Project Details
Projekt
Anomalous Transport and Acceleration of Energetic Particles in Astrophysical Environments: Fractional Diffusion-Advection and Stochastic Differential Equations
Applicants
Privatdozent Dr. Horst Fichtner; Dr. Lukas Merten
Subject Area
Astrophysics and Astronomy
Term
since 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 434200803
With the proposed continuation project we will quantitatively explore the anomalous transport and acceleration of energetic particles in astrophysical plasma environments. Building upon the findings of the predecessor project, we will now address critical questions about the implications and refinements of models that describe anomalous processes in energetic particle transport and acceleration. In the previous project it was established, theoretically and observationally, that the diffusive transport of energetic particles can deviate significantly from Gaussian behavior: in various astrophysical systems the mean square displacement is not linearly depending on time, indicating the importance of incorporating non-Gaussian transport into models describing particle dynamics in environments shaped by plasma flows, shocks, and turbulence. In the second project phase proposed here we will, in direct collaboration with four international experts, explore the consequences of this result, by refining the models that describe anomalous transport processes of energetic particles. In particular, we will address the interplay between anomalous transport and acceleration processes in astrophysical settings, focusing on key observables such as particle energy spectra and spatial distributions, including the formation of intensity peaks at shock fronts. The main goal of the proposed research project is to develop a framework for the simulation of the anomalous transport and acceleration of energetic particles in astrophysical environments. With the simulations carried out within this framework we will address the main science question: What are the consequences of employing fractional transport equations representing Levy flights, tempered Levy flights, and Levy walks for the anomalous transport and the acceleration of energetic particles? This question will be addressed through three science objectives: (i) the development and validation of advanced models for anomalous transport and acceleration based on stochastic differential equations as well as on grid-based approaches, (ii) the application of the models to study the transport of solar energetic particles and Galactic cosmic rays, and (iii) a comparison of model predictions with observations to clarify the relevance of anomalous transport and acceleration regimes. Whereever possible we will solve both the relevant system of stochastic differential equations and the equivalent fractional transport equation in order to validate the numerical solutions. With the corresponding comprehensive simulations we will not only contribute to the contemporary research on the significance of anomalous transport in astrophysical environments but also clarify how this transport has to be described quantitatively, i.e. in terms of Levy walks or (tempered) Levy flights.
DFG Programme
Research Grants
International Connection
Italy, South Africa, USA
