[Table of Contents]

Plasma and Fusion Research

Volume 5, S2025 (2010)

Regular Articles

Preliminary Study of Uncertainty-Driven Plasma Diffusion II
Shun-ichi OIKAWA, Takahiro SHIMAZAKI and Tsuyoshi OIWA
Graduate school of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan
(Received 7 December 2009 / Accepted 27 March 2010 / Published 10 December 2010)


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.


anomalous diffusion, uncertainty, distribution function, Coulomb potential, magnetic length, Schrödinger equation

DOI: 10.1585/pfr.5.S2025


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This paper may be cited as follows:

Shun-ichi OIKAWA, Takahiro SHIMAZAKI and Tsuyoshi OIWA, Plasma Fusion Res. 5, S2025 (2010).