The constraint imposed by magnetic helicity conservation on the alpha effect is considered for both magnetically and flow dominated self-organizing plasmas. Direct numerical simulations are presented for a dominant contribution to the alpha effect, w
hich can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven alpha ( H$alpha$) effect. Direct numerical simulations of the H$alpha$ effect are prese nted for two examples---the magnetically dominated toroidal plasma unstable to tearing modes, and the flow-dominated accretion disk.
Filamentation due to the growth of a Weibel-type instability was observed in the interaction of a pair of counter-streaming, ablatively-driven plasma flows, in a supersonic, collisionless regime relevant to astrophysical collisionless shocks. The flo
ws were created by irradiating a pair of opposing plastic (CH) foils with 1.8 kJ, 2-ns laser pulses on the OMEGA EP laser system. Ultrafast laser-driven proton radiography was used to image the Weibel-generated electromagnetic fields. The experimental observations are in good agreement with the analytical theory of the Weibel instability and with particle-in-cell simulations.
In a recent numerical study [Ng et al., Astrophys. J. {bf 747}, 109, 2012], with a three-dimensional model of coronal heating using reduced magnetohydrodynamics (RMHD), we have obtained scaling results of heating rate versus Lundquist number based on
a series of runs in which random photospheric motions are imposed for hundreds to thousands of al time in order to obtain converged statistical values. The heating rate found in these simulations saturate to a level that is independent of the Lundquist number. This scaling result was also supported by an analysis with the assumption of the Sweet-Parker scaling of the current sheets, as well as how the width, length and number of current sheets scale with Lundquist number. In order to test these assumptions, we have implemented an automated routine to analyze thousands of current sheets in these simulations and return statistical scalings for these quantities. It is found that the Sweet-Parker scaling is justified. However, some discrepancies are also found and require further study.
New developments in the theory and numerical simulation of a recently proposed one-dimensional nonlinear time-dependent fluid model [K. Avinash, A. Bhattacharjee, and S. Hu, Phys. Rev. Lett. 90, 075001 (2003)] for void formation in dusty plasmas are
presented. The model describes an initial instability caused by the ion drag, rapid nonlinear growth, and a nonlinear saturation mechanism that realizes a quasi-steady state containing a void. The earlier one-dimensional model has been extended to two and three dimensions (the latter, assuming spherical symmetry), using a more complete set of dynamical equations than was used in the earlier one-dimensional formulation. The present set of equations includes an ion continuity equation and a nonlinear ion drag operator. Qualitative features of void formation are shown to be robust with respect to different functional forms of the ion drag operator.
An analytical and numerical treatment is given of a constrained version of the tectonics model developed by Priest, Heyvaerts, & Title [2002]. We begin with an initial uniform magnetic field ${bf B} = B_0 hat{bf z}$ that is line-tied at the surfaces
$z = 0$ and $z = L$. This initial configuration is twisted by photospheric footpoint motion that is assumed to depend on only one coordinate ($x$) transverse to the initial magnetic field. The geometric constraints imposed by our assumption precludes the occurrence of reconnection and secondary instabilities, but enables us to follow for long times the dissipation of energy due to the effects of resistivity and viscosity. In this limit, we demonstrate that when the coherence time of random photospheric footpoint motion is much smaller by several orders of magnitude compared with the resistive diffusion time, the heating due to Ohmic and viscous dissipation becomes independent of the resistivity of the plasma. Furthermore, we obtain scaling relations that suggest that even if reconnection and/or secondary instabilities were to limit the build-up of magnetic energy in such a model, the overall heating rate will still be independent of the resistivity.
A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs
at the resistive skin depth $d_eta equiv S_L^{-1/2} sqrt{L v_A/gamma}$, where $S_L$ is the Lundquist number, $L$ the length of the current sheet, $v_A$ the Alfv{e}n speed, and $gamma$ the growth rate. Modifications to a recent resistive MHD analysis [N. F. Loureiro, A. A. Schekochihin, and S. C. Cowley, Phys. Plasmas {bf 14}, 100703 (2007)] arise when collisions are sufficiently weak that $d_eta$ is shorter than the ion skin depth $d_i equiv c/omega_{pi}$. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as $(d_i/L)^{6/13} S_L^{7/13} v_A/L$ and the number of plasmoids as $(d_i/L)^{1/13} S_L^{11/26}$, compared to $S_L^{1/4} v_A/L$ and $S^{3/8}$, respectively, in resistive MHD.
Whether the phenomenology governing MHD turbulence is Kolmogorov or Iroshnikov-Kraichnan (IK) remains an open question, theoretically as well as observationally. The ion heating profile observed in the solar wind provides a quantitative, if indirect,
observational constraint on the relevant phenomenology. Recently, a solar wind heating model based on Kolmogorov spectral scaling has produced reasonably good agreement with observations, provided the effect of turbulence generation due to pickup ions is included in the model. Without including the pickup ion contributions, the Kolmogorov scaling predicts a proton temperature profile that decays too rapidly beyond a radial distance of 15 AU. In the present study, we alter the heating model by applying an energy cascade rate based on IK scaling, and show that the model yields higher proton temperatures, within the range of observations, with or without the inclusion of the effect due to pickup ions. Furthermore, the turbulence correlation length based on IK scaling seems to follow the trend of observations better.
In recent years, a phenomenological solar wind heating model based on a turbulent energy cascade prescribed by the Kolmogorov theory has produced reasonably good agreement with observations on proton temperatures out to distances around 70 AU, provid
ed the effect of turbulence generation due to pickup ions is included in the model. In a recent study [Ng et al., J. Geophys. Res., 115, A02101 (2010)], we have incorporated in the heating model the energy cascade rate based on Iroshnikov-Kraichnan (IK) scaling. We showed that the IK cascade rate can also produce good agreement with observations, with or without the inclusion of pickup ions. This effect was confirmed both by integrating the model using average boundary conditions at 1 AU, and by applying a method [Smith et al., Astrophys. J., 638, 508 (2006)] that uses directly observed values as boundary conditions. The effects due to pickup ions is found to be less important for the IK spectrum, which is shallower than the Kolmogorov spectrum. In this paper, we will present calculations of the pickup ions effect in more details, and discuss the physical reason why a shallower spectrum generates less waves and turbulence.
Recent experiments have observed magnetic reconnection in high-energy-density, laser-produced plasma bubbles, with reconnection rates observed to be much higher than can be explained by classical theory. Based on fully kinetic particle simulations we
find that fast reconnection in these strongly driven systems can be explained by magnetic flux pile-up at the shoulder of the current sheet and subsequent fast reconnection via two-fluid, collisionless mechanisms. In the strong drive regime with two-fluid effects, we find that the ultimate reconnection time is insensitive to the nominal system Alfven time.
