Session VO1: Turbulence, Reconnection, and Complex Plasmas

The effect of negative ions on the charging of dust in a plasma

We have studied the charging of dust particles in a plasma containing positive ions, negative ions and electrons. In electron/positive ion plasmas, dust particles are typically negatively charged due to the preferential collection of electrons since the electron thermal speed is much higher than the ion thermal speed. However, if the electrons are attached to heavy negative ions, the charging conditions for dust particles can be significantly different. If a substantial fraction of the electrons are attached to negative ions, and if the positive ion mass is less than the negative ion mass, calculations show that it is possible to produce positively charged dust. This possibility was investigated in a Q machine plasma with potassium positive ions and with the addition of an electron attaching gas. The low energy (0.2 eV) Q machine electrons readily attach to the molecules, with resulting electron densities less than 1/10,000$^{th}$ of the positive ion density. Results will be presented indicating that under these conditions, glass microspheres (d=35 micron) acquire a positive charge.   

Spherical crystals in dusty plasmas - Simulation and theory

Coulomb crystals in spherically symmetric traps have been found in trapped cold ions and, recently, in dusty plasmas at room temperature [1] allowing for precision measurements, including individual particle positions and trajectories. Thus, for the first time, strong correlation phenomena can be studied directly on the microscopic level which allows for detailed comparisons with theoretical results and computer simulations. We present molecular dynamics and Monte Carlo simulations of Coulomb crystals in the range from 10 to 10,000 particles which agree very well with the measurements [3]. The results include the ground state shell configurations and symmetry properties [2,3], the crystal stability and melting behavior. Finally, a thermodynamic theory is developed and compared to simpler models, such as shell models [4]. [1] O. Arp, D. Block, A. Piel, and A. Melzer, Phys. Rev. Lett. \textbf{93}, 165004 (2004). [2] P. Ludwig, S. Kosse, and M. Bonitz, Phys. Rev. E \textbf{71}, 046403 (2005). [3] M. Bonitz, D. Block, O. Arp, V. Golubnychiy, H. Baumgartner, P. Ludwig, A. Piel, and A. Filinov, Phys. Rev. Lett. \textbf{96}, 075001 (2006). [4] C. Henning et al., submitted for publication.   

Attraction of positively charged dust grains in a plasma

In two recent papers, Delzanno et al. [1-2] have pointed out that an electron emitting dust grain immersed in a plasma can sustain profiles of the shielding potential having an attractive potential well. The existence of attractive potential wells around dust grains in a plasma is of considerable interest as it provides an alternative mechanism for the attraction of the grains. Moreover, this mechanism can play an important role in astrophysical scenarios, for example in star forming regions where a substantial UV field is responsible for grain photoemission. We have therefore developed a three-dimensional PIC code with the aim of studying the collapse of a system of grains undergoing gravitational and electrostatic forces (the latter modeled via the potential well discovered in Refs. [1,2]). We will show how the attractive potential well can indeed lead to the collapse of the system, at rates which can be higher with respect to the pure gravitational analogue. Further on, a pure monotonic Debye-Huckel electrostatic potential can impede the collapse, depending on the charge to mass ratio of the grains. These results are in agreement with the predictions of the linear theory we have recently developed [3]. [1] G. L. Delzanno, G. Lapenta, M. Rosenberg, Phys. Rev. Lett. 92 (3), 035002 (2004). [2] G. L. Delzanno, A. Bruno, G. Sorasio, G. Lapenta, Phys. Plasmas 12, 062102 (2005). [3] G. L. Delzanno, G. Lapenta, Phys. Rev. Lett. 94, 175005 (2005).   

External DC Biases in Complex Plasmas

Dust particles imbedded within plasma are charged by collisions with free electrons and ions in the plasma. If the ratio of the inter-particle potential energy to the average kinetic energy is sufficient, the particles form a ``liquid'' structure with short range ordering or a crystalline structure with longer range ordering. When the dust particles form a crystalline structure and reside within two-dimensionally extended lattice planes, different stable crystalline phases have been observed experimentally. It has recently been found that an external DC bias allows for the formation of new energetically favored structures. Experimental results will be discussed and shown to be in good agreement with current theoretical predictions.   

