dr. Gergely Papp ppg Max-Planck-Institut für Plasmaphysik, Garching, Germany
For enquiries about this webpage or the tools presented here, please contact either Mathias or Tünde.
Former members and contributors
Name Institution
Dr. Matt Landreman University of Maryland, MD, USA
Dr. Adam Stahl Chalmers
Dr. George Wilkie Chalmers


Below you will find a list of references to scientific publications involving the tools presented on this page. The references that are underlined are considered to be key references that should be cited by any publication using the tool in question.

Have you published results with any of our tools and would like the publication to appear below? We'd love to include it, so please contact us!