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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)

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 τ_r ∼ × 10⁷ Δl/g_th, where g_th = √ 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.

Copyright (c) 2010 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

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).