The Effects of Parallel Ion Motion of Zonal Flow Generation in Ion-Temperature-Gradient Mode Turbulence

The ubiquitous phenomenon of Zonal Flows driven by drift-type turbulence have been intensively investigated in recent years since it was shown that Zonal Flows (ZF) reduces the anomalous transport generated by such turbulence in magnetic confinement devices. The generation of ZF in ion-temperature-gradient (ITG- ) mode turbulence has been studied previously using different analytical and numerical models, however, the effects of parallel ion motion have not been considered. In the present work the role of parallel ion motion for ZF generation by ITG mode turbulence is studied analytically and numerically using a fluid description. The analytical modeling is based on the coherent mode coupling models[1,2] using the fluid model in Ref. [3] extended for treating the parallel ion motion. Numerical studies are performed to corroborate the findings in the analytical models. It is found that the ratio of the growth rate and the frequency is decreasing with increasing $\eta_i$ (Ln is fixed). It is indicated that in the region close to the linear ITG threshold the ZF are stationary and may have a significant stabilizing effect on the background turbulence whereas at higher $\eta_i$ the ZF becomes oscillatory. [1] L. Chen, Z. Lin and R. White, Phys. Plasmas 7, 3129 (2000)[2] J. Li and Y. Kishimoto, Phys. Plasmas 9 1241 (2002)[3] J. Anderson, H. Nordman, R. Singh et al, Phys. Plasmas 9, 4500 (2002)   

Bifurcation structure in resistive drift wave turbulence

In this study, we have analyzed the modified Hasegawa-Wakatani (MHW) model, which describes the electrostatic resistive drift wave turbulence in 2D slab geometry, by direct numerical simulation. We have shown that, at a certain parameter range, a coherent zonal flow structure is generated, and the zonal flow significantly suppresses cross-field turbulent transport. A systematic parameter study of the MHW model has been performed to construct a bifurcation diagram in the parameter space. The result shows that a sudden transition from a zonal flow dominated state to a zonal flow suppressed state occurs if we increase the turbulent drive (the length scale of the background density profile), or decrease the electron adiabaticity (inverse of the parallel resistivity). The zonal flow suppressed rather turbulent state appears in the linearly unstable region.   

Long lifetime current driven rotating kink modes in a non line-tied plasma column with a free end

We show the first experimental evidence [1] for a magnetohydrodynamic kink instability in a current rope with one end that is free to move. This free end is insulated by sheath resistivity, which breaks MHD, and is thus not line tied to the axial boundary. We find instability threshold well below the classical Kruskal-Shafranov threshold. The presence of an axial flow gives rise to a doppler shifted frequency and rotation of the kink where the eigenfunction is axially pushed in the flow direction. This oscillating and rotating state persists indefinitely without disruptions for a long lifetime. Striking agreement with a theoretical analysis is demonstrated. \newline \newline [1] I. Furno, T. P. Intrator, D.D. Ryutov et al. ``Current-Driven Rotating-Kink Mode in a Plasma Column with a Non-Line-Tied Free End.'' \underline {Physical Review Letters}, \textbf{97}: 015002 (2006).   

Motion of a Localized Region of High-Density Plasma across Magnetic Flux Surfaces

Injecting small pellets of frozen hydrogen into a tokamak is a proven method of fueling. Previous results of 3D extended MHD simulations of pellets injection into tokamaks are in qualitative agreement with experiments, i.e., high-field-side (HFS) fueling is more efficient than low-field-side (LFS) fueling. A key issue is understanding the pellet-mass redistribution processes involving the density equilibrating along field lines and transport across surfaces (in the large-major-radius direction). At least two viewpoints exist: one is that the transport of mass across flux surface is accompanied by reconnection; while the other one suggests that the flow in the vicinity of the pellet is in the low-magnetic-Reynolds number regime so that high-density cloud simply slips through the magnetic field. In this talk , we present results from idealized simulations of the motion of localized regions of high-density plasma as they move across magnetic field lines and identify the mechanisms which are related to the motion of the ablated pellet mass across flux surfaces in a tokamak. The simulations are performed both in idealized Cartesian geometry and in tokamak geometry. The numerical method is based on generalized upwinding techniques. We employ the Chombo framework for adaptive mesh refinement to mitigate the need for large spatial resolution requirements.   

Magnetic Energy Release from Electron Scale Reconnection

Magnetic reconnection may occur as bursts of nonlinear plasma dynamics on the electron collisionless skin length scale $d_e = c/\omega_{pe}$ during which a large fraction of the magnetic energy is converted to electron thermal energy and plasma flow energy. The energization mechanism is the crossfield compression of the electron gas between interacting magnetic islands and the parallel electric fields accelerating the small pitch angle electrons. Solutions of the reduced Hall-MHD equations show the heating pulses in nearly collisionless, energy conserving simulations. The electron energization appears to be measured in the 4s, 200km resolution data from Cluster crossing thin, multipeaked current sheets in the geotail at -17 $R_E$ (JGR, Nakamura et al (2006)). The electron PAD and energy fluxes change rapidly consistent with the magnetic fluctuations. In short time (10 ion cyclotron periods or 30s) from 0.5-0.8 keV up to 5 keV in ninety degree pitch angle flux and weak parallel electron beams formed at small pitch angles. Work partially supported by US Dept of Energy, NSF 0539099, and CEA Cadarache.   

