Session KI1: Turbulence

Spectrum of MHD turbulence: theory, modeling, observations

Magnetohydrodynamic (MHD) turbulence plays an essential role in a variety of astrophysical systems, from intergalactic and interstellar media, to stars and planets. Despite more than 40 years of analytical, numerical and observational research, the MHD turbulent cascade is not completely understood. I will present a brief introduction to the theory, and discuss the new analytic and numerical results on the spectrum and structure of strong incompressible MHD turbulence. \\ \vskip1mm In collaboration with Fausto Cattaneo and Joanne Mason (U. Chicago)   

Spatial transport and spectral dynamics of turbulence spectra

The basic physical processes that lead to nonlinear evolution of the probability distribution function of turbulence in space as well as in scale space, will be discussed. It will be argued that the primary means by which the turbulence evolves from regions where it is excited into regions where it is dissipated is via nonlinear mode-coupling processes. Those same processes leads to the evolution in the usual Kolmogorov picture, in which the turbulence evolves by cascading from the scales at which it is excited, towards scales where it is dissipated. It will be shown that these two processes of spreading and cascade are inherently linked. Different models that aim to describe different aspects of this generic, ubiqiutous phenomenon will be introduced. Basic implications of such models and underlying assumptions will be discussed. The simple ``ballistic front'' solution, which is a common solution of these models, will be discussed. Also, the analogy to the evolution of the particle distribution function (ala' Boltzmann's equation) will be discussed and it will be shown that the nonlinear bi-evolution of the spectrum based on a Markovian closure approximation of two-scale dynamics, conserves energy, and satisfies a simple Boltzmann's H-theorem. In addition, it will be pointed out that spatial evolution of turbulence results in self-consistent evolution of the background gradient profiles that drives the turbulence in the first place. It will be argued that for simple models of drift-wave turbulence, this evolution can be described simply by the evolution of mean potential vorticity (PV) under the action of the Reynolds stresses generated by the fluctuations. Thus, we will argue that PV homogenization and spreading are two processes that needs to be considered together.   

Observation and Identification of Zonal Flows in a Basic Plasma Physics Experiment

The role of self-generated zonal flows (ZF) in transport regulation in magnetic confinement devices via its shear is a potent concept and a physics issue [1]. A basic physics experimental study of zonal flows associated with ITG (ion temperature gradient) drift modes has been performed in the Columbia Linear Machine [2]. The difficult problem of detection of ZF has been solved via a novel diagnostic using the paradigm of FM (frequency modulation) in radio transmission. Using this and Discrete Short Time Fourier Transform, we find a power spectrum peak at ITG (‘carrier’) frequency of $\sim 120kHz$ and FM sidebands at frequency of $\sim 2kHz$ . We have definitively identified ZF with azimuthal (poloidal) and axial (toroidal) symmetry $(k_\theta \approx 0, k_\parallel \approx 0 )$ and radially inhomogeneous $(k_r \neq 0 )$ flow structures in cylindrical plasmas. However, the stabilizing effect of ZF shear appears to be small and no significant isotopic effects are observed. The dependence of amplitude of ZF versus presumed damping ratio ${\nu}_{ii}$ is also reported. Collaborators: X.Wei and A.K.Sen, Plasma Research Laboratory, Columbia University, New York, New York 10027. \newline \newline $[1]$ P.H. Diamond, S-I Itoh, K.Itoh and T.S.Hahm, Plasma Phys.Controlled Fusion 47, R35 (2005). \newline $[2]$ V. Sokolov and A. K. Sen, Nucl. Fusion 45, 439 (2005).   

Numerical study of nonrelativistic and relativistic ion and electron holes in plasmas

We present analytical and numerical studies of the formation and dynamics of electron and ion holes in a collisionless plasma [1]. Both nonrelativistic [2,3] and relativistic [4,5] electron and ion holes are considered. Stationary and non-stationary solutions for the electron and ion holes are obtained on the basis of non-isothermal particle distribution functions that are different from the Maxwellian. Analytical solutions for the holes are then used as initial conditions in simulations to investigate the dynamics and stability of those phase space holes. Our results reveal that both the electron and ion holes are robust, and interacting holes show an interesting dynamics in which they sometimes merge to form new and stable holes. Furthermore, we consider the trapping of intense electromagnetic waves in relativistic electron holes [6], accounting for the combined effects of the relativistic ponderomotive force driven electron density depletion and relativistic electron mass increase in the electromagnetic fields. We present conditions under which the trapping of localized electromagnetic waves in relativistic electron holes occur. It is found that the electrons can be accelerated to ultra-high (MeV to GeV) energies by localized potential of relativistic electron and ion holes. The relevance of our investigation to intense laser-plasma interaction experiments and to astrophysical settings is discussed. \begin{thebibliography}{99} \bibitem{PREP} B. Eliasson and P. K. Shukla, Phys. Rep. {\bf 422}, 225 (2006). \bibitem{PRL1} B. Eliasson and P. K. Shukla, Phys. Rev. Lett. {\bf 93}, 045001 (2004). \bibitem{PRL2} B. Eliasson and P. K. Shukla, Phys. Rev. Lett. {\bf 92}, 095006 (2004). \bibitem{PLA1} B. Eliasson and P. K. Shukla, Phys. Lett. A {\bf 338}, 237 (2005). \bibitem{NJP} B. Eliasson, P. K. Shukla, and M. E. Dieckmann, New J. Phys. {\bf 8}, 55 (2006). \bibitem{PRL3} P. K. Shukla anb B. Eliasson, Phys. Rev. Lett. {\bf 94}, 065002 (2005). \end{thebibliography}