
Physics Highlights, 2012
Distribution of plasmoids in HighLundquistNumber Magnetic Reconnection
Plasmoid distribution functions from (a) direct numerical simulations, and (b) kinetic model. Click on image to enlarge
In recent years, significant advances have been made in understanding the role of plasmoids (or secondary islands) in magnetic reconnection, which is believed to be the underlying mechanism of energy release for phenomena such as solar flares, magnetospheric substorms, and sawtooth crashes in fusion plasmas. Plasmoids often form spontaneously in resistive magnetohydrodynamics (MHD), Hall MHD, and kinetic particleincell (PIC) simulations of largescale systems. Evidences of plasmoids have also been found in the magnetotail and the solar atmosphere, where they are demonstrated to play a significant role in particle acceleration. In the framework of resistive MHD it has become clear that when the Lundquist number S is above a critical value Sc ~104 , the SweetParker current sheet becomes unstable to the plasmoid instability, with a growth rate that increases with S. The reconnection layer changes to a chain of plasmoids connected by secondary current sheets that, in turn, may become unstable again. Eventually the reconnection layer will tend to a statistical steady state characterized by a hierarchical structure of plasmoids. The hierarchical structure suggests selfsimilarity across different scales, which often gives rise to power laws. We have carried out statistical studies of the plasmoid distribution with respect to the magnetic flux content of plasmoids, with highLindquistnumber simulations up to S =10^7. We find that over an extended range of J , the plasmoid distribution function
f(J) follows a power law f (J) ~ J−1 . We further develop a kinetic model of plasmoid dynamics that reproduces the observed distribution. Figure 5 shows plasmoid distributions from direct numerical simulations and our kinetic model. High velocity turbulent MHD wind tunnel on SSX
Evolution of the fluctuation spectrum over time, showing the growing dominance of a narrow band of wavenumbers. The horizontal line is the wavenumber of the lowest energy state which the plasma can attain while conserving magnetic helicity. Bottom: The red curve outlines a fieldline in the preferred final state; the blue points are data points. Click on image to enlarge
We designed a fourfoot extension to SSX to give us over 2 meters for injected plasma plumes to flow and evolve. Typical flow speeds are 50 km/s with densities and temperatures in the 1015 cm3 and 20 eV ranges respectively. Mean magnetic fields are about 0.25 T. Our main observation is the relaxation of the turbulence to a single twisted helical structure with kz = 2.2 m1. Magnetic fluctuations are measured with high resolution probe arrays (4 mm spacing) and using 96 channels of new digitizers at 65 MHz and 14 bits. This allows us to study fluctuations above the ion cyclotron frequency (> 3 MHz) with a dynamic range of gauss to tesla. Preliminary fluctuation spectra show a f5/3 dependence for about a decade, followed by a steeper spectrum at frequencies above the ion cyclotron frequency. Simulation of Dynamo and Flow Generation in the Reversed Field Pinch
Comparison of measured (stars) and simulated (solid curve) flow in the MST RFP; previous, single fluid simulations qualitatively and quantitatively disagreed with the data. Click on image to enlarge
Relaxation of the Reversed Field Pinch (RFP) to a selforganized state can be understood at the most basic level through single fluid magnetohydrodynamics, (MHD) but certain key features, such as the generation of flow, cannot be explained in MHD. We showed for the first time that these phenomena can be successfully reproduced by incorporating effects beyond MHD into the simulations. Our twofluid simulationbased study of magnetic tearing and relaxation in pinch profiles has produced three new theoretical results. The first concerns the influence of finite gyroradius effects from warm ions, where stresses from the variation in the magnitude of magnetic field and from magnetic curvature in the poloidal direction lead to drifting and partial stabilization of linear tearing modes. The net effect is analogous to previous drift tearing results, but others have considered configurations where drifts are from pressure gradients. The importance of ''gradB'' and poloidal curvature drifts had not been appreciated for pinches. The second finding is that the ion gyroviscous stresses are also important for large, nonlinearly saturated magnetic islands. They are not diminished by nonlinear transport effects, unlike pressurebased drift effects, and the residual forces are balanced by net Lorentz forces that maintain a Hall dynamo effect. Our third result concerns warmion effects when multiple tearing fluctuations are active. The magnetic relaxation that results from the Hall dynamo effect from net Lorentz forces is accompanied by changes in the plasma flow profile, and the magnitude and direction of the computational results are consistent with measurements in the Madison Symmetric Torus RFP (Figure). These results confirm our understanding of the physics, and help to validate the NIMROD code. [This work is leveraged by support from U.S. Dept. of Energy grant DEFG0206ER54840 for theoretical research in fusion energy science.] Stirring Unmagnetized Plasma
