Open Issues in Non-Gaussian Transport and Acceleration of Charged Energetic Particles in Space and Astrophysical Plasmas

Abstract This review explores the anomalous transport and acceleration of charged energetic particles in heliospheric and astrophysical plasmas. Traditional diffusion-advection models can be insufficient to fully describe the observed behavior of energetic particles, prompting the need for alternative frameworks based on non-Gaussian stochastic processes and fractional differential equations to capture regimes of subdiffusion and superdiffusion of energetic particles. We discuss the theoretical basis of these non-Gaussian transport processes and examine the influence of magnetic turbulence, nonlinear diffusion, and field line random walk on particle dynamics. Superdiffusion, where the particle mean-square displacement grows faster than linear with time, and subdiffusion, with slower-than-linear growth, are observed across a range of environments from solar energetic particles to supernova remnants. This review highlights several examples from space and astrophysical plasmas that demonstrate instances of anomalous transport and acceleration, with a particular focus on its potential influence on fundamental processes such as shock acceleration and heliospheric energetic particle propagation. Long-range correlations and structures in space plasmas can impact both parallel and perpendicular transport. In the context of interplanetary shocks in the solar wind, parallel superdiffusion predominates due to a distinct pitch-angle scattering process not accounted for by quasi-linear theory, emphasizing the significance of nonlinear interactions and trapping effects. At quasi-parallel shocks in supernova remnants, parallel superdiffusion can also occur, leading to different acceleration spectra. In contrast to this superdiffusion along the magnetic field, field line random walk in combination with parallel particle diffusion can result in compound subdiffusion perpendicular to it. The review concludes with open questions and future directions for research that could deepen our understanding of particle transport in the turbulent environments of space and astrophysical plasmas.