# Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

## Abstract

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman−Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron−electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron−electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic fieldmore »

- Authors:

- Russian Academy of Sciences, Space Research Institute (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22763283

- Resource Type:
- Journal Article

- Journal Name:
- Plasma Physics Reports

- Additional Journal Information:
- Journal Volume: 44; Journal Issue: 4; Other Information: Copyright (c) 2018 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-780X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; ASYMPTOTIC SOLUTIONS; BOLTZMANN EQUATION; ELECTRON COLLISIONS; ELECTRONS; MAGNETIC FIELDS; MAGNETIZATION; POLYNOMIALS; THERMAL CONDUCTIVITY

### Citation Formats

```
Bisnovatyi-Kogan, G. S., E-mail: gkogan@iki.rssi.ru, and Glushikhina, M. V., E-mail: m.glushikhina@iki.rssi.ru.
```*Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter*. United States: N. p., 2018.
Web. doi:10.1134/S1063780X18040013.

```
Bisnovatyi-Kogan, G. S., E-mail: gkogan@iki.rssi.ru, & Glushikhina, M. V., E-mail: m.glushikhina@iki.rssi.ru.
```*Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter*. United States. doi:10.1134/S1063780X18040013.

```
Bisnovatyi-Kogan, G. S., E-mail: gkogan@iki.rssi.ru, and Glushikhina, M. V., E-mail: m.glushikhina@iki.rssi.ru. Sun .
"Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter". United States. doi:10.1134/S1063780X18040013.
```

```
@article{osti_22763283,
```

title = {Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter},

author = {Bisnovatyi-Kogan, G. S., E-mail: gkogan@iki.rssi.ru and Glushikhina, M. V., E-mail: m.glushikhina@iki.rssi.ru},

abstractNote = {The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman−Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron−electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron−electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.},

doi = {10.1134/S1063780X18040013},

journal = {Plasma Physics Reports},

issn = {1063-780X},

number = 4,

volume = 44,

place = {United States},

year = {2018},

month = {4}

}