Computer Simulation of Anomalous Plasma Diffusion and Numerical Solution of Poisson's Equation

摘要

The purpose of this research was to study the diffusion of a collisionless plasma across a constant magnetic field by means of a two-dimensional Lagrangian computer model. This model represents the plasma by means of approximately 1000 charged rods and calculates their motion, stepwise in time, as they move according to the laws of Newton and Maxwell. The model is quasi-electrostatic and takes 1.7 sec to perform a time-step on the IBM 7090 computer. The heart of the model is a fast, direct method, utilizing Fourier analysis, for solving Poisson's equation. For simple geometrical configurations, this technique is faster than the best iterative methods. The speed of the Poisson solver is made possible by the development of systematic techniques for performing Fourier analysis over certain numbers of points. These techniques, which reduce computer time by using the symmetries of the sine functions, are faster and more accurate than other published algorithms. Results of the investigation of anomalous diffusion wer displayed in a 2-minute motion picture, which shows the position of every plasma particle and the shape of the potential surface. The buildup of a 'steady-state' potential distribution that is unstable can be observed in a sequence of frames. The diffusion, which can all be attributed to the coherent E-field of an unstable wave, is several orders of magnitude greater than that due to binary collisions in a real plasma with the same constants. Classical collisional diffusion between rods in the model is negligible, and the model simulates essentially collective phenomena such as instabilities and 'anomalous' diffusion.