Preliminary Study of Uncertainty-Driven Plasma Diffusion II

Abstract

We have constructed a semiclassical collisional diffusion model. In this model, a field particle is treated as either a point charge or a spatially distributed charge. The test particle is treated as a distributed point charge with Gaussian distribution. It was shown that the collisional changes in velocity in our model is of the same order as the classical theory for a typical proton in a fusion plasma of T = 10 keV and n = 1020 m−3. It was also shown that the spatial extent of the distribution, or the quantum-mechanical uncertainty in position, for the test particle obtained in our model grows in time, and becomes of the order of the average interparticle separation Δl ≡ n−1/3 during a time interval τr ∼ × 107 Δl/gth, where gth = √ 2T/m is the thermal speed, with m being the mass of the particle under consideration. The time interval is 3-4 order of magnitudes smaller than the collision time. This suggests that particle transport cannot be understood in the framework of classical mechanics, and that the quantum-mechanical distribution of individual particles in plasmas may cause the anomalous diffusion.