# Hyper-resistivity and electron thermal conductivity due to destroyed magnetic surfaces in axisymmetric plasma equilibria

## Abstract

In order to model the effects of small-scale current-driven magnetic fluctuations in a mean-field theoretical description of a large-scale plasma magnetic field B(x,t), a space and time dependent hyper-resistivity {Lambda}(x,t) can be incorporated into the Ohm's law for the parallel electric field E Dot-Operator B. Using Boozer coordinates, a theoretical method is presented that allows for a determination of the hyper-resistivity {Lambda}({psi}) functional dependence on the toroidal magnetic flux {psi} for arbitrary experimental steady-state Grad-Shafranov axisymmetric plasma equilibria, if values are given for the parallel plasma resistivity {eta}({psi}) and the local distribution of any auxiliary plasma current. Heat transport in regions of plasma magnetic surfaces destroyed by resistive tearing modes can then be modeled by an electron thermal conductivity k{sub e}({psi})=({epsilon}{sub 0}{sup 2}m{sub e}/e{sup 2}){Lambda}({psi}), where e and m{sub e} are the electron charge and mass, respectively, while {epsilon}{sub 0} is the permittivity of free space. An important result obtained for axisymmetric plasma equilibria is that the {psi}{psi}-component of the metric tensor of Boozer coordinates is given by the relation g{sup {psi}{psi}}({psi}){identical_to}{nabla}{psi} Dot-Operator {nabla}{psi}=[{mu}{sub 0}G({psi})][{mu}{sub 0}I({psi})]/{iota}({psi}), with {mu}{sub 0} the permeability of free space, G({psi}) the poloidal current outside a magnetic surface, I({psi}) the toroidal current inside a magnetic surface,more »

- Authors:

- Department of Radiologic Sciences, Thomas Jefferson University, 901 Walnut Street, Philadelphia, Pennsylvania 19107-5233 (United States)

- Publication Date:

- OSTI Identifier:
- 22072462

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 6; Other Information: (c) 2012 American Institute of Physics; 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; AXIAL SYMMETRY; COORDINATES; ELECTRIC CURRENTS; ELECTRIC FIELDS; ELECTRONS; FLUCTUATIONS; HEAT TRANSFER; MAGNETIC FIELDS; MAGNETIC FLUX; MAGNETIC SURFACES; MEAN-FIELD THEORY; PERMEABILITY; PERMITTIVITY; PLASMA; ROTATIONAL TRANSFORM; STEADY-STATE CONDITIONS; TEARING INSTABILITY; TENSORS; THERMAL CONDUCTIVITY; TIME DEPENDENCE

### Citation Formats

```
Weening, R. H.
```*Hyper-resistivity and electron thermal conductivity due to destroyed magnetic surfaces in axisymmetric plasma equilibria*. United States: N. p., 2012.
Web. doi:10.1063/1.4728080.

```
Weening, R. H.
```*Hyper-resistivity and electron thermal conductivity due to destroyed magnetic surfaces in axisymmetric plasma equilibria*. United States. doi:10.1063/1.4728080.

```
Weening, R. H. Fri .
"Hyper-resistivity and electron thermal conductivity due to destroyed magnetic surfaces in axisymmetric plasma equilibria". United States. doi:10.1063/1.4728080.
```

```
@article{osti_22072462,
```

title = {Hyper-resistivity and electron thermal conductivity due to destroyed magnetic surfaces in axisymmetric plasma equilibria},

author = {Weening, R. H.},

abstractNote = {In order to model the effects of small-scale current-driven magnetic fluctuations in a mean-field theoretical description of a large-scale plasma magnetic field B(x,t), a space and time dependent hyper-resistivity {Lambda}(x,t) can be incorporated into the Ohm's law for the parallel electric field E Dot-Operator B. Using Boozer coordinates, a theoretical method is presented that allows for a determination of the hyper-resistivity {Lambda}({psi}) functional dependence on the toroidal magnetic flux {psi} for arbitrary experimental steady-state Grad-Shafranov axisymmetric plasma equilibria, if values are given for the parallel plasma resistivity {eta}({psi}) and the local distribution of any auxiliary plasma current. Heat transport in regions of plasma magnetic surfaces destroyed by resistive tearing modes can then be modeled by an electron thermal conductivity k{sub e}({psi})=({epsilon}{sub 0}{sup 2}m{sub e}/e{sup 2}){Lambda}({psi}), where e and m{sub e} are the electron charge and mass, respectively, while {epsilon}{sub 0} is the permittivity of free space. An important result obtained for axisymmetric plasma equilibria is that the {psi}{psi}-component of the metric tensor of Boozer coordinates is given by the relation g{sup {psi}{psi}}({psi}){identical_to}{nabla}{psi} Dot-Operator {nabla}{psi}=[{mu}{sub 0}G({psi})][{mu}{sub 0}I({psi})]/{iota}({psi}), with {mu}{sub 0} the permeability of free space, G({psi}) the poloidal current outside a magnetic surface, I({psi}) the toroidal current inside a magnetic surface, and {iota}({psi}) the rotational transform.},

doi = {10.1063/1.4728080},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 6,

volume = 19,

place = {United States},

year = {2012},

month = {6}

}