Top: plots of the angular velocities of Ar and He plasmas, and the viscosities responsible for transmitting torques. Bottom: a vertical slice through the cylindrical Plasma Couette Experiment (PCX), showing how the alternating cathodes and anodes at the wall produce a strong magnetic field that drops nearly to zero in the volume. Click on image to enlarge
Mechanical stirring of fluids is common in experimental physics and everyday life, and strongly magnetized plasmas can be stirred by electromagnetic torques. But generating flow in an unmagnetized plasma has been elusive. This past year, CMSO researchers experimentally demonstrated a new concept for spinning unmagnetized plasma, marking an important first step towards laboratory studies of a wide variety of phenomenon in plasma astrophysics. The ability to produce a hot, fast flowing, magnetic fieldfree plasma (in contrast to highly magnetized plasmas used for fusion energy research) may help us better understand the dynamo, a process thought to be responsible for the creation of magnetic fields in stars in galaxies. Flows can be adjusted in the experiment to mimic those of accretion disks, making it possible to study, for the first time, the magnetorotational instability in a plasma, a mechanism of interest for its roles in providing the fuel for high energy emission from compact objects, and aiding in the formation of stars and planets. In the experiment, plasma is confined by a cylindrical “bucket” assembly of permanent magnets, arranged in rings of alternating polarity, to form an axisymmetric cusp magnetic field. The field is localized to the boundaries, leaving a large, unmagnetized plasma in the bulk. The plasma is stirred using JxB torques, where current is driven by electrostatically biased electrodes in the magnetized edge region. Measurements show that the azimuthal flow viscously couples momentum from the magnetized edge (where the plasma viscosity is small) into the unmagnetized bulk (where the viscosity is large) so that the bulk rotates like a solid body. Flow speeds can be adjusted by simply increasing the bias voltage of the electrodes, and the addition of electrodes at the inner boundary will allow studies of shear flow profiles, including the Keplerianlike flows in accretion disks, where v_φ /sqrt(r). Flows as high as 6 km/s have been observed in subsequent experiments. See C. Collins et al. Phys. Rev. Lett. 108, 115001 (2012). Effect of Magnetic Shear on Hall – Mediated Magnetic Reconnection
Reconnection electric field (E) and the “Hall Electric Field” versus normalized guide field, Bg /Brec. The reconnection electric field is normalized by x VA, where Brec is the magnitude of the reconnecting field, and VA is the Alfven speed calculated using Brec. Click on image to enlarge
It has been known for many years that when electrons and ions can follow separate dynamics  the Hall regime  reversing magnetic fields can rapidly reconnect. But most instances of reconnection in nature and the laboratory involve a significant sheared, or guide field, rather than a full reversal. In magnetosphere reconnection, for example, guide fields often reach the level of the reconnecting field, while reconnection in fusion plasmas can have guide fields much larger than the reconnecting field. This is prompting the study of this type of guide field, both theoretically and numerically. It has been generally observed that reconnection of antiparallel field lines proceeds much faster than guide field reconnection in which field lines meet with smaller angles with the effect of guide field. We are now studying the transition on MRX. As shown in this figure, we observed that the addition of guide field substantially reduces the reconnection rate, and we confirm that the Hall currents in the reconnection plane determine the reconnection electric field (the reconnection rate) over a wide range of applied guide field strengths. Also we have measured quantitative dependence of the reconnection characteristics and the reconnection rate on guide field by systematically applying an external guide field using central conductor coil which creates controlled guide field. Our results will be quantitatively compared with 2D numerical simulations in the future.
