ABSTRACT
Computer s imulat ion has become a powerfu l tool for the study of plas mas . Much effort and computer t ime is being expended in appl icat ions to new and more d ifficult problems. In support of this work , we have per formed theoretical analyses for a common class of many-particle s imulat ion methods. As one does to learn basic properties of real plasmas, we examine osci l lat ions, fluctuations, and col l is ions in the idealized case of un iform and infinite or periodic plasma. Even in this s imple s i tuation there are several instances in which the models fai l (mildly to gross ly) to reproduce plasma behavior. This chapter and the next four contain the theory and discuss such nonphysical behavior caused by the finite-difference methods. The plasma interacts coherently with the periodici ty of the spatial grid on which the elec tromagnetic fields are defined and with the periodic i ty of the fini te-d ifference time in tegration . Various parametric instabil i t ies are somet imes induced, which may be e i ther weak or strong and may be d ifficul t to dist inguish from real i nstab i l i ties . There i s a lso high-frequency noise associated wi th the rate at which particles cross the spatial-grid cel ls . I f the t ime step is large enough that the frequency of this noise exceeds the time sampling frequency, then
this noise degrades normal fluctuations and coll i s ions and can become exces sive . The theory has helped others examine experimentally the nature of such nonphysical effects.
