ABSTRACT
The codes described in this chapter run on large mainframe computers; however, the hardware improvement of small computers today has reached a level that makes it possible to implement most of these codes on a PC. The memory of these small computers can be expanded to several MB, which was not an easy task just several years ago even on a large computer. The solution of the Vlasov equation depends on a known distribution of the charged particles at the origin, for example, the cathode for the case of electrons. The current distribution of the beam is unknown; however, it can be calculated by applying the Child-Langmuir law. In plasma sources the Child-Langmuir law still applies, but the gap distance is not defined anymore. The magnetic field might be obtained by integration or by a finite difference method. If the magnetic flux density is known on a closed surface, the Laplace equation can be applied for each component separately.
