Bulletin of the American Physical Society
49th Annual Meeting of the Division of Plasma Physics
Volume 52, Number 11
Monday–Friday, November 12–16, 2007; Orlando, Florida
Session PO7: Turbulence, Reconnection, Phase-Space Holes |
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Chair: Troy Carter, UCLA Room: Rosen Centre Hotel Salon 7/8 |
Wednesday, November 14, 2007 2:00PM - 2:12PM |
PO7.00001: Spectra and structure of MHD turbulence S. Boldyrev, J.C. Perez, J. Mason, F. Cattaneo We present recent results on magnetohydrodynamic (MHD) turbulent cascades. We concentrate on the physical processes that determine the structure of MHD turbulence in the regimes of weak and strong turbulence, and discuss the corresponding turbulent spectra. The results are compared with numerical simulations and geophysical (solar wind) and astrophysical (interstellar scintillation) observations. [Preview Abstract] |
Wednesday, November 14, 2007 2:12PM - 2:24PM |
PO7.00002: Numerical simulations of Alfv\'enic turbulence in extended reduced MHD Jean C. Perez, Stanislav Boldyrev We present the results of numerical investigation of anisotropic Shear-Alfven turbulence in the framework of extended reduced MHD model. The turbulence is randomly stirred at large scales until it reaches a steady state. By properly choosing the forcing parameters we investigate both weak and strong turbulence, and address the question of its transition to the Kinetic-Alfven regime at the ion-sound-radius scale. We observe that the energy spectrum in the weak turbulence regime is flatter than $k^{-2}$ predicted by weak turbulence models. [Preview Abstract] |
Wednesday, November 14, 2007 2:24PM - 2:36PM |
PO7.00003: Numerical Measurements of the Spectrum in Strong Magnetohydrodynamic Turbulence Joanne Mason, Fausto Cattaneo, Stanislav Boldyrev We discuss the results of an extensive set of direct numerical simulations of forced, incompressible, strong MHD turbulence with a strong guide field. Our aim is to resolve the controversy regarding the power law exponent of the field perpendicular energy spectrum. The two main theoretical predictions, -3/2 and -5/3, have both received some support from numerical simulations carried out by different groups, however, the design of those calculations also differ. Our simulations have a resolution of $512^3$ mesh points, a strong guide field, an anisotropic simulation domain, and implement a broad range of large-scale forcing routines. Our findings indicate that the spectrum of well developed, strong incompressible MHD turbulence with a strong guide field has the exponent -3/2. [Preview Abstract] |
Wednesday, November 14, 2007 2:36PM - 2:48PM |
PO7.00004: Magnetic dynamo action in helical turbulence Leonid Malyshkin, Stanislav Boldyrev We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model. We present the numerical solution of the model for the practically important case of Kolmogorov distribution of velocity fluctuations, with a large magnetic Reynolds number. We found that in contrast with the nonhelical case where growing magnetic fields are described by a few bound eigenmodes concentrated inside the inertial interval of the velocity field, in the helical case the number of bound eigenmodes considerably increases, moreover, new unbound eigenmodes appear. Both bound and unbound eigenmodes contribute to the large-scale magnetic field. This indicates a limited applicability of the conventional alpha-model of a large-scale dynamo action, which captures only unbound modes. [Preview Abstract] |
Wednesday, November 14, 2007 2:48PM - 3:00PM |
PO7.00005: Dissipation of Energy, Cross Helicity, and Magnetic Helicity in Ideal MHD Hussein Aluie, Gregory L. Eyink, Ethan T. Vishniac The ``invariants'' of ideal MHD--energy, cross helicity, and magnetic helicity--need not be conserved in the limit of zero viscosity and resistivity if the solution fields become singular. This is observed to occur in MHD turbulence, where the effective dissipation is due to nonlinear cascade of the invariants to small-scales. We study the large-scale balances of the three invariants via a ``coarse-graining'' approach related to Wilson-Kadanoff renormalization group. The ideal dissipation in this framework is due to ``turbulent stress'' and ``turbulent EMF'' generated by eliminated plasma motions below the coarse-graining length. We derive upper bounds on these turbulent contributions to the MHD equations and improve the necessary conditions of [1] for ideal dissipation. In particular, we show that the conditions for turbulent dissipation/forward cascade of magnetic helicity are so severe--infinite 3rd-order moments of the velocity \& magnetic fields!