Random walk of magnetic field lines in dynamical turbulence: A field line tracing method. I. Slab turbulence

To study the wandering of magnetic field lines is an important subject in theoretical physics. Results of field line random walk theories can be applied in plasma physics as well as astrophysics. Previous investigations are based on magnetostatic models. These models have been used in analytical work as well as in computer simulations to warrant mathematical and numerical tractability. To replace the magnetostatic model by a dynamical turbulence model is a difficult task. In the present article, a field line tracing method is used to describe field line wandering in dynamical magnetic turbulence. As examples different models are employed, namely, the plasma wave model, the damping model of dynamical turbulence, and the random sweeping model. It is demonstrated that the choice of the turbulence model has a very strong influence on the field line structure. It seems that if dynamical turbulence effects are included, Markovian diffusion can be found for other forms of the wave spectrum as in the magnetostatic model. Therefore, the results of the present paper are useful to specify turbulence models. As a further application we consider charged particle transport at early times.