[Table of Contents]

Plasma and Fusion Research

Volume 6, 2401058 (2011)

Regular Articles

Numerical Analysis of Quantum Mechanical ∇B Drift
Shun-ichi OIKAWA, Takahiro SHIMAZAKI and Emi OKUBO
Faculty of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan
(Received 6 December 2010 / Accepted 1 April 2011 / Published 1 July 2011)


We have solved the two-dimensional time-dependent Schrödinger equation for a single particle in the presence of a nonuniform magnetic field for initial speeds of 10-100 m/s. By linear extrapolation, it is shown that the variance, or the uncertainty, in position would reach the square of the interparticle separation n−2/3 with a number density of n = 1020 m−3 in a time interval of the order of 10−4 sec. After this time the wavefunctions of neighboring particles would overlap, as a result the conventional classical analysis may lose its validity: Plasmas may behave more-or-less like extremely-low-density liquids, not gases, since the size of each particle is of the same order of the interparticle separation.


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

DOI: 10.1585/pfr.6.2401058


  • [1] S. Oikawa, T. Oiwa and T. Shimazaki, Plasma Fusion Res. 5, S2024 (2010).
  • [2] S. Oikawa, T. Shimazaki and T. Oiwa, Plasma Fusion Res. 5, S2025 (2010).
  • [3] L.D. Landau and E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 3rd ed., translated from the Russian by J.B. Sykes and J.S. Bell (Pergamon Press, Oxford, 1977).
  • [4] S. Oikawa, T. Shimazaki and E. Okubo, ITC20, P1-93 (2010).
  • [5] H. Natori and T. Munehisa, J. Phys. Soc. Jpn. 66, 351 (1997).
  • [6] http://www.nvidia.com.
  • [7] R.S. Cohen, L. Spitzer, Jr. and P.McR. Routly, Phys. Rev. 80, 230 (1950).
  • [8] S.I. Braginskii, Reviews of Plasma Physics, M.A. Leontovich (ed.), (Consultants Bureau, New York, 1965).
  • [9] R.J. Hawryluk, Rev. Mod. Phys. 70, 537 (1998).

This paper may be cited as follows:

Shun-ichi OIKAWA, Takahiro SHIMAZAKI and Emi OKUBO, Plasma Fusion Res. 6, 2401058 (2011).