Stochastic Acceleration of Charged Particles in Turbulent Regions

Th is work investigates the stochastic acceleration of charged particles in various types of space plasmas, taking into account the intermittent nature of turbulence. Th e study compares the classical diff usion approach described by the Fokker—Planck equation with the generalized Continuous Time Random Walk (CTRW) framework, which incorporates heavy-tailed waiting-time distributions between acceleration events. Numerical simulations are performed for plasma conditions typical of the solar corona, the heliosphere at 1 AU, the Earth’s radiation belts, and the magnetotail. Physically motivated parameters are used for each environment, including turbulence intensity and characteristic timescales of acceleration, escape, and adiabatic losses. Th e Fokker—Planck equation is solved numerically in logarithmic momentum space, while the CTRW approach is implemented using Monte Carlo simulations. It is shown that turbulence intermittency causes a systematic soft ening of particle energy spectra, reducing the contribution of the high-energy, “hard” part compared to the diff usion approximation. Th e diff erence in spectral indices, s = sFP – sCTRW , is found to be positive in all considered cases and reaches values of s = 0.3—1.2 depending on the environment and the intermittency parameter. Th is indicates that diff usion-based models systematically overestimate the effi ciency of stochastic acceleration. We demonstrate that achieving the same spectral hardness within the CTRW framework requires a higher acceleration coeffi cient 0 D , refl ecting a reduced eff ective energy-gain rate due to long waiting periods between acceleration events. Th e eff ect of intermittency is strongest in regimes where particle escape or adiabatic cooling plays a signifi cant role. In heliospheric conditions, a transition between loss- and acceleration-dominated regimes is identifi ed, which shift s toward higher turbulence levels in the CTRW framework. In the Earth’s radiation belts, spectra remain relatively hard, but intermittency still leads to noticeable soft ening. In the solar corona and magnetotail, particle escape strongly infl uences spectral formation, with this eff ect being enhanced in the presence of anomalous transport. Th e results demonstrate that intermittency is a key factor controlling stochastic acceleration effi ciency and spectral formation. Th ey highlight the limitations of the classical diff usion approach and emphasize the importance of anomalous transport models for interpreting high-energy particle spectra in space plasmas.