Turbulence and Energetic Particles in Interplanetary and Interstellar Spaces

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Two fundamental problems in space and astrophysics are the understanding of turbulence and energetic particles such as cosmic rays. Both problems are linked to each other because the particles are strongly influenced by turbulent magnetic fields. The problems described here can be found in a variety of scenarios ranging from the interplanetary space to the interstellar media of our own and external galaxies. Furthermore, similar problems can be found in experimental fusion reactors such as ITER. Turbulence is a complex non-linear dynamical phenomenon and, therefore, there is no simple way of describing it. One has to rely on a combination of analytical work, computer simulations, as well as observations usually performed via magnetometers onboard space probes such as Voyager 1. It was found that in the solar wind and the very local interstellar medium, turbulence is nearly incompressible in most cases. Furthermore, all ranges of the von-Karman-Kolmogorov cascade can be observed. The motion of solar energetic particles as well as cosmic rays is influenced by all ranges of the aforementioned cascade including energy, inertial, and dissipation range. The motion of energetic particles is, like turbulence, also a complicated non-linear phenomenon and simple tools such as perturbation theory fail in the general case. One way to tackle this problem is the development of computer simulations. Within such a pure numerical approach, the turbulence is created with the help of random number generators. Then one solves the Newton-Lorentz equation for an ensemble of particles numerically. If this is done for thousands of particles, one can obtain the statistics of the energetic particles. Although such simulations are indeed powerful, a pure numerical description of the transport is incomplete. First, one cannot obtain a detailed insight into the mechanisms of particle scattering. Furthermore, there is a variety of applications where one desires analytical forms of particle diffusion coefficients. Therefore, in addition to the numerical tools described above, we develop advanced non-linear theories to describe the motion of energetic particles. The research outlined in the proposal deals with the development and improvement of non-linear theories, their test via simulations, the derivation of simple analytical forms for the different diffusion parameters, and applications. The proposed work includes topics such as investigating diffusive shock acceleration at interplanetary and supernova shocks. This mechanism is responsible for the creation of cosmic rays. The results obtained via the proposed work will also be important for other investigations such as space weather and solar modulation studies. Furthermore, we shall explore turbulence and its transport based on nearly incompressible magnetohydrodynamics. The main goal of the proposed work is to improve our understanding of turbulence, the motion of energetic particles, and diffusive shock acceleration.