--that they are unlikely to ever naturally occur. We also establish local balance equations in space-time of the three invariants, both for measurable ``coarsed-grained'' variables and also for ``bare'' fields. On this basis we give physical interpretations of the turbulent cascades, in terms of work concepts for energy and in terms of topological linkage [2] for the two helicities. [1] Caflisch et al. 1997 Comm. Math. Phys. 184, 443-455 [2] Moffatt, H. K. 1969 J. Fluid Mech. 35, 117-129. [Preview Abstract] |
Wednesday, November 14, 2007 3:00PM - 3:12PM |
PO7.00006: MHD Turbulence: Generalized Formulation and Extension to Compressible Cases Bhimsen Shivamoggi A general framework that incorporates the Iroshnikov-Kraichnan (IK) and Goldreich-Sridhar (GS) phenomenologies of MHD turbulence is developed. This affords a clarification of the regimes of validity of the IK and GS models. This formulation is generalized further to include compressibility effects. [Preview Abstract] |
Wednesday, November 14, 2007 3:12PM - 3:24PM |
PO7.00007: Condition for Transition to Fast Collisionless Reconnection and its Role in Regulating Solar Coronal Heating Dmitri Uzdensky I suggest that solar coronal heating is a self-regulating process keeping the plasma marginally collisionless. The proposed mechanism is based on the interplay of two effects. The first one is the transition between the slow collisional (Sweet--Parker) and the fast collisionless reconnection regimes. I formulate a simple criterion for this transition, highlighting the strong effect of the ambient density on gas collisionality. When the density drops below critical, fast reconnection can occur causing magnetic energy release. The second key effect is the chromospheric evaporation caused by the coronal energy release. It increases the density and thereby temporarily inhibits any subsequent reconnection involving a given loop. As a result, statistically, the density fluctuates around a critical value which is found to be comparable with the observed coronal density. On a longer time-scale, coronal heating can be seen as a repeating cycle of fast reconnection events, followed by evaporation episodes, followed by long and quiet periods of magnetic stress build-up and gradual radiative cooling. [Preview Abstract] |
Wednesday, November 14, 2007 3:24PM - 3:36PM |
PO7.00008: Evidence for unsteady fast reconnection in a compressible medium Dongwook Lee, Fausto Cattaneo, Zoran Mikic, Robert Rosner, Roald Sagdeev, Samuel Vainshtein We present numerical evidence based on 2.5-dimensional simulations with constant classical resistivity of unsteady reconnection in a compressible medium. The initial configuration consists of a magnetic arcade with a nonzero longitudinal field embedded in a background stratified corona. In the strong compressibility regime the reconnection speed is observed to exceed the Sweet-Parker rate. The crucial ingredient that leads to the fast reconnection rate is the compressive collapse of the current sheet driven by the efficient diffusion of the longitudinal field. The calculation were carried out in a regime in which gravity was dominant in the sense that $F={gl}\big/(C_A C_S) >> 1$ where $g$ is the gravitational acceleration, $l$ is the magnetic scale, and $C_A$ and $C_S$ are the Alfv\'en and sound speeds respectively. Although the present model is not applicable to the solar case, it describes stars with stronger surface gravity. [Preview Abstract] |
Wednesday, November 14, 2007 3:36PM - 3:48PM |
