Bulletin of the American Physical Society
51st Annual Meeting of the APS Division of Plasma Physics
Volume 54, Number 15
Monday–Friday, November 2–6, 2009; Atlanta, Georgia
Session UO6: Basic Plasma Phenomena: Theory and Simulation |
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Chair: Gurudas Ganguli, Naval Research Laboratory Room: Hanover FG |
Thursday, November 5, 2009 2:00PM - 2:12PM |
UO6.00001: Stochastic Flux-Freezing for Non-Ideal Hydromagnetic Plasmas Gregory Eyink Non-ideal (viscous and resistive) magnetohydrodynamic plasmas are shown to possess stochastic versions of ideal flux-freezing laws. The magnetic field at a point is equal to the average of an infinite ensemble of field-lines advected to that point by the plasma velocity perturbed with a random white-noise (stochastic Lundquist formula). This implies a stochastic Alfv\'{e}n theorem, valid for any value of the magnetic Prandtl number. At unit Prandtl number there is also a random version of the generalized Kelvin theorem derived by Bekenstein-Oron for ideal MHD. These stochastic conservation laws are not only consequences of the non-ideal MHD equations, but are in fact equivalent to those equations. Similar results hold for Hall magnetohydrodynamics and the two-fluid plasma model. We argue that flux-conservation remains stochastic for turbulent MHD plasmas in the limit of infinite Reynolds numbers. Infinitely-many field lines are advected to each point by turbulent Richardson diffusion. The reconnection speed for pairs of field lines is the relative velocity of the turbulent fluid at their initial locations. Small-scale turbulent dynamo effect is rigorously related to angular correlation of the individual field vectors before reconnection. [Preview Abstract] |
Thursday, November 5, 2009 2:12PM - 2:24PM |
UO6.00002: Scale-locality of energy transfer in magnetohydrodynamic turbulence. Hussein Aluie, Gregory L. Eyink We investigate scale-locality of energy cascade in magnetohydrodynamic (MHD) turbulence at high kinetic and magnetic Reynolds numbers. There is a growing consensus that large-scale flow can transfer energy to the magnetic field at arbitrarily small scales in the inertial range (Alexakis et al. (2005,2007), Carati et al. (2006), Yousef et al. (2007), Schekochihin et al. (2008), etc.) However, we rigorously prove that such non-local transfer cannot occur, under very weak scaling conditions for velocity and magnetic-field increments accepted to hold in the inertial-inductive range of turbulent MHD flows. Our analysis shows that inter-scale fluxes of two conserved quantities, total energy and cross helicity, are dominated by local triadic interactions. Nonlocal triads make an asymptotically negligible contribution, decaying as a power of the scale-disparity. Furthermore, nonlocal-in-scale triads may dominate in field-line stretching, but energy conversion by stretching is primarily between velocity and magnetic-field modes at comparable scales. To verify our analytical results, we present data of forced MHD turbulence from a pseudospectral simulation on a grid of $1024^3$ points with phase-shift dealiasing. [Preview Abstract] |
Thursday, November 5, 2009 2:24PM - 2:36PM |
UO6.00003: New approach to MHD spectral theory of stationary plasma flows Hans Goedbloed The basic equations of MHD spectral theory date back to 1958 for static plasmas (Bernstein et al.) and to 1960 for stationary plasma flows (Frieman and Rotenberg). The number of papers on the two subjects appears to be inversely proportional to their complexity, with the vast majority of contributions to MHD stability of tokamaks being restricted to static equilibria and stationary equilibrium flows mostly being discussed analytically for trivial equilibria or numerically for complicated geometries. The problem with the latter is not that numerical approaches are inaccurate, but that they suffer from lack of analytical guidance concerning the structure of the spectrum. One of the reasons is the usual misnomer of ``non-self adjointness'' of the stationary flow problem. In fact, self-adjointness of the two occurring operators was proved right away. Based on the two quadratic forms corresponding to these operators, (a) we constructed an effective method to compute the eigenvalues in the complex plane, (b) we found the counterpart of the oscillation theorem for eigenvalues of static equilibria~(Goedbloed and Sakanaka, 1974) for the eigenvalues of stationary flows, enabling one to map out sequences of eigenvalues in the complex plane. Examples will be given for Rayleigh-Taylor, Kelvin-Helmholtz and magneto-rotational instabilities. [Preview Abstract] |
Thursday, November 5, 2009 2:36PM - 2:48PM |
