[Table of Contents]

Plasma and Fusion Research

Volume 8, 2401142 (2013)

Regular Articles


Numerical Analysis of Quantum Mechanical ∇B Drift III
Shun-ichi OIKAWA, Poh Kam CHAN1) and Emi OKUBO1)
Faculty of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan
1)
Graduate School of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan
(Received 19 November 2012 / Accepted 25 August 2013 / Published 15 November 2013)

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 8 - 100 m/s, mass of the particle at 1 - 10 mp, where mp is the mass of a proton. Magnetic field at the origin of 5 - 10 T, charge of 1 - 4 e, where e is the charge of the particle and gradient scale length of 2.610 × 10−5 - 5.219 m. Previously, we found out that the variance, or the uncertainty, in position can be expressed as dσr2 /dt = 4.3hv0/qB0LB, 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 LB is the gradient scale length of the magnetic field. In this research, it was numerically found that the variance, or the uncertainty, in total momentum can be expressed as dσP2/dt = 0.57hqB0v0/LB. In this expression, we found out that mass, m does not affect both our newly developed expression for uncertainty in position and total momentum.


Keywords

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

DOI: 10.1585/pfr.8.2401142


References

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  • [4] http://www.nvidia.com
  • [5] 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:

Shun-ichi OIKAWA, Poh Kam CHAN and Emi OKUBO, Plasma Fusion Res. 8, 2401142 (2013).