# Numerical calculation of ion runaway distributions

## Abstract

Ions accelerated by electric fields (so-called runaway ions) in plasmas may explain observations in solar flares and fusion experiments; however, limitations of previous analytic work have prevented definite conclusions. In this work, we describe a numerical solver of the 2D non-relativistic linearized Fokker-Planck equation for ions. It solves the initial value problem in velocity space with a spectral-Eulerian discretization scheme, allowing arbitrary plasma composition and time-varying electric fields and background plasma parameters. The numerical ion distribution function is then used to consider the conditions for runaway ion acceleration in solar flares and tokamak plasmas. Typical time scales and electric fields required for ion acceleration are determined for various plasma compositions, ion species, and temperatures, and the potential for excitation of toroidal Alfvén eigenmodes during tokamak disruptions is considered.

- Authors:

- Department of Applied Physics, Chalmers University of Technology, SE-412 96 Göteborg (Sweden)
- CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22410302

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCELERATION; ALFVEN WAVES; DISTRIBUTION FUNCTIONS; EIGENFREQUENCY; ELECTRIC FIELDS; EXCITATION; FOKKER-PLANCK EQUATION; IONS; PLASMA; RELATIVISTIC RANGE; SOLAR FLARES; TOKAMAK DEVICES; VELOCITY

### Citation Formats

```
Embréus, O., Stahl, A., Hirvijoki, E., Fülöp, T., and Newton, S.
```*Numerical calculation of ion runaway distributions*. United States: N. p., 2015.
Web. doi:10.1063/1.4921661.

```
Embréus, O., Stahl, A., Hirvijoki, E., Fülöp, T., & Newton, S.
```*Numerical calculation of ion runaway distributions*. United States. doi:10.1063/1.4921661.

```
Embréus, O., Stahl, A., Hirvijoki, E., Fülöp, T., and Newton, S. Fri .
"Numerical calculation of ion runaway distributions". United States. doi:10.1063/1.4921661.
```

```
@article{osti_22410302,
```

title = {Numerical calculation of ion runaway distributions},

author = {Embréus, O. and Stahl, A. and Hirvijoki, E. and Fülöp, T. and Newton, S.},

abstractNote = {Ions accelerated by electric fields (so-called runaway ions) in plasmas may explain observations in solar flares and fusion experiments; however, limitations of previous analytic work have prevented definite conclusions. In this work, we describe a numerical solver of the 2D non-relativistic linearized Fokker-Planck equation for ions. It solves the initial value problem in velocity space with a spectral-Eulerian discretization scheme, allowing arbitrary plasma composition and time-varying electric fields and background plasma parameters. The numerical ion distribution function is then used to consider the conditions for runaway ion acceleration in solar flares and tokamak plasmas. Typical time scales and electric fields required for ion acceleration are determined for various plasma compositions, ion species, and temperatures, and the potential for excitation of toroidal Alfvén eigenmodes during tokamak disruptions is considered.},

doi = {10.1063/1.4921661},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 5,

volume = 22,

place = {United States},

year = {2015},

month = {5}

}