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Register a new userMagnetohydrodynamic Turbulence in the Plasmoid-Mediated Regime
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Magnetohydrodynamic turbulence and magnetic reconnection are ubiquitous in astrophysical environments. In most situations, these processes do not occur in isolation, but interact with each other. This renders a comprehensive theory of these processes highly challenging. Here, we propose a theory of magnetohydrodynamic turbulence driven at large scale that self-consistently accounts for the mutual interplay with magnetic reconnection occurring at smaller scales. Magnetic reconnection produces plasmoids that grow from turbulence-generated noise and eventually disrupt the sheet-like structures in which they are born. The disruption of these structures leads to a modification of the turbulent energy cascade, which, in turn, exerts a feedback effect on the plasmoid formation via the turbulence-generated noise. The energy spectrum in this plasmoid-mediated range steepens relative to the standard inertial range and does not follow a simple power law. As a result of the complex interplay between turbulence and reconnection, we also find that the length scale which marks the beginning of the plasmoid-mediated range and the dissipation length scale do not obey true power laws. The transitional magnetic Reynolds number above which the plasmoid formation becomes statistically significant enough to affect the turbulent cascade is fairly modest, implying that plasmoids are expected to modify the turbulent path to dissipation in many astrophysical systems.
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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.
A general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of plasmoids are derived, and shown to depend on the initial perturbation amplitude $left({hat w}_0right)$, the characteristic rate of current sheet evolution $left(1/tauright)$, and the Lundquist number $left(Sright)$. They are not simple power laws, and are proportional to $S^{alpha} tau^{beta} left[ln f(S,tau,{hat w}_0)right]^sigma$. The detailed dynamics of the instability is also elucidated, and shown to comprise of a period of quiescence followed by sudden growth over a short time scale.
We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity) and threaded by a parallel uniform background magnetic field. This flow is spectrally stable, so the turbulence is subcritical by nature and hence it can be energetically supported just by transient growth mechanism due to shear flow nonnormality. This mechanism appears to be essentially anisotropic in spectral (wavenumber) plane and operates mainly for spatial Fourier harmonics with streamwise wavenumbers less than a ratio of flow shear to the Alfv{e}n speed, $k_y < S/u_A$ (i.e., the Alfv{e}n frequency is lower than the shear rate). We focused on the analysis of the character of nonlinear processes and underlying self-sustaining scheme of the turbulence, i.e., on the interplay between linear transient growth and nonlinear processes, in spectral plane. Our study, being concerned with a new type of the energy-injecting process for turbulence -- the transient growth, represents an alternative to the main trends of MHD turbulence research. We find similarity of the nonlinear dynamics to the related dynamics in hydrodynamic flows -- to the emph{bypass} concept of subcritical turbulence. The essence of the analyzed nonlinear MHD processes appears to be a transverse redistribution of kinetic and magnetic spectral energies in wavenumber plane [as occurs in the related hydrodynamic flow, see Horton et al., Phys. Rev. E {bf 81}, 066304 (2010)] and differs fundamentally from the existing concepts of (anisotropic direct and inverse) cascade processes in MHD shear flows.
Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry. We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal guide field. As helicity is injected, two types of current sheets are formed from 1) the oppositely directed field lines in the injector region (primary reconnecting current sheet), and 2) the poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetic fluctuations arising from the current-sheet instability isolated near the plasma edge have tearing parity but can nevertheless grow fast (on the poloidal Alfven time scale). These modes saturate by breaking up the current sheet. Second, for the first time a dynamo poloidal flux amplification is observed at the reconnetion site (in the region of the oppositely directed magnetic field). This fluctuation-induced flux amplification increases the local Lundquist number, which then triggers a plasmoid instability and breaks the primary current sheet at the reconnection site. The plasmoids formation driven by large-scale flux amplification, i.e. a large-scale dynamo, observed here has strong implications for astrophysical reconnection as well as fast reconnection events in laboratory plasmas.
In presence of an externally supported, mean magnetic field a turbulent, conducting medium, such as plasma, becomes anisotropic. This mean magnetic field, which is separate from the fluctuating, turbulent part of the magnetic field, has considerable effects on the dynamics of the system. In this paper, we examine the dissipation rates for decaying incompressible magnetohydrodynamic (MHD) turbulence with increasing Reynolds number, and in the presence of a mean magnetic field of varying strength. Proceeding numerically, we find that as the Reynolds number increases, the dissipation rate asymptotes to a finite value for each magnetic field strength, confirming the Karman-Howarth hypothesis as applied to MHD. The asymptotic value of the dimensionless dissipation rate is initially suppressed from the zero-mean-field value by the mean magnetic field but then approaches a constant value for higher values of the mean field strength. Additionally, for comparison, we perform a set of two-dimensional (2DMHD) and a set of reduced MHD (RMHD) simulations. We find that the RMHD results lie very close to the values corresponding to the high mean-field limit of the three-dimensional runs while the 2DMHD results admit distinct values far from both the zero mean field cases and the high mean field limit of the three-dimensional cases. These findings provide firm underpinnings for numerous applications in space and astrophysics wherein von Karman decay of turbulence is assumed.
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