UO6.00004: Variational principle for multi region three dimensional relaxed magnetohydrodynamic equilibria R.L. Dewar, S.R. Hudson, M.J. Hole, M. McGann, Z. Yoshida Relaxed-magnetohydrodynamic (RXMHD) plasma equilibria are force-free states obtained by minimizing the magnetic energy subject to the constraint of constant magnetic helicity and magnetic fluxes within perfectly conducting toroidal boundaries, giving rise to the Beltrami equation, $\nabla\times{\bf B} = \mu {\bf B}$, with ${\bf B}$ the magnetic field and $\mu$ const. The Beltrami equation being consistent with the existence of field-line chaos, such a principle is suitable as a starting point for three-dimensional equilibrium theory. An extension of this variational principle to finite-pressure \emph{multi-region} relaxed MHD (MRXMHD) is developed, in which the total plasma energy, magnetic plus kinetic, is to be minimized assuming arbitrarily thin, ideal-MHD toroidal interfaces act as flexible barriers to thermal and magnetic relaxation. Formal expressions for the variations of total energy with respect to Lagrangian displacements of the barrier interfaces are derived. Generalized magnetic coordinates and the need for control of rotational transforms on the surfaces of the interfaces are discussed. [Preview Abstract] |
Thursday, November 5, 2009 2:48PM - 3:00PM |
UO6.00005: Discontinuous Galerkin Methods for Magnetohydrodynamics James Rossmanith Standard shock-capturing numerical methods fail to give accurate solutions to the equations of magnetohydrodynamics (MHD). The essential reason for this failure is that by ignoring the divergence-free constraint on the magnetic field, these methods can be shown to be entropy unstable. In this talk we will briefly review the entropy stability theorem for discontinuous Galerkin (DG) methods. We will then present a class of constrained transport (CT) methods that we will show give both stable and accurate results on several test cases. The proposed CT approach can be viewed as a predictor-corrector method, where an approximate magnetic field is first {\it predicted} by a standard DG method, and then {\it corrected} through the use of a magnetic potential. Finally, we will briefly describe efforts to extend this approach to Hall MHD and genuinely two-fluid plasma models. [Preview Abstract] |
Thursday, November 5, 2009 3:00PM - 3:12PM |
UO6.00006: Two Dimensional Computer Modeling of Plasmas Using Adaptive Mesh Refinement Mark Berrill, Jorge Rocca An understanding of the physics of laser-created plasma which is important for a wide range of applications often requires a detailed modeling of multi-dimensional effects. We report on a new 2D hydrodynamic plasma model to simulate laser created plasmas. The computer model simulates the plasma by solving the hydrodynamic equations with an atomic model. The equations are discretized on a rectangular Eulerian grid using adaptive mesh refinement (AMR). Multiple levels of refinement with an automatic grid generation allows for accurate simulations while minimizing the run time. The model is capable of running on high performance computers. The current capabilities of the model will be discussed and results of simulations performed to model plasma-based table-top soft x-ray lasers. Work supported by the NSF EUV ERC Award {\#}EEC-0310717 and the NNSA SSAA program through DOE Grant {\#}DE-FG52-060NA26152. M.B. was support by DOE CSGF Grant {\#}DE-FG02-97E. [Preview Abstract] |
Thursday, November 5, 2009 3:12PM - 3:24PM |
UO6.00007: Vlasov simulation in multiple spatial dimensions Harvey Rose, William Daughton One of the outstanding challenges encountered in modeling plasma is simulating the Vlasov equation over length and time scales that are physically relevant to real experiments. Plasma processes that depend sensitively on spatial dimension include linear ones such as diffraction and its nonlinear variant, self-focusing, cannot be simulated in one spatial dimension (1D). Direct multi-D Vlasov simulations are prohibitive while unphysical particle noise and Debye length resolution may severely constrain multi-D particle in cell (PIC) simulations. We have developed a Vlasov Multi-Dimensional (VMD) model that is specifically designed to take advantage of solution properties in regimes when plasma waves are confined to a narrow cone. Perpendicular grid spacing large compared to a Debye length is then possible without instability, enabling a factor of order 10 decrease in required computational resources compared to standard PIC methods in 2D and another factor of that order in 3D. Further advantage accrues in regimes where particle noise is an issue. VMD and PIC results in a 2D model of localized Langmuir waves are in quantitative agreement. [Preview Abstract] |
Thursday, November 5, 2009 3:24PM - 3:36PM |
