# Monte Carlo Sampling of Negative-temperature Plasma States

## Abstract

A Monte Carlo procedure is used to generate N-particle configurations compatible with two-temperature canonical equilibria in two dimensions, with particular attention to nonlinear plasma gyrokinetics. An unusual feature of the problem is the importance of a nontrivial probability density function R0(PHI), the probability of realizing a set {Phi} of Fourier amplitudes associated with an ensemble of uniformly distributed, independent particles. This quantity arises because the equilibrium distribution is specified in terms of {Phi}, whereas the sampling procedure naturally produces particles states gamma; {Phi} and gamma are related via a gyrokinetic Poisson equation, highly nonlinear in its dependence on gamma. Expansion and asymptotic methods are used to calculate R0(PHI) analytically; excellent agreement is found between the large-N asymptotic result and a direct numerical calculation. The algorithm is tested by successfully generating a variety of states of both positive and negative temperature, including ones in which either the longest- or shortest-wavelength modes are excited to relatively very large amplitudes.

- Authors:

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab., NJ (US)

- Sponsoring Org.:
- USDOE Office of Science (US)

- OSTI Identifier:
- 808375

- Report Number(s):
- PPPL-3729

TRN: US0301994

- DOE Contract Number:
- AC02-76CH03073

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 19 Jul 2002

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALGORITHMS; AMPLITUDES; DIMENSIONS; DISTRIBUTION; PLASMA; POISSON EQUATION; PROBABILITY; SAMPLING; COMPUTER SIMULATION; GYROKINETIC EQUATIONS; MONTE CARLO METHODS

### Citation Formats

```
John A. Krommes, and Sharadini Rath.
```*Monte Carlo Sampling of Negative-temperature Plasma States*. United States: N. p., 2002.
Web. doi:10.2172/808375.

```
John A. Krommes, & Sharadini Rath.
```*Monte Carlo Sampling of Negative-temperature Plasma States*. United States. doi:10.2172/808375.

```
John A. Krommes, and Sharadini Rath. Fri .
"Monte Carlo Sampling of Negative-temperature Plasma States". United States.
doi:10.2172/808375. https://www.osti.gov/servlets/purl/808375.
```

```
@article{osti_808375,
```

title = {Monte Carlo Sampling of Negative-temperature Plasma States},

author = {John A. Krommes and Sharadini Rath},

abstractNote = {A Monte Carlo procedure is used to generate N-particle configurations compatible with two-temperature canonical equilibria in two dimensions, with particular attention to nonlinear plasma gyrokinetics. An unusual feature of the problem is the importance of a nontrivial probability density function R0(PHI), the probability of realizing a set {Phi} of Fourier amplitudes associated with an ensemble of uniformly distributed, independent particles. This quantity arises because the equilibrium distribution is specified in terms of {Phi}, whereas the sampling procedure naturally produces particles states gamma; {Phi} and gamma are related via a gyrokinetic Poisson equation, highly nonlinear in its dependence on gamma. Expansion and asymptotic methods are used to calculate R0(PHI) analytically; excellent agreement is found between the large-N asymptotic result and a direct numerical calculation. The algorithm is tested by successfully generating a variety of states of both positive and negative temperature, including ones in which either the longest- or shortest-wavelength modes are excited to relatively very large amplitudes.},

doi = {10.2172/808375},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Jul 19 00:00:00 EDT 2002},

month = {Fri Jul 19 00:00:00 EDT 2002}

}