QM theory of the thermal electron gyroradius

TL;DR

This paper re-examines the thermal electron gyroradius using quantum mechanics, confirming classical results and quantifying fluctuations, thus bridging quantum and classical descriptions of particle motion in magnetic fields.

Contribution

It provides a quantum-mechanical analysis of the thermal electron gyroradius, validating classical calculations and quantifying the magnitude of fluctuations.

Findings

Quantum calculation reproduces classical rms gyroradius.

Fluctuations in gyroradius are about 21.5% of the rms value.

Quantum and classical approaches are consistent in this context.

Abstract

The average (thermal) gyroradius of charged particles is re-examined from a quantum-mechanical point of view. The straight quantum-mechanical calculation clearly reproduces its conventionally used random-mean-square (rms) expectation value. The quasi-classical approach reproduces its mean expectation value as well thus confirming the purely classical calculation. It shows that the fluctuations in the gyroradius amount to 21.5% of its rms value. This fluctuation is, however, within the usual $\sqrt{2}$-"freedom" range of choice in the definition of the rms gyroradius respectively the mean thermal speed on which the rms value is based, its correct (nonrelativistic) value $v_t^2= 2T_\perp/m_e$ and its simplified version $v_t^2=T_\perp/m_e$.