Nonlinear and Anomalous Diffusion of Energetic Particles: Transport and Acceleration in Astrophysical Environments

• Applicant: Privatdozent Dr. Horst Fichtner, since 11/2020
• Subject Area: Astrophysics and Astronomy
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 434200803

With the proposed project we will quantitatively explore the nonlinear as well as anomalous transport and acceleration of energetic particles in astrophysical plasma environments. Such a modelling approach is required to answer a question that has been raised repeatedly in recent years, namely: Can the diffusive transport of energetic particles be significantly non-Gaussian, i.e. can the mean square displacement dependent nonlinearly on time? Such `anomalous' scalings can be obtained with solutions of both nonlinear and fractional differential equations. Of particular interest in the astrophysical context is the effect of non-Gaussian diffusion on the first- and second-order acceleration of energetic particles by shocks and by plasma turbulence, respectively. The developed methods will be applied primarily to interplanetary shocks and flare plasmas, where a wealth of remote and in-situ observations exist. Therefore, the goals of the proposed research program are (1) to derive (approximate) analytical solutions of nonlinear and fractional diffusion-advection equations describing anomalous particle transport, (2) to numerically simulate transport and acceleration with the time evolution of particle distributions described by generalized diffusion-advection equations, and (3) to validate the analytical and numerical results with observations and to employ them to determine key parameters describing the nonlinear and anomalous diffusion. These analyses will deepen the understanding of both the nonlinear and anomalous diffusion of energetic particles, provide useful tools for the quantitative modelling of such transport and acceleration processes, and clarify their significance in astrophysical environments. The numerical simulations regarding the nonlinear diffusion-advection equations will be performed with the VLUGR3 code that we successfully employed in our preparatory work. The system of stochastic differential equations corresponding to a given fractional Fokker-Planck equation will be solved with a code that has been developed by one of the applicants and that has been tested thoroughly before it was applied to astrophysical scenarios. The data regarding the interplanetary shocks and flares are publicly available. The determination of the key parameters of nonlinear and anomalous transport and acceleration, e.g., the non-linear and anomalous diffusion exponents and diffusion coefficients, through their comparison with observational data, will provide closure on the three science goals outlined above.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Dr. Frederic Effenberger, until 11/2020