# Analytic model for the runaway distribution function in the presence of spatial diffusion

## Abstract

A steady-state kinetic model for runaway electrons in the presence of radial diffusion in a stochastic magnetic field is adopted and solved for a constant magnetic diffusivity. The model is constructed to recover the correct runaway production rate in the absence of spatial diffusion. The parallel energetic electron distribution function [ital f] is found by matching the solutions from three regions in parallel velocity space and is employed to form moments of [ital f]. Upper and lower bounds on the spatial diffusion are obtained by using these moments and the model exhibits the strong sensitivity to collisionality needed to explain the difference between similar plasmas with little or no hard x-ray signal and those with significant hard x-ray signals.

- Authors:

- (Fusion Research Center, University of Texas at Austin, Austin, Texas 78712 (United States) Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States))
- (Lodestar Research Corporation, 2400 Central Avenue, Boulder, Colorado 80301 (United States))
- (Fusion Research Center and Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States))

- Publication Date:

- OSTI Identifier:
- 5311483

- DOE Contract Number:
- FG05-88ER53267; FG05-80ET53088; FG02-88ER53263; FG02-91ER54109

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas; (United States)

- Additional Journal Information:
- Journal Volume: 1:3; Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; RUNAWAY ELECTRONS; DIFFUSION; DISTRIBUTION FUNCTIONS; FLUCTUATIONS; HARD X RADIATION; KINETIC EQUATIONS; MAGNETIC FIELDS; STOCHASTIC PROCESSES; TOKAMAK DEVICES; TRANSPORT THEORY; CLOSED PLASMA DEVICES; ELECTROMAGNETIC RADIATION; ELECTRONS; ELEMENTARY PARTICLES; EQUATIONS; FERMIONS; FUNCTIONS; IONIZING RADIATIONS; LEPTONS; RADIATIONS; THERMONUCLEAR DEVICES; VARIATIONS; X RADIATION; 700330* - Plasma Kinetics, Transport, & Impurities- (1992-); 700320 - Plasma Diagnostic Techniques & Instrumentation- (1992-)

### Citation Formats

```
Catto, P.J., Myra, J.R., and Wootton, A.J.
```*Analytic model for the runaway distribution function in the presence of spatial diffusion*. United States: N. p., 1994.
Web. doi:10.1063/1.870814.

```
Catto, P.J., Myra, J.R., & Wootton, A.J.
```*Analytic model for the runaway distribution function in the presence of spatial diffusion*. United States. doi:10.1063/1.870814.

```
Catto, P.J., Myra, J.R., and Wootton, A.J. Tue .
"Analytic model for the runaway distribution function in the presence of spatial diffusion". United States. doi:10.1063/1.870814.
```

```
@article{osti_5311483,
```

title = {Analytic model for the runaway distribution function in the presence of spatial diffusion},

author = {Catto, P.J. and Myra, J.R. and Wootton, A.J.},

abstractNote = {A steady-state kinetic model for runaway electrons in the presence of radial diffusion in a stochastic magnetic field is adopted and solved for a constant magnetic diffusivity. The model is constructed to recover the correct runaway production rate in the absence of spatial diffusion. The parallel energetic electron distribution function [ital f] is found by matching the solutions from three regions in parallel velocity space and is employed to form moments of [ital f]. Upper and lower bounds on the spatial diffusion are obtained by using these moments and the model exhibits the strong sensitivity to collisionality needed to explain the difference between similar plasmas with little or no hard x-ray signal and those with significant hard x-ray signals.},

doi = {10.1063/1.870814},

journal = {Physics of Plasmas; (United States)},

issn = {1070-664X},

number = ,

volume = 1:3,

place = {United States},

year = {1994},

month = {3}

}