This Research Equipment Grant will enable acquisition of a Macintosh IIci computer and the program Mathematica as essential aides in the Principal Investigator's research activities. The research projects encompass diverse topics which share two common attributes: the collective motion of charged particles, chiefly in plasmas, and nonlinear processes. The research is theoretical with a mixture of analytical and numerical approaches where symbolic computation will be increasingly important in the analytical portions. The investigation of ion beams, used in neutral beam heating and sputtering, attempts to derive analytical expressions for the ion distribution functions, the electric fields, potentials, etc. with a model for the measured beam density as the starting point. Finding more realistic and stable distribution functions is possible. Analytical expressions for the carrier speed in collisional semiconductors are useful in the investigation of possible spatially periodic space charge and device applications. The research of the nonlinear Vlasov-Maxwell equations on integrable systems will become an investigation of the boundaries of chaotic behavior for time-dependent electric fields. Chaotic solutions may exist for the carrier speed in semiconductors also. In all projects nonlinear solutions found by using Lie group symmetries of differential equations have given results either not known before or found much more efficiently.
