Computer Simulation of Plasmas

A plasma consists of charged particles moving relatively freely, but interacting through the electric and magnetic fields produced by each particle. It is well known that all except a very small (but nevertheless important) fraction of the detectable universe is a plasma. Most plasma physics can be expressed in terms of five fairly straightforward equations, the four Maxwell equations for electromagnetism and the equation of motion for charged particles in electromagnetic fields. Why then is plasma physics such a mathematically difficult subject and why is numerical simulation so important? The most basic reason is that any experimental plasma contains a very large number of particles, 1018–1020 in a typical fusion experiment. Moreover, particles in plasmas have a tendancy to act independently of each other. In conventional hydrodynamics, large numbers of particles can be described by a few simple numbers such as their temperature, density and mean velocity. Sometimes we can do this with a plasma but even then we have a few more numbers to include such as current and charge density, along with the electromagnetic fields. More usually, plasmas are not so simply described. Plasmas are not usually Maxwellian and we have to think in terms of distribution functions in phase space. Whenever we can, we model the non—Maxwellian nature of the plasma by transport models, e.g. for heat flow, but this is a specialised skill in itself. When one considers that conventional hydrodynamics is very complex and involves advanced numerical simulation, it is hardly surprising that simulation plays such an important role in plasma physics.