open access

https://hdl.handle.net/2115/53687

Numerical Analysis of Quantum Mechanical ∇B Drift III

英語

expansion rate of variance

2013

Plasma and Fusion Research

8

2401142-1-2401142-4

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 - 100m/s, mass of the particle at 1 - 10mp, 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 dσ2r/dt = 4.3 v0/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 dσ2P/dt = 0.57 qB0v0/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.

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