# Numerical Realization of a Shell Model for Impurity Spreading in Plasmas

## Abstract

In plasmas of fusion devices impurity particles are released as a consequence of wall erosion and are seeded deliberately for diverse purposes. Often they enter the plasma volume from small spots and spread away both along and perpendicular to the magnetic field. This process is described by continuity, motion and heat balance equations taking into account such physical processes as ionization by electrons, friction and heating in coulomb collisions with background ions, etc. In present paper we introduce a shell model where solutions of these equations, such as the densities of different impurity ions, are approximated by functions decaying exponentially from the source region due to the ionization into higher charged states. By integrating the original transport equations over several space regions, we get a set of ordinary differential equations describing the time evolution of the characteristic values for the impurity ion densities, fluxes, temperatures, and the dimensions along and across the magnetic field of the clouds where different states are predominantly localized. The equations obtained include time derivatives of complex non-linear combinations of the variables in question. Two numerical approaches to solve such equations are elaborated and compared by considering the spreading of lithium particles in deuterium plasma.

- Authors:

- Institute for Energy and Climate Research-Plasma Physics, Research Center Juelich GmbH, Juelich, 52428 (Germany)

- Publication Date:

- OSTI Identifier:
- 21611601

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1389; Journal Issue: 1; Conference: ICNAAM 2011: Conference on numerical analysis and applied mathematics, Halkidiki (Greece), 19-25 Sep 2011; Other Information: DOI: 10.1063/1.3636928; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CHARGED-PARTICLE TRANSPORT; DEUTERIUM; DIFFERENTIAL EQUATIONS; ELECTRONS; ION COLLISIONS; ION DENSITY; ION TEMPERATURE; IONIZATION; IONS; LITHIUM; MAGNETIC FIELDS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PLASMA; PLASMA DENSITY; PLASMA IMPURITIES; THERMONUCLEAR DEVICES; TRANSPORT THEORY; ALKALI METALS; CHARGED PARTICLES; COLLISIONS; ELEMENTARY PARTICLES; ELEMENTS; EQUATIONS; FERMIONS; HYDROGEN ISOTOPES; IMPURITIES; ISOTOPES; LEPTONS; LIGHT NUCLEI; METALS; NUCLEI; ODD-ODD NUCLEI; RADIATION TRANSPORT; STABLE ISOTOPES

### Citation Formats

```
Tokar, M. Z., and Koltunov, M.
```*Numerical Realization of a Shell Model for Impurity Spreading in Plasmas*. United States: N. p., 2011.
Web. doi:10.1063/1.3636928.

```
Tokar, M. Z., & Koltunov, M.
```*Numerical Realization of a Shell Model for Impurity Spreading in Plasmas*. United States. doi:10.1063/1.3636928.

```
Tokar, M. Z., and Koltunov, M. Wed .
"Numerical Realization of a Shell Model for Impurity Spreading in Plasmas". United States. doi:10.1063/1.3636928.
```

```
@article{osti_21611601,
```

title = {Numerical Realization of a Shell Model for Impurity Spreading in Plasmas},

author = {Tokar, M. Z. and Koltunov, M.},

abstractNote = {In plasmas of fusion devices impurity particles are released as a consequence of wall erosion and are seeded deliberately for diverse purposes. Often they enter the plasma volume from small spots and spread away both along and perpendicular to the magnetic field. This process is described by continuity, motion and heat balance equations taking into account such physical processes as ionization by electrons, friction and heating in coulomb collisions with background ions, etc. In present paper we introduce a shell model where solutions of these equations, such as the densities of different impurity ions, are approximated by functions decaying exponentially from the source region due to the ionization into higher charged states. By integrating the original transport equations over several space regions, we get a set of ordinary differential equations describing the time evolution of the characteristic values for the impurity ion densities, fluxes, temperatures, and the dimensions along and across the magnetic field of the clouds where different states are predominantly localized. The equations obtained include time derivatives of complex non-linear combinations of the variables in question. Two numerical approaches to solve such equations are elaborated and compared by considering the spreading of lithium particles in deuterium plasma.},

doi = {10.1063/1.3636928},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1389,

place = {United States},

year = {2011},

month = {9}

}