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Numerical Analysis of Quantum Mechanical ∇B Drift II

Poh Kam CHAN, Shun-ichi OIKAWA¹⁾ and Emi OKUBO

Graduate School of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan

1)

Faculty of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan

(Received 8 December 2011 / Accepted 2 March 2012 / Published 10 May 2012)

Abstract

We have solved the two-dimensional time-dependent Schrödinger equation for a single particle in the presence of a non-uniform magnetic field for initial speed of 10-100m/s, mass of the particle at 1-10m_p, where m_p is the mass of a proton. Magnetic field at the origin of 5-10T, charge of 1-4 e, where e is the charge of the particle and gradient scale length of 2.610 × 10⁻⁵ -5.219m. It was numerically found that the variance, or the uncertainty, in position can be expressed as dσ_r² /dt = 4.1 ħv₀/qB₀L_B, where m is the mass of the particle, q is the charge, v₀ is the initial speed of the corresponding classical particle, B₀ is the magnetic field at the origin and L_B is the gradient scale length of the magnetic field. In this expression, we found out that mass, m does not affect our newly developed expression.

Copyright (c) 2012 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

grad-B drift, magnetic length, Landau state, quantum mechanical scattering, plasma, diffusion, expansion time, expansion rate of variance

DOI: 10.1585/pfr.7.2401034

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References

• [1] S. Oikawa, T. Shimazaki and E. Okubo, Plasma Fusion Res. 6, 2401058 (2011).
• [2] http://www.nvidia.com
• [3] L.D. Landau and E.M. Lifshitz, Quantum Mechanics: Nonrelativistic Theory, 3rd ed., translated from the Russian by J.B. Sykes and J.S. Bell (Pergamon Press, Oxford, 1977).

This paper may be cited as follows:

Poh Kam CHAN, Shun-ichi OIKAWA and Emi OKUBO, Plasma Fusion Res. 7, 2401034 (2012).