Equipment Grant: Symbolic Computing Equipment for NonlinearPlasma and Semiconductor Research

这项研究设备赠款将使人们能够购买一台Macintosh IIci计算机和作为首席调查员研究活动基本助手的MATHEMICA程序。这些研究项目包括有两个共同属性的不同主题：带电粒子的集体运动，主要是在等离子体中，以及非线性过程。这项研究是理论上的，混合了分析和数值方法，其中符号计算在分析部分将变得越来越重要。对用于中性束加热和溅射的离子束的研究，试图以测量的束流密度模型为起点，推导出离子分布函数、电场、电势等的解析表达式。找到更真实和稳定的分布函数是可能的。碰撞半导体中载流子速度的解析表达式对于研究可能的空间周期性空间电荷和器件应用是有用的。对可积系统上的非线性Vlasov-Maxwell方程的研究将成为对含时电场混沌行为边界的研究。半导体中的载流子速度也可能存在混沌解。在所有的工程中，利用微分方程的李群对称性找到的非线性解要么给出了以前未知的结果，要么得到了更有效的结果。

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.