Jörg Reuss

Lagrangian versus Eulerian correlations and transport scaling

The effect of the shape of the Eulerian correlation of an electrostatic turbulence on the scaling of the diffusion coefficient is studied using the decorrelation trajectory method. We show that a strong influence appears due to trajectory trapping when the Kubo number is larger than 1.

Percolation scaling for transport in turbulent plasmas

Abstract Guiding centre trajectories in an electrostatic turbulence spectrum can be reduced to the motion of charged particles in a two-dimensional randomly phased potential varying in time, which is known to be described by a Hamiltonian with 3 2 degrees of freedom and chaotic trajectories. In order to compute spatial diffusion, a refined model is built here to describe a broad wavenumber k−3 spectrum with a very large number of waves in a periodic square with a box size larger than the Grusinov coherence length. The root mean square displacement is computed on a parallel CRAY T3E computer and averaged over time and 1024 initial conditions. Contrary to the traditional Bohm prediction for plasma turbulence, it is found that, in the domain of small frequencies or large Kubo numbers A ∼ E/ωB, the reduced diffusion coefficient behaves like Aγ with γ = 0.692 ± 0.010 in total agreement with the percolation prediction γ = 7 10 .

Motion in a stochastic layer described by symbolic dynamics

The motion in the stochastic layer surrounding an island can be studied by using the standard map: This problem is of direct relevance to the diffusion of magnetic field lines in a tokamak. In a previous work it was shown that this process can be adequately modelled by a continuous time random walk (CTRW) describing transitions of the running point between three basins representing, respectively, trapped motion around the island, and passing motion above or below the island. The sticking property of the island deeply modifies the nature of the transport process, leading to subdiffusive behavior. In the present work it is shown that the motion can be analyzed in terms of a symbolic dynamics which leads to the possibility of an automatic measurement of the data necessary for the construction of the CTRW. The logical features of the procedure are described, and the method is applied to an analysis of long time series, thus completing the results of the previous work. (c) 1998 American Institute of Physics.

Transport scaling and trapping

It is shown that particle trapping plays an important role in the appearance of anomalous or strange diffusion in turbulent fields, mainly by inducing a non-Gaussian statistics of the stochastic displacements. Trapping processes are responsible for the important deviation observed between the traditional prediction of Bohm scaling for diffusion in low-frequency turbulence and the numerically checked prediction by Isichenko. Also, several theoretical models are proposed or reviewed.

On the intermittency of the transport in the tokamak plasma

The experimentally observed fluctuations of the plasma parameters and of the output fluxes suggest that the transport is intermittent with stationary statistical properties. With the aim of describing the random modulation of the properties of fully developed turbulence we propose a model based on random rise and decay of instabilities and with non-diffusive contributions to the fluxes. We examine sources of intermittency and perform numerical simulations of intermittent transport.