# Plasma and Fusion Research

## Volume 7, 2401034 (2012)

# Regular Articles

- 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

### 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_{r}^{2} /dt = 4.1 ħv_{0}/qB_{0}L_{B}, where m is the mass of the particle, q is the charge, v_{0} is the initial speed of the corresponding classical particle, B_{0} 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.

### Keywords

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

### Full Text

### 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).