Charged particle dynamics in the presence of non-Gaussian L\'evy electrostatic fluctuations

TL;DR

This study investigates how non-Gaussian Le9vy electrostatic fluctuations influence charged particle dynamics in a magnetic field, revealing non-Gaussian statistics and potential limitations of common approximations in plasma physics.

Contribution

It introduces a Monte Carlo simulation framework to analyze full orbit dynamics under Le9vy fluctuations, highlighting the impact of non-Gaussian turbulence on particle behavior.

Findings

Energy and displacement distributions shift from exponential to power law decay.

Power law exponents are linearly related to the Le9vy index b1.

Non-Gaussian Le9vy statistics affect gyro-averaging and guiding center approximations.

Abstract

Full orbit dynamics of charged particles in a $3$-dimensional helical magnetic field in the presence of $\alpha$-stable L\'evy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The L\'evy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of L\'evy fluctuations. The absolute value of the power law decay exponents are linearly proportional to the L\'evy index $\alpha$. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian L\'evy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.