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Full orbit dynamics of charged particles in a $3$-dimensional helicalmagnetic field in the presence of $\alpha$-stable L\'evy electrostaticfluctuations and linear friction modeling collisional Coulomb drag is studiedvia Monte Carlo numerical simulations. The L\'evy fluctuations are introducedto model the effect of non-local transport due to fractional diffusion invelocity space resulting from intermittent electrostatic turbulence. Theprobability distribution functions of energy, particle displacements, andLarmor radii are computed and showed to exhibit a transition from exponentialdecay, in the case of Gaussian fluctuations, to power law decay in the case ofL\'evy fluctuations. The absolute value of the power law decay exponents arelinearly proportional to the L\'evy index $\alpha$. The observed anomalousnon-Gaussian statistics of the particles' Larmor radii (resulting from outliertransport events) indicate that, when electrostatic turbulent fluctuationsexhibit non-Gaussian L\'evy statistics, gyro-averaging and guiding centreapproximations might face limitations and full particle orbit effects should betaken into account.

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