UO6.00008: Enabling Global Kinetic Simulations of the Magnetosphere via Petascale Computing H. Karimabadi, H.X. Vu, Y.A. Omelchenko, M. Tatineni, A. Majumdar, U.V. Catalyurek, E. Saule The ultimate goal in magnetospheric physics is to understand how the solar wind transfers its mass, momentum and energy to the magnetosphere. This problem has turned out to be much more complex intellectually than originally thought. MHD simulations have proven useful in predicting eminent features of substorms and other global events. Given the complexity of solar wind-magnetosphere interactions, hybrid (electron fluid, kinetic ion) simulations have recently been emerging in the studies of the global dynamics of the magnetosphere with the goal of accurately predicting the energetic particle transport and structure of plasma boundaries. We take advantage of our recent innovations in hybrid simulations and the power of massively parallel computers to make breakthrough 3D global kinetic simulations of the magnetosphere. The preliminary results reveal many major differences with global MHD simulations. For example, the hybrid simulations predict the formation of the quadruple structure associated with reconnection events, ion/ion kink instability in the tail, turbulence in the magnetosheath, and formation of the ion foreshock region. [Preview Abstract] |
Thursday, November 5, 2009 3:36PM - 3:48PM |
UO6.00009: A Multifluid Interpenetration Mix Model Baolian Cheng, Anthony Scannapieco In this work, we present a multifluid interpenetration mix model that consists of a set of multifluid moment equations, with and without both internal and external fields. This model is derived from the collisional Boltzmann equation in a self-consistent manner. The external fields can be either grativational as in astrophysics and Rayleigh-Taylor (RT) mixing problems, or shock acceleration as in Richtmyer-Meshkov (RM) mixing problems, electric and magnetic fields as in magnetic confinement fusion, and rotational forces as in chemical applications. The model equations are mathematically closed and physically consistent with one free parameter, contained in a phenomenological closure for the collisional frequency, which is determined by experimental data. The set of model equations provide a theoretical foundation for a large fraction of phenomenological mix models. They contain all the physical terms, particularly the terms associated with the Reynolds stress due to both species interpenetrations and random chaotic motions. Under certain assumptions, these model equations successfully reduce to the various other mix models. The successful applications of this model in both direct drive and radiatively driven inertial confinement fusion (ICF) capsule implosions are discussed. [Preview Abstract] |
Thursday, November 5, 2009 3:48PM - 4:00PM |
UO6.00010: ABSTRACT WITHDRAWN |
Thursday, November 5, 2009 4:00PM - 4:12PM |
UO6.00011: Dynamics and Melting of Finite Plasma Crystals Patrick Ludwig, Hanno K\"ahlert, Henning Baumgartner, Hauke Thomsen, Michael Bonitz Interacting few-particle systems in external trapping potentials are of strong current interest since they allow to realize and control strong correlation and quantum effects [1]. Here, we present our recent results on the structural and thermodynamic properties of the crystal-like Wigner phase of complex plasma confined in a 3D harmonic potential. We discuss the linear response of the strongly correlated system to external excitations, which can be described in terms of normal modes [2]. By means of first-principle simulations the details of the melting phase transitions of these mesoscopic systems are systematically analysed with the melting temperatures being determined by a modified Lindemann parameter for the pair distance fluctuations [3]. The critical temperatures turn out to be utmost sensitive to finite size effects (i.e., the exact particle number), and form of the (screened) interaction potential.\\[4pt] [1] PhD Thesis, P. Ludwig, U Rostock (2008)\\[0pt] [2] C. Henning et al., J. Phys. A 42, 214023 (2009)\\[0pt] [3] B\"oning et al., Phys. Rev. Lett. 100, 113401 (2008) [Preview Abstract] |
Thursday, November 5, 2009 4:12PM - 4:24PM |