PO7.00009: Ohm's Law in 3D turbulent magnetic Reconnection Haihong Che, J. Drake, M. Swisdak The evolution of kinetic instabilities and their role in fast magnetic reconnection are long-standing puzzles. In this paper we investigate these two issues by studying the role of Buneman instability in the electron diffusion region of collisionless magnetic reconnection. We obtain a second-order approximation of the first moment of Vlasov equation for evolving kinetic instabilities in which non-linear wave-particle interactions dominate. The resulting Ohm's law shows two new important characteristics: the drag force and turbulence viscosity. Using particle-in-cell simulations we study the evolution of this new Ohm's law. We perform 2D and 3D simulations with a strong guide field for both low and high initial electron temperatures. In the high temperature 3D simulation turbulence around x-line is absent. In the low temperatures 3D simulation the Buneman instability develops and evolves into a state with strong turbulence. Our simulations show that the turbulence effects can support fast reconnection: 1) The turbulence-induced drag force and viscosity are important factors in supporting the reconnection electric field at the late stages of reconnection; 2) Turbulence heating enhances the role of non-gyrotropic pressure and weakens the role of electron inertia in supporting the reconnection electric field. [Preview Abstract] |
Wednesday, November 14, 2007 3:48PM - 4:00PM |
PO7.00010: Merging Spheromak as Axisymmetric Plasma Equilibrium with Flow Jang-Yu Hsu, ChangMo Ryu It was reported that merging two spheromaks with opposite toroidal magnetic fields does not always lead to another spheromak, but may relax to a Field Reversed Configuration (FRC) with a high-$\beta$ value when the initial magnetic helicity is below certain critical value. The high-$\beta$ FRC rules out the relaxation to the force-free Taylor state. The plasma is self-organized under other invariant than the magnetic helicity. It was shown by Montgomery et. al. that maximizing the entropy for the given total current leads to the canonical profile. Hsu et. al. applied successfully the total current constraint to describe the tokamak plasma relaxation to bifurcated equilibrium solutions. The current conservation seems likely during the annihilation process of equal but opposite currents of merging spheromaks. In this paper, we show that a poloidal flow faster than the poloidal Alfven velocity provides a high-$\beta$ plasma equilibrium. As the toroidal current is annihilated and the poloidal Alfven velocity is vanishingly small, it goes to the hydrodynamic limit. [Preview Abstract] |
Wednesday, November 14, 2007 4:00PM - 4:12PM |
PO7.00011: Nonlinear Dynamics of Fluctuations in the Presence of Sheared Flows in a Magnetized Laboratory Plasma M. Gilmore, L. Yan, S. Xie, C. Watts Velocity shear is known to play an important role in the stability threshold of drift modes, as well as the suppression of drift turbulence, in both fusion and space plasmas. In addition, shear can destabilize modes such as Kelvin-Helmholtz (K-H). A set of laboratory experiments is described which utilize a set of concentric bias rings to affect the velocity (flow) shear in a linear device. With increasing ring bias, relative to the vacuum chamber wall, it is found that both axial and azimuthal flow shear change by only a small amount in magnitude, but move inward to the plasma core from the wall. As bias is increased, drift waves decrease in magnitude and are eventually fully suppressed, then the K-H mode is destabilized. While bias applied to rings at any radii suppresses drift fluctuations with nearly equal effectiveness, the K-H mode is more easily excited by biasing at the plasma edge. Fluctuations show increasingly chaotic and intermittent behavior as bias increases, up to V $\sim $ 10kTe/e, when the chaos disappears, as indicated by a rapid drop in correlation dimension. Experimental results and comparisons with theory are described. [Preview Abstract] |
Wednesday, November 14, 2007 4:12PM - 4:24PM |
PO7.00012: Turbulent transport in drift wave turbulence: the role of coherent vorticity Wouter Bos, Shinpei Futatani, Kai Schneider, Marie Farge, Sadruddin Benkadda A wavelet based technique for extracting coherent vortices, called coherent vortex extraction, is applied to simulations of drift wave turbulence. We show that the coherent vorticity, represented by few degrees of freedom, is responsible for the dynamics and transport. The radial density flux is carried by these coherent vorticity modes. The quasi-hydrodynamic limit shows a local depletion of nonlinearity and can be quantitatively distinguished from the quasi-adiabatic case by the skewness of the probability distribution function of the Weiss-field. [Preview Abstract] |
Wednesday, November 14, 2007 4:24PM - 4:36PM |