Forced Reconnection in the Hall Limit

We present new numerical results of the dynamics of forced magnetic reconnection in the Hall limit using the NRL Hall MHD code VooDoo. The system is forced by imposing inflow boundary conditions on the plasma density and velocity, and the magnetic field. A magnetic field of opposite polarity is injected from opposite boundaries. The inflow velocity is spatially uniform but the density profile is spatially nonuniform which allows an X-line to develop and magnetic reconnection to proceed. We present simulation results for various inflow conditions in both 2D and 3D geometries. We apply our results to laboratory and space plasma processes.   

On Hall magnetohydrodynamics equilibria

Steady states are studied in the framework of ideal Hall magnetohydrodynamics (HMHD) model in arbitrary and axisymmetric geometries. In arbitrary geometry, conditions are found under which certain magnetohydrodynamics (MHD) equilibrium solutions can also satisfy the HMHD equations. For axisymmetric plasmas reduced equations are derived for uniform electron temperatures on magnetic surfaces and either barotropic ions or incompressible ion flows. The Hall and electron pressure gradient terms result in a deviation of the magnetic from the ion velocity surfaces and consequently the axisymmetric equilibria obey a set of coupled partial differential equations, one for the poloidal magnetic flux function and the other for a flux function labeling the ion velocity surfaces. Furthermore, the characteristics of certain particular axisymmetric steady states with side conditions, as flows parallel to the magnetic field or purely poloidal incompressible flows, are identified and compared with respective MHD equilibria. Unlike in the frame of MHD, steady states with parallel axisymetric flows must be incompressible and equilibria with purely poloidal incompressible flows are possible. Certain analytic axisymmetric solutions are also constructed.   

Hall Currents in Current Sheets Formed in Magnetic Fields with the \textit{X} Line

Current sheets are a key element in magnetic reconnection processes, which play an important part in flare-type phenomena in astrophysics and laboratory experiments. Two-fluid plasma properties and appearing the Hall currents can be essential for the structure and dynamics of current sheets, modifying the properties of magnetic reconnection. We present direct evidences for generating the Hall currents in the current sheets formed in 3D and 2D magnetic configurations with the \textbf{\textit{X}} line. It was reported earlier that asymmetric and tilted shape of plasma sheets indicated the Hall current interaction with the guide field [1]. On the base of space-temporal evolution of 3D magnetic fields caused by plasma currents we obtained the current distributions, including distributions in the plane perpendicular to the applied voltage. In the 3D configuration, with the guide field along the \textbf{\textit{X}} line, two different processes take place: an enhancement of the guide field inside the sheet, and the Hall current generation [2]. In the 2D configuration (without the guide field) there is only the effect of the Hall currents, which transform the initial 2D magnetic configuration to the 3D one. The structure and time evolution of additional magnetic fields produced by the Hall currents were obtained for plasmas with different ion masses. It was shown that the Hall currents are decaying with time, and the heavier are the plasma ions, the Hall current generation [2]. 1. A.G. Frank, S.Yu. Bogdanov, G.V. Dreiden et al., \textit{Phys. Letters A} \textbf{348}, 318-325 (2006). 2. A.G. Frank, S.Yu. Bogdanov, V.S. Markov et al., \textit{Phys. Plasmas} \textbf{12}, 052316 (2005).   

Magnetic Field Effects on Turbulent Plasmas from Ionizing Shock Waves

The effects of weak magnetic fields on turbulent plasmas from normal ionizing shock waves created in an Arc Driven Shock Tube (ADST) are examined. The ADST is discharged at 18kV, and filled with argon gas to pressures ranging from 80 and 160 mTorr. This produces hypersonic shock waves ranging between Mach 60 and Mach 10. An axial magnetic field is created using Helmholtz Coils with strengths ranging from 0 and 500 Gauss. Finally, using Laser Induced Fluorescence, multiple-point ion density measurements enable standard turbulent parameters such as spectral index, turbulent energy, characteristic frequency, and chaotic dimension to be determined as well as direct determinations of local Reynolds stresses. This research is relevant to shock wave studies in both laboratory and astrophysical plasmas as well as fusion plasmas.   

Critical phenomena Aspects of Fully Developed Turbulence in Fluids and Plasmas

A new perspective on the critical phenomena aspects of fully-developed turbulence (FDT) is considered [1]. The ``energy'' dissipation rate is identified as the suitable order parameter for the FDT problem. Multi-fractal model has been used to provide a detailed structure for the critical exponent associated with this order parameter. This exhibits an interesting universality covering radically different FDT systems in fluids and plasmas. \newline \newline \underline {References:} \newline [1] B.K.Shivamoggi : \textit{Chaos, Solitons and Fractals}, In press (2006)