UO6.00012: Thermodynamic Theory of Spherically Trapped Coulomb Clusters Jeffrey Wrighton, James Dufty, Michael Bonitz, Hanno K\"{a}hlert The radial density profile of a finite number of identical charged particles confined in a harmonic trap is computed over a wide ranges of temperatures (Coulomb coupling) and particle numbers. At low temperatures these systems form a Coulomb crystal with spherical shell structure which has been observed in ultracold trapped ions and in dusty plasmas. The shell structure is readily reproduced in simulations. However, analytical theories which used a mean field approach\footnote[1]{C. Henning et al., Phys. Rev. E 74, 056403 (2006) } or a local density approximation\footnote[2]{C. Henning et al., Phys. Rev. E 76, 036404 (2007)} have, so far, only been able to reproduce the average density profile. Here we present an approach to Coulomb correlations based on the hypernetted chain approximation with additional bridge diagrams. It is demonstrated that this model reproduces the correct shell structure within a few percent and provides the basis for a thermodynamic theory of Coulomb clusters in the strongly coupled fluid state.\footnote[3]{J. Wrighton, J.W. Dufty, H. K\"{a}hlert and M. Bonitz, J. Phys. A 42, 214052 (2009) and Phys. Rev. E (2009) (to be submitted)} [Preview Abstract] |
Thursday, November 5, 2009 4:24PM - 4:36PM |
UO6.00013: Breathing is different in the quantum world Michael Bonitz, Sebastian Bauch, Karsten Balzer, Christian Henning, David Hochstuhl Interacting classicle particles in a harmonic trap are known to possess a radial collective oscillation -- the breathing mode (BM). In case of Coulomb interaction its frequency is universal -- it is independent of the particle number and system dimensionality [1]. Here we study strongly correlated quantum systems. We report a qualitatively different breathing behavior: a quantum system has {\em two BMs} one of which is universal whereas the frequency of the other varies with system dimensionality, the particle spin and the strength of the pair interaction. The results are based on exact solutions of the time-dependent Schr\"odinger equation for two particles and on time-dependent many-body results for larger particle numbers. Finally, we discuss experimental ways to excite and measure the breathing frequencies which should give direct access to key properties of trapped particles, including their many-body effects [2]. \\[4pt] [1] C. Henning et al., Phys. Rev. Lett. 101, 045002 (2008) \\[0pt] [2] S. Bauch, K. Balzer, C. Henning, and M. Bonitz, submitted to Phys. Rev. Lett., arXiv:0903.1993 [Preview Abstract] |
Thursday, November 5, 2009 4:36PM - 4:48PM |
UO6.00014: Thomson scattering in warm dense matter R. Thiele, T. Bornath, R.R. F\"austlin, C. Fortmann, S. Glenzer, G. Gregori, B. Holst, T. Tschentscher, V. Schwarz, R. Redmer Free electron lasers employing scattering of high-brilliant, coherent photons in the extreme ultraviolet (VUV), e.g. at FLASH (DESY Hamburg) or LCLS (Stanford), allow for a systematic study of basic plasma properties in the region of warm dense matter (WDM). WDM is characterized by condensed matter-like densities and temperatures of several eV. Collective Thomson scattering with VUV or x-ray has demonstrated its capacity for robust measurements of the free electron density and temperature in WDM. Collective excitations like plasmons (``electron feature'') appear as maxima in the scattering signal. The respective frequencies can be related to the free electron density. Furthermore, the asymmetry of the red- and blue shifted plasmon intensity gives the electron temperature due to detailed balance. We treat collective Thomson scattering in the Born-Mermin-approximation which includes collisions and present a generalized Gross-Bohm dispersion for plasmas. The influence of plasma inhomogeneities on the scattering spectrum is studied by comparing density and temperature averaged scattering signals with calculations assuming homogeneous targets. For the ``ion feature,'' results of semi-classical hypernetted chain (HNC) calculations and of quantum molecular dynamics simulations are shown for dense beryllium. [Preview Abstract] |
Thursday, November 5, 2009 4:48PM - 5:00PM |
UO6.00015: Molecular dynamics simulations of electron-ion temperature equilibration in an SF6 plasma Lorin X. Benedict, James N. Glosli, David F. Richards, Frederick H. Streitz, Stefan P. Hau-Riege, Richard A. London, Frank R. Graziani, Michael S. Murillo, John F. Benage We describe classical non-equilibrium molecular dynamics simulations aimed at studying electron-ion temperature equilibration in a two-temperature SF$_{6}$ plasma. We choose a density of $1.0 \times 10^{6}$ (dissociated) SF$_{6}$ molecules per cm$^{3}$ and initial temperatures of $T_{e}$= 100 eV and $T_{S}= T_{F}$= 15 eV, in accordance with experiments currently underway at Los Alamos National Lab. Our computed relaxation time lies between two oft-used variants of the Landau-Spitzer relaxation formula. Discrepancies are also found when comparing to the predictions of more recent theoretical approaches. These differences should be large enough to be measured in the upcoming experiments. We highlight one particular source of discrepancy arising from the strong ion-ion coupling: the time-dependent specific heat of the screened ion subsystem. [Preview Abstract] |
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