# Plasma simulation

The complexity of fusion-grade plasmas and the increased computational power that has become available in recent years has made the simulation of plasmas a prime object of study in the field of fusion research. Although the basic equations governing the behaviour of magnetised plasmas are known, approximations are always necessary in any code of practical interest; e.g. the extreme disparity of the transport timescales (seconds) and turbulent timescales (microseconds) make it hard to perform detailed turbulence simulations for the whole three-dimensional plasma volume and for several transport timescales.

This page discusses plasma transport calculations, not the MHD equilibrium.

## Codes

Codes can either be interpretative (taking some input from experiment) or predictive. They can be full-tokamak (or full-stellarator), or simulate only a small portion of plasma (a flux tube, the edge, or the Scrape-Off Layer). They can be fluid models for one (electrons), two (electrons + ions) or more (impurities) fluid species, Monte Carlo type (particle tracing) codes, or gyro-kinetic codes. The latter are again subdivided into full-f or delta-f codes (delta-f referring to the fact that only the deviation from a background Maxwellian particle velocity distribution function is simulated).

Recent years have seen an increased effort in the field of cross code benchmarking. [1] [2] [3] [4]

### Fluid codes

In the fluid model approach, equations are derived for the moments of the distribution function f. This approach requires making several more or less strong assumptions regarding the relative importance of physical phenomena and closing the infinite set of moment equations, thus possibly losing some interesting physics.

### Monte Carlo codes

The Monte Carlo or single particle approach solves the kinetic single-particle equations (the Lorentz force equation) in a fixed background.

### Gyrokinetic codes

The gyrokinetic treatment simplifies the Vlasov equation for the evolution of the single-particle distribution function $f(\vec{x},\vec{v},t)$ by averaging over the gyration angle, resulting in an evolution equation for the particle guiding centre. See Gyrokinetic simulations.

## References

1. Nevins W.M. et al, Phys. Plasmas 13 (2006) 122306
2. A.M. Dimits et al, Nucl. Fusion 47 (2007) 817-824
3. G L Falchetto et al, Plasma Phys. Control. Fusion 50 (2008) 124015
4. National Transport Code Collaboration
5. Gyro homepage
6. Plasma Simulation Group