PO7.00013: A field theoretical model of self-organization of the vorticity field in two-dimensional plasma and in planetary atmosphere Florin Spineanu, Madalina Olimpia Vlad Starting from plasma/fluids models of interacting point-like vortices we develop a field theoretical description for the 2D Euler fluid (non-dissipative incompressible fluids) and for the 2D plasma in strong magnetic field (Hasegawa-Mima) and planetary atmosphere (Charney) fluids. We find the Lagrangian densities and action functionals, and derive the equations of motion. We prove that between the states that attain the extrema of the action there is a subset of stationary states that correspond to absolute minima and are reached by the system asymptotically. We show that they are respectively described by the sinh-Poisson equation (confirming by purely analytical means a previous result) and by a new equation for 2D plasma and atmosphere. Solving numerically the second equation we show that it reproduces large scale 2D flows in tokamak plasma. We argue that the states of high confinement are connected with states of organization of plasma vorticity. [Preview Abstract] |
Wednesday, November 14, 2007 4:36PM - 4:48PM |
PO7.00014: What Can We Learn About Electron Distributions From Measurements of Weak Bipolar Fields?$^*$ Martin V. Goldman, David L. Newman, Andr\'e Mangeney A given bipolar field that is stationary in a co-moving frame can correspond either to an ion soliton or an electron phase-space hole. In the limit of weak potential, $\phi$, with $e\phi_{\mathrm{max}}/T_e\ll1$, either of these structures can have the asymptotic shape $\phi= \phi_{\mathrm{max}}\mathrm{sech}^4(x/\alpha)$. For ion solitons, the half width ($\propto\alpha$) depends on $\phi_{\mathrm{max}}$, whereas for electron holes the half-width is independent of $\phi_{\mathrm{max}}$. We show analytically for holes in this limit that $\phi_{\mathrm{max}}$ depends on the (finite) energy derivative of the trapped distribution at the separatrix, while $\alpha$ depends only on a ``screening'' integral over the untrapped distribution. Idealized trapped and passing electron distributions are shown to be \textit{inferrable} from the speed, amplitude, and shape of weak bipolar waveform measurements. For measurements$^1$ of hundreds of weak bipolar field events in Earth's cusp, the theory is shown to be consistent with the most frequently observed \textit{half-width} between bipolar field peaks, and with various other features of the measured$^1$ distribution of hole velocities vs hole half-widths. \\ $^*$ Work supported by NSF, NASA, and DOE, and submitted in part to \textit{Phys.~Rev.~Lett.} as ``Theory of Weak Bipolar Fields and Electron Holes with Space Applications,'' (2007). \\ $^1$ Franz, J.R., \textit{et al}., \textit{J.~Geophys.~Res.} \textbf{110}, A09212, 2005. [Preview Abstract] |
Wednesday, November 14, 2007 4:48PM - 5:00PM |
PO7.00015: New Route to Shallow Electron Phase-Space Holes via a ``Velocity-Notch'' Instability$^*$ David L. Newman, Martin V. Goldman Properties of weak bipolar fields observed in space are found to be consistent with a theory for shallow electron phase space holes.$^1$ Here, we show that shallow phase space holes can develop \textit{dynamically} as a result of trapping during the saturation of a new electron ``velocity-notch'' instability. This instability occurs when there is a ``notch'' of width $\Delta v$ and density deficit $\Delta n$ in a unimodal electron velocity distribution with density $n_{e0}$ and thermal speed $v_{e0}$, provided $\Delta v/v_{e0}$ is sufficiently smaller than $\sqrt{\Delta n/n_{e0}}$. In the narrow-notch limit, the growth rate is the \textit{plasma frequency of the missing notch electrons}. The nonlinear saturation of this instability is studied using Vlasov simulations initiated with two different classes of electron distributions: Spatially uniform electron distributions with a shallow velocity notch result in holes whose form depends on the degree to which the instability threshold is exceeded. Distributions initialized with a \textit{spatially local} temperature enhancement develop a notch in velocity due to time-of-flight effects. This notch becomes progressively narrower until the instability threshold is crossed. The bipolar fields in the simulations are compared with those corresponding to the weak potential solutions $\phi=\phi_{\mathrm{max}}\mathrm{sech}^4(x/\alpha)$ from theory.$^1$ \\ $^*$ Work supported by NSF, NASA, and DOE \\ $^1$ M.~V.~Goldman, \textit{et al}., this meeting. [Preview Abstract] |
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