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Preliminary Study of Uncertainty-Driven Plasma Diffusion

Shun-ichi OIKAWA, Tsuyoshi OIWA and Takahiro SHIMAZAKI

Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan

(Received 6 January 2009 / Accepted 28 April 2009 / Published 26 March 2010)

Abstract

Quantum mechanical plasma diffusion is studied using a semi-classical model with two different characteristic lengths; one is the average interparticle separation, and the other is the magnetic length. The diffusion coefficients D derived in this study show a dependence on several plasma parameters, such as temperature T, mass m, density n, and magnetic field B, similar to that observed experimentally. The numerical values of the diffusion coefficient D in this study are as large as that for neoclassical diffusion. We have pointed out in this study that (i) for distant encounters in typical fusion plasmas of T = 10 keV and n = 10²⁰ m⁻³, the average potential energy ⟨U⟩ ∼ 30 meV is as small as the uncertainty in energy ΔE ∼ 40 meV, and (ii) for a magnetic field B = 3 T, the spatial size of the wavefunction in the plane perpendicular to the magnetic field is as large as l_B ∼ 1.4 × 10⁻⁸m, which is much larger than the typical electron wavelength λ_e ∼ 10⁻¹¹m.

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

Keywords

magnetic length, uncertainty principle, quantum mechanical diffusion, anomalous diffusion, neoclassical theory.

DOI: 10.1585/pfr.5.S1050

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This paper may be cited as follows:

Shun-ichi OIKAWA, Tsuyoshi OIWA and Takahiro SHIMAZAKI, Plasma Fusion Res. 5, S1050 (2010).