# Analysis of the time integration in plasma simulation

## Abstract

This paper treats the collective behavior of hot plasma as modified by the numerical time integration methods used to integrate the particle equations of motion in computer simulation of plasmas. No approximation, other than ignoring roundoff errors, is made in analyzing the finie-difference algorithms. Our results reduce simply and exactly to the corresponding results of plasma theory in the limit ..delta.. t ..-->.. 0. The possibility of nonphysical instability is considered. The results of this and of previous papers are combined to describe both the spatial and temporal difference algorithms. The theory is generalized to a class of integration schemes, some algorithms are analyzed, and a new example is synthesized. The difficulty of developing algorithms stable at very large time steps is examined. The present analysis may be combined with an earlier rigorous analysis of the spatial grid used for field equations, to develop a kinetic theory of simulation plasmas paralleling that for real plasmas. This theory may be of use in the design and interpretation of computer simulation experiments.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of California, Livermore

- OSTI Identifier:
- 5292823

- Resource Type:
- Journal Article

- Journal Name:
- J. Comput. Phys.; (United States)

- Additional Journal Information:
- Journal Volume: 30:2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; PLASMA SIMULATION; ALGORITHMS; EQUATIONS OF MOTION; HOT PLASMA; NUMERICAL SOLUTION; TIME DEPENDENCE; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL LOGIC; PLASMA; 700105* - Fusion Energy- Plasma Research- Plasma Kinetics-Theoretical- (-1987)

### Citation Formats

```
Langdon, A.B.
```*Analysis of the time integration in plasma simulation*. United States: N. p., 1979.
Web. doi:10.1016/0021-9991(79)90099-8.

```
Langdon, A.B.
```*Analysis of the time integration in plasma simulation*. United States. doi:10.1016/0021-9991(79)90099-8.

```
Langdon, A.B. Thu .
"Analysis of the time integration in plasma simulation". United States. doi:10.1016/0021-9991(79)90099-8.
```

```
@article{osti_5292823,
```

title = {Analysis of the time integration in plasma simulation},

author = {Langdon, A.B.},

abstractNote = {This paper treats the collective behavior of hot plasma as modified by the numerical time integration methods used to integrate the particle equations of motion in computer simulation of plasmas. No approximation, other than ignoring roundoff errors, is made in analyzing the finie-difference algorithms. Our results reduce simply and exactly to the corresponding results of plasma theory in the limit ..delta.. t ..-->.. 0. The possibility of nonphysical instability is considered. The results of this and of previous papers are combined to describe both the spatial and temporal difference algorithms. The theory is generalized to a class of integration schemes, some algorithms are analyzed, and a new example is synthesized. The difficulty of developing algorithms stable at very large time steps is examined. The present analysis may be combined with an earlier rigorous analysis of the spatial grid used for field equations, to develop a kinetic theory of simulation plasmas paralleling that for real plasmas. This theory may be of use in the design and interpretation of computer simulation experiments.},

doi = {10.1016/0021-9991(79)90099-8},

journal = {J. Comput. Phys.; (United States)},

number = ,

volume = 30:2,

place = {United States},

year = {1979},

month = {2}

}