Random and quasi-coherent aspects in particle motion and their effects on transport and turbulence evolution

Abstract

The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not strongly perturbed. The trajectories are, in these conditions, random sequences of large jumps and trapping or eddying events. Trapping determines quasicoherent trajectory structures, which have a micro-confinement effect that is reflected in the transport coefficients. They determine non-Gaussian statistics and flows associated to an average velocity. Trajectory structures also influence the test modes on turbulent plasmas. Nonlinear damping and generation of zonal flow modes is found in drift turbulence in uniform magnetic field. The coupling of test particle and test mode studies permitted to evaluate the self-consistent evolution of the drift turbulence in an iterated approach. The results show an important nonlinear effect of ion diffusion, which can prevent the transition to the nonlinear regime at small drive of the instability. At larger drive, quasi-coherent trajectory structures appear and they have complex effects on turbulence.eddying. The general conclusion of these studies is that trajectory trapping or eddying determines non-standard statistics of trajectories: non-Gaussian distributions, long time Lagrangian correlations (memory), strongly modified transport coefficients and an increased degree of coherence. The trapped trajectories form quasicoherent structures similar to fluid vortices.Very recent results [15] have shown that these methods could be the basis for the development of a theoretical approach for the study of test modes in turbulent plasmas. It is similar to the Lagrangian approach initiated by Dupree [16,17] and developed in the 1970s. The assumption of random trajectories with Gaussian distribution limited the application of Dupree's method to the quasilinear regime. The DTM and NSA enable the evaluation of the average propagator of the test modes in the nonlinear regime and extend the theoretical procedure to the complex processes that are generated in these conditions. The tendency of drift turbulence evolution beyond the quasilinear regime was obtained in [15].We present a theoretical approach to the study of turbulence evolution, the iterated self-consistent method (ISC). It is based on the analysis of the test particles and test modes in turbulent plasmas. Both test particle and test mode studies start from given statistical description of the turbulence. However, the coupling of these problems can lead to the evaluation of turbulence evolution and to the understanding of the nonlinear processes that are generated. The ISC is applied here to the drift turbulence in plasmas confined in uniform magnetic fields.The paper is organized as follows. The physical processes analyzed in this paper and the main ideas that are followed in this study are presented in section 2. Section 3 contains the test particle studies of transport, the DTM and the NS...

Quasi-coherent structures and flows in turbulent transport

“…The existence of an average velocity in the equation of motion determines modifications of the DTs in the nonlinear regime [8], [15]. A new type of DTs appears.…”

“…The main idea of this approach [6][7][8] is to determine the Lagrangian averages not on the whole set of trajectories but to group together trajectories that are similar, to average on them and then to perform averages of these averages. Similar trajectories are obtained by imposing supplementary initial conditions besides the necessary one.…”

“…The LVC, Di(t), the probability of the small scale displacements P m (x,t) and other Lagrangian correlations are evaluated using the DTs. The detailed effective calculations are presented in [6][7][8]. Applications of the DTM for more complicated transport processes can be found in [14]- [19] for plasma turbulence and in [20]- [21] for space plasmas.…”

“…Trapping was associated to a process of micro-confinement [8]. At a given moment, the microconfinement affects a fraction of the particle, and, in a large time interval, every particle is subjected to micro-confinement events during a fraction of this time.…”

“…At a given moment, the microconfinement affects a fraction of the particle, and, in a large time interval, every particle is subjected to micro-confinement events during a fraction of this time. The micro-confinement determines the existence of transport reservoirs [8] in the sense that diffusion can be strongly enhanced when these trapped particles are released by the increase of the perturbation strength.…”