ABSTRACT
A second difference is the use of a spatial grid on which the fields wi l l be calculated. One might ask, why not use Coulomb 's law d i rectly (for forces between charges separated by distance r , where ' the force decays as 1 / r2, 1 / r 1 , 1 / rO in three, two, and one d imensions) ? Consider the calculat ion of these forces in terms of both the numerical operat ions required and in terms of the actual physics; i. e. , are we interested in the detai ls of close encounters among particles and are close encounters at all frequent ? The answer to both parts of the quest ion is a lmost always no. We recal l our first course on electromagnetic theory where we met Coulomb's law and went qu ickly on to the notion of an electric field E and found that E was seldom to be found by summing the effect of each i ndividual charge. I nstead, we were in troduced to the notion of a charge density p, and that E was to be obtained from this density, which was to be thought of as varying cont inuously in space. The idea of working with something l i ke 1 0 25 charges with as many calculat ions of 1 / r2 was dismissed, wi th rel ief; the problem of what to do wi th 1 025 singularit ies (at r - 0) also vanished. Nearly a l l of the plasma physics which we wi l l do requires knowledge only down to some scale length, with charge density (and current densi ty) considered continuous; the finer gra ined behavior i s omit ted . Furthermore , in p lasmas , with many particles in a characterist ic length (which is the Debye length), there are relat ively few c lose part icle encounters, that is, few large angle deflect ions from si ngle encounters; rather large deflections come mostly from the cumulat ive effect of many small deflections. Hence , we are encouraged by the nature of plasma problems to take advantage of the s impl ifications that come about in using a mathematical spatial grid, as shown in Figure 2 -2b , usual ly fine enough to resolve a Debye length, in order to measure the charge dens i ty and , thence , calculate the electr ic field E.
