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# Customizable two-species kinetic equilibria for nonuniform low-beta plasmas

## Abstract

Here, two methods are developed for constructing self-consistent two-species kinetic equilibria for low-beta electrostatic plasmas, in which the magnetic field is uniform and fixed in time. The first method uses Taylor series approximations to construct distribution functions that can be specified analytically. The second method relies on numerically solving a nonlinear ordinary differential equation and produces exact—to numerical precision—equilibria. In both methods, the equilibrium distribution functions for ions and electrons are expressed in terms of constants of motion and satisfy the steady-state Vlasov-Poisson equation system. Provided that the ion drift speed does not exceed the ion thermal speed, the equilibria can be specified with customizable density and electrostatic potential profiles. The methods can thereby be tailored to different applications and are successfully applied to construct kinetic equilibria for cross-field plasmas with sheared flows, large density variations, and different levels of magnetization. The equilibria are used to initialize fourth-order finite-volume Vlasov-Poisson simulations in (x, v _{x}, v _{y}) coordinates and the associated temporal evolution is used to assess the accuracy of each method. Lastly, the low-amplitude deviations observed in these simulations demonstrate that the kinetic equilibria are robust and that they provide a valuable means of studying the dynamics of nonuniformmore »

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1543072

- Alternate Identifier(s):
- OSTI ID: 1508440

- Report Number(s):
- LLNL-JRNL-765801

Journal ID: ISSN 1070-664X; 955924

- Grant/Contract Number:
- AC52-07NA27344; 18-ERD-048

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 26; Journal Issue: 4; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Vogman, G. V., Hammer, J. H., and Farmer, W. A. Customizable two-species kinetic equilibria for nonuniform low-beta plasmas. United States: N. p., 2019.
Web. doi:10.1063/1.5089465.
```

```
Vogman, G. V., Hammer, J. H., & Farmer, W. A. Customizable two-species kinetic equilibria for nonuniform low-beta plasmas. United States. doi:10.1063/1.5089465.
```

```
Vogman, G. V., Hammer, J. H., and Farmer, W. A. Tue .
"Customizable two-species kinetic equilibria for nonuniform low-beta plasmas". United States. doi:10.1063/1.5089465.
```

```
@article{osti_1543072,
```

title = {Customizable two-species kinetic equilibria for nonuniform low-beta plasmas},

author = {Vogman, G. V. and Hammer, J. H. and Farmer, W. A.},

abstractNote = {Here, two methods are developed for constructing self-consistent two-species kinetic equilibria for low-beta electrostatic plasmas, in which the magnetic field is uniform and fixed in time. The first method uses Taylor series approximations to construct distribution functions that can be specified analytically. The second method relies on numerically solving a nonlinear ordinary differential equation and produces exact—to numerical precision—equilibria. In both methods, the equilibrium distribution functions for ions and electrons are expressed in terms of constants of motion and satisfy the steady-state Vlasov-Poisson equation system. Provided that the ion drift speed does not exceed the ion thermal speed, the equilibria can be specified with customizable density and electrostatic potential profiles. The methods can thereby be tailored to different applications and are successfully applied to construct kinetic equilibria for cross-field plasmas with sheared flows, large density variations, and different levels of magnetization. The equilibria are used to initialize fourth-order finite-volume Vlasov-Poisson simulations in (x, vx, vy) coordinates and the associated temporal evolution is used to assess the accuracy of each method. Lastly, the low-amplitude deviations observed in these simulations demonstrate that the kinetic equilibria are robust and that they provide a valuable means of studying the dynamics of nonuniform magnetized plasmas.},

doi = {10.1063/1.5089465},

journal = {Physics of Plasmas},

number = 4,

volume = 26,

place = {United States},

year = {2019},

month = {4}

}

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