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Quantum Mechanical Plasma Scattering

Shun-ichi OIKAWA, Tsuyoshi OIWA and Takahiro SHIMAZAKI

Faculty of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan

(Received 7 December 2009 / Accepted 16 April 2010 / Published 10 December 2010)

Abstract

We have solved the two-dimensional time-dependent Schödinger equation for a particle with and without the interparticle potential in a fusion plasma. It was shown that spatial extent of a free particle grows monotonically in time. Such expansion leads to a spatial extent or size of a proton of the order of the average interparticle separation Δl ≡ n^−1/3 ∼ 2 × 10⁻⁷ m in a time interval of 10⁶ × Δl/v_th ∼ 10⁻⁷ sec for a plasma with a density n ∼ 10²⁰ m⁻³ and a temperature T = mv_th²/2 ∼ 10 keV. It was also shown that, under a Coulomb potential, the wavefunction of a charged particle first shrink and expand in time. In the expansion phase, at times t ≥ 10⁻¹⁰ sec, the size of particle in the presence of a Coulomb potential is much larger than that in the absence of it.

Copyright (c) 2010 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

Ehrenfest's theorem, quantum mechanical scattering, plasma, diffusion

DOI: 10.1585/pfr.5.S2024

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References

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This paper may be cited as follows:

Shun-ichi OIKAWA, Tsuyoshi OIWA and Takahiro SHIMAZAKI, Plasma Fusion Res. 5, S2024 (2010).