# Plasma and Fusion Research

## Volume 5, S2025 (2010)

# Regular Articles

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

### Abstract

We have constructed a semiclassical collisional diffusion model.
In this model, a field particle is treated as either a point charge or a spatially distributed charge.
The test particle is treated as a distributed point charge with Gaussian distribution.
It was shown that the collisional changes in velocity in our model is of the same order as the classical theory for a typical proton in a fusion plasma of T = 10 keV and n = 10^{20} m^{−3}.
It was also shown that the spatial extent of the distribution, or the quantum-mechanical uncertainty in position, for the test particle obtained in our model grows in time, and becomes of the order of the average interparticle separation Δl ≡ n^{−1/3} during a time interval τ_{r} ∼ × 10^{7} Δl/g_{th}, where g_{th} = √ 2T/m is the thermal speed, with m being the mass of the particle under consideration.
The time interval is 3-4 order of magnitudes smaller than the collision time.
This suggests that particle transport cannot be understood in the framework of classical mechanics, and that the quantum-mechanical distribution of individual particles in plasmas may cause the anomalous diffusion.

### Keywords

anomalous diffusion, uncertainty, distribution function, Coulomb potential, magnetic length, Schrödinger equation

### Full Text

### References

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This paper may be cited as follows:

Shun-ichi OIKAWA, Takahiro SHIMAZAKI and Tsuyoshi OIWA, Plasma Fusion Res. 5, S2025 (2010).