# 3D Burgers Equation in Relativistic Plasma in the Presence of Electron and Negative Ion Trapping: Evolution of Shock Wave

## Abstract

The characteristics of shock waves in a relativistic plasma in the presence of nonisothermal electrons and nonisothermal negative ions is investigated by deriving the evolution equation in terms of a modified 3D Burgers equation, or trapped 3D Burgers equation. The solution of this equation is examined analytically to study the salient characteristics of shock waves in such plasma. The nonlinear coefficient is found to have the lowest (highest) value when the negative ions move toward thermal equilibrium with a dip-shaped electron distribution (when both electrons and negative ions follow a dip-shaped distribution) for a particular value of relativistic factor, and it remains in an intermediate state when both electrons and negative ions follow a flat-topped distribution. On the other hand, the dissipative coefficient is found to decrease (increase) with increasing relativistic parameter (viscous parameter). A profound effect of the trapped state of both electrons and negative ions and the temperature ratio between positive ions and electrons (negative ions and electrons) on the structure of the shock wave is also seen. However, it has been noticed that the trapped parameter of electrons has a dominating control over the shock potential profile than the trapped parameter of negative ions.

- Authors:

- Gauhati University, Department of Applied Sciences (India)
- Siksha ‘O’ Anusandhan, Computer Science and Information Technology (India)

- Publication Date:

- OSTI Identifier:
- 22763221

- Resource Type:
- Journal Article

- Journal Name:
- Plasma Physics Reports

- Additional Journal Information:
- Journal Volume: 44; Journal Issue: 10; 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:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANIONS; ELECTRONS; EVOLUTION EQUATIONS; INTERMEDIATE STATE; NONLINEAR PROBLEMS; RELATIVISTIC PLASMA; RELATIVISTIC RANGE; THERMAL EQUILIBRIUM

### Citation Formats

```
Deka, M. Kr., E-mail: manojd143@gmail.com, and Dev, A. N.
```*3D Burgers Equation in Relativistic Plasma in the Presence of Electron and Negative Ion Trapping: Evolution of Shock Wave*. United States: N. p., 2018.
Web. doi:10.1134/S1063780X18100021.

```
Deka, M. Kr., E-mail: manojd143@gmail.com, & Dev, A. N.
```*3D Burgers Equation in Relativistic Plasma in the Presence of Electron and Negative Ion Trapping: Evolution of Shock Wave*. United States. doi:10.1134/S1063780X18100021.

```
Deka, M. Kr., E-mail: manojd143@gmail.com, and Dev, A. N. Mon .
"3D Burgers Equation in Relativistic Plasma in the Presence of Electron and Negative Ion Trapping: Evolution of Shock Wave". United States. doi:10.1134/S1063780X18100021.
```

```
@article{osti_22763221,
```

title = {3D Burgers Equation in Relativistic Plasma in the Presence of Electron and Negative Ion Trapping: Evolution of Shock Wave},

author = {Deka, M. Kr., E-mail: manojd143@gmail.com and Dev, A. N.},

abstractNote = {The characteristics of shock waves in a relativistic plasma in the presence of nonisothermal electrons and nonisothermal negative ions is investigated by deriving the evolution equation in terms of a modified 3D Burgers equation, or trapped 3D Burgers equation. The solution of this equation is examined analytically to study the salient characteristics of shock waves in such plasma. The nonlinear coefficient is found to have the lowest (highest) value when the negative ions move toward thermal equilibrium with a dip-shaped electron distribution (when both electrons and negative ions follow a dip-shaped distribution) for a particular value of relativistic factor, and it remains in an intermediate state when both electrons and negative ions follow a flat-topped distribution. On the other hand, the dissipative coefficient is found to decrease (increase) with increasing relativistic parameter (viscous parameter). A profound effect of the trapped state of both electrons and negative ions and the temperature ratio between positive ions and electrons (negative ions and electrons) on the structure of the shock wave is also seen. However, it has been noticed that the trapped parameter of electrons has a dominating control over the shock potential profile than the trapped parameter of negative ions.},

doi = {10.1134/S1063780X18100021},

journal = {Plasma Physics Reports},

issn = {1063-780X},

number = 10,

volume = 44,

place = {United States},

year = {2018},

month = {10}

}