Media in which fusion reactions occur consist mainly of interspersed charged particles which are affected by short and long range forces. The cumulative effect of these forces combined with the intractability of an analytical description of each individual particle suggests that various approaches be used in the determination of the macroscopic behaviour of an ensemble of moving and colliding particles.

5.3 Particle Motion

The motion of a single particle of mass m is described by Newton’s Law

d Vі / f.4

тТГ (6Л)

where Fj is the j-th force vector acting on the particle and v is its velocity. For example, an isolated particle of mass m and charge q moving in a gravitational field g, an electric field E, and a magnetic field B, has its space-time trajectory described by

d

m— = mg + ^E + q( v x В ) . (6.2)

dt

While Eq.(6.2) is indeed very useful for some applications, it suffers from an overriding restriction: it describes the motion of an isolated particle only and thus excludes any possible interaction with other particles. This is indeed a severe restriction for fusion energy applications because power density requirements demand that about 1020 fusile ions be contained in one m3; with such a large number of ions nearby each possessing a different velocity, it is evident that Coulomb interactions alone will lead to a most complex collection of time varying electrostatic forces acting on the particles. While in principle, one might specify a dynamical equation of the form of Eq.(6.1) for each particle, one would need perhaps 1020 force terms on the right hand side per unit volume; solving such equations for each of the interacting particles is, of course, totally unmanageable for computational purposes, due to the enormous number of these coupled equations and the lack of knowledge of individual initial conditions.

As an alternative to using an exceedingly large number of equations each containing many terms, it has been found that other approaches which are mathematically tractable provide, in selected applications, satisfactory agreement

with experiments and a useful predictive quality. One frequently used conceptual approach is to consider a plasma as a multicomponent interpenetrating low — density fluid and then employ suitable continuum mechanics methods. Another approach is to use probabilistic considerations for each group of particle species and then perform an analysis based on methods of sampling statistical physics.

While no one approach is generally applicable to all cases of conceivable interest, a careful choice of conceptual constructs and methodologies can lead to descriptions which are remarkably useful in characterizing selected space — velocity-time aspects of a particular species’ population in a fusion medium. It is important therefore to develop a good understanding of the imposed assumptions in order to recognize important restrictions of a particular conceptual development and its consequent mathematical description.