Background of Plasma Modelling

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• Maxwell’s equations
• Lorentz force

A snapshot: plasma's ions and electrons with arbitrary positions and velocities. Further evolution of the system is governed by laws of electromagnetism. Notice that in reality, the size of the particles is negligible compared to their mutual distances.

After these general remarks let us move into the realm of computer modelling of fusion plasmas. The first statement sounds quite promising: there is very reliable theoretical knowledge of fundamental physics acting in plasmas. Plasma can be modelled as a large set of free charged particles that move chaotically at very high velocities. All plasma particles are subject to electromagnetic interactions that were understood back in the 19th century (Maxwell’s equations, Lorentz force). This understanding has been validated time and again ever since. In most cases the plasma models do not need any aspects of “modern physics” like space-time or quantum effects.

Unfortunately, this is about the only positive statement concerning the simplicity of plasma modelling. Real plasma is an extremely complex system of an unimaginable number of charged particles that follow the “basic rules” of electromagnetism. It is beyond the means of any model to follow the positions of billions of billions of these particles as they move rapidly in electric fields that are formed by the very same particles (the fields are “self-generated”). Due to this entanglement, plasmas are capable of building up many special phenomena, called “collective effects”. These collective effects, even if very obvious in experiments, may still lack a clear and validated explanation in terms of theory and/or modelling. In plain words, some of the phenomena observed in plasma physics are not understood yet.

Besides, with respect to high velocities of plasma particles, there is hardly any realistic plasma volume to which one could apply a simpler model of the “infinite homogeneous plasma”. When modelling real plasmas, steep gradients of basic parameters (temperature, density, electric and magnetic fields…) can never be omitted. External electric and magnetic fields, to which plasmas are extremely sensitive, must also be taken into account – in the case of our research, external magnetic fields play a fundamental role in shaping and containing the plasma. Last, but not least, models have to reflect that finite plasmas continuously exchange large amounts of energy and particles with the external world.