Plasma and Fusion Research
Volume 8, 2401142 (2013)
Regular Articles
- 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
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
Full Text
References
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This paper may be cited as follows:
Shun-ichi OIKAWA, Poh Kam CHAN and Emi OKUBO, Plasma Fusion Res. 8, 2401142 (2013).