Oscillation and chaos in a plasma filled diode-Three different computational models

Summary form only given. It is well established by now that from the computational point of view the system is by no means simple, the inherent non-linearity of the beam/field interaction process greatly adding to the difficulties. In principle there are three different approaches to the problem of computer modeling of the system: we can either represent the electron beam by a large number of charged sheets and follow their travel through the inter-electrode space using Lagrange formulation to allow for possible overtaking; or we can derive two integral equations of Volterra type in order to obtain the time dependence of the transit time and the electric field at the entrance electrode; or one can use a PIC code, such as MAGIC, in order to obtain a time resolved distribution of electric field and space charge between the electrodes. In our presentation we wish to compare the three methods of simulation emphasizing their advantages and weaknesses. In particular we wish to consider their suitability for tackling the more difficult problem of modeling the system with a resonant load. The problem of mobile ions should also he considered in this context.