C. S. Ng

Weakly Compressible Magnetohydrodynamic Turbulence in the Solar Wind and the Interstellar Medium

A new four-field system of equations is derived from the compressible magnetohydrodynamic (MHD) equations for low Mach number turbulence in the solar wind and the interstellar medium, permeated by a spatially varying magnetic field. The plasma beta is assumed to be of order unity or less. It is shown that the full MHD equations can be reduced rigorously to a closed system for four fluctuating field variables: magnetic flux, vorticity, pressure, and parallel flow. Although the velocity perpendicular to the magnetic field is shown to obey a two-dimensional incompressibility condition (analogous to the Proudman-Taylor theorem in hydrodynamics), the three-dimensional dynamics exhibit the effects of compressibility. In the presence of spatial inhomogeneities, the four dynamical equations are coupled to each other, and pressure fluctuations enter the weakly compressible dynamics at leading order. If there are no spatial inhomogeneities and or if the plasma beta is low, the four-field equations reduce to the well-known equations of reduced magnetohydrodynamics (RMHD). For pressure-balanced structures, the four-field equations undergo a remarkable simplification which provides insight on the special nature of the fluctuations driven by these structures. The important role of spatial inhomogeneities is elucidated by 2.5-dimensional numerical simulations. In the presence of inhomogeneities, the saturated pressure and density fluctuations scale with the Mach number of the turbulence, and the system attains equipartition with respect to the kinetic, magnetic, and thermal energy of the fluctuations. The present work suggests that if heliospheric and interstellar turbulence exists in a plasma with large-scale, nonturbulent spatial gradients, one expects the pressure and density fluctuations to be of significantly larger magnitude than suggested in nearly incompressible models such as pseudosound.

Scaling of anisotropic spectra due to the weak interaction of shear-Alfven wave packets

Weak magnetohydrodynamic turbulence in the presence of a uniform magnetic field is dominated by three-wave interactions that mediate the collisions of shear-Alfven wave packets propagating in opposite directions parallel to the magnetic field. The scaling of three-wave couplings is calculated by asymptotic analysis and a direct numerical evaluation of the nonlinear interaction based on the reduced magnetohydrodynamic equations. A new relation is derived between the spectral index of three-wave coupling and the spectral indices of two random-amplitude wave packets. This relation has significant implications for the anisotropic energy spectrum.

Current singularities: Drivers of impulsive reconnectiona)

Reconnection in nature is generically not quasi-steady. Most often, it is impulsive or bursty, characterized not only by a fast growth rate but a rapid change in the time-derivative of the growth rate. New results, obtained by asymptotic analyses and high-resolution numerical simulations [using Adaptive Mesh Refinement] of the Hall magnetohydrodynamics (MHD) or two-fluid equations, are presented. Within the framework of Hall MHD, a two-dimensional collisionless reconnection model is considered in which electron inertia provides the mechanism for breaking field lines, and the electron pressure gradient plays a crucial role in controlling magnetic island dynamics. Current singularities tend to form in finite time and drive fast and impulsive reconnection. In the presence of resistivity, the tendency for current singularity formation slows down, but the reconnection rate continues to accelerate to produce large magnetic islands that eventually become of the order of the system size, quenching near-explosive ...

Anisotropic fluid turbulence in the interstellar medium and solar wind

The interstellar medium and solar wind is permeated by a magnetic field that renders magnetohydrodynamic turbulence anisotropic. In the classic work of Iroshnikov [Astron. Zh. 40, 742 (1963)] and Kraichnan [Phys. Fluids 8, 1385 (1965)], it is assumed that the turbulence is isotropic, and an inertial range energy spectrum that scales as k−3/2 is deduced based on the nonlinear interaction of Alfven wave packets. Much insight can be gained by analysis and high-resolution numerical simulations of such interactions. In the weak-turbulence limit in which three-wave interactions dominate, analytical and high-resolution numerical results based on random scattering of shear-Alfven waves propagating parallel to a large-scale magnetic field demonstrate an anisotropic energy spectrum that scales as k⊥−2. Even in the absence of a background magnetic field, when the energy spectrum is globally isotropic, anisotropy is found to develop with respect to the local magnetic field. The two-dimensional case is studied by mean...

Nonequilibrium and current sheet formation in line-tied magnetic fields

Parker’s model of coronal heating [E. N. Parker, Astrophys. J. 174, 499 (1972)] is considered within the framework of ideal reduced magnetohydrodynamics. It is shown that there can be at most one smooth magnetostatic equilibrium for a given smooth footpoint mapping between two end plates to which field lines are line-tied. If such a smooth equilibrium is deformed continuously by further footpoint motion so that it becomes unstable, there is no other smooth equilibrium for the plasma to relax to, and the system tends to a nonequilibrium state containing singular currents (“current sheets”). It is shown that this process can occur as the system relaxes asymptotically to a state of minimum energy (possibly in infinite time). Numerical simulations that begin from smooth initial conditions containing current layers are presented. As the current layers become increasingly intense due to footpoint motion and eventually cross a threshold for instability, the magnetic relaxation observed in the simulation shows a ...

Dynamics and waves near multiple magnetic null points in reconnection diffusion region

Identifying the magnetic structure in the region where the magnetic field lines break and how reconnection happens is crucial to improving our understanding of three-dimensional reconnection. Here we show the in situ observation of magnetic null structures in the diffusion region, the dynamics, and the associated waves. Possible spiral null pair has been identified near the diffusion region. There is a close relation among the null points, the bipolar signature of the Z component of the magnetic field, and enhancement of the flux of energetic electrons up to 100 keV. Near the null structures, whistler-mode waves were identified by both the polarity and the power law of the spectrum of electric and magnetic fields. It is found that the angle between the fans of the nulls is quite close to the theoretically estimated maximum value of the group-velocity cone angle for the whistler wave regime of reconnection.

Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems

Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of undamped eigenmodes, the so-called Case–Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still being discovered. For Landau damping, we show that the textbook picture of phase mixing is altered profoundly in the presence of collision. In particular, the continuous spectrum of Case–Van Kampen modes is eliminated and replaced by a discrete spectrum, even in the limit of zero collision. Furthermore, we show that these discrete eigenmodes form a complete set of solutions. Landau-damped solutions are then recovered ...

Dynamics of current sheet formation and reconnection in two‐dimensional coronal loops

Current sheet formation and magnetic reconnection in a two‐dimensional coronal loop with an X‐type neutral line are simulated numerically using compressible, resistive magnetohydrodynamic equations. Numerical results in the linear and nonlinear regimes are shown to be in good agreement with a recent analytical theory [X. Wang and A. Bhattacharjee, Astrophys. J. 420, 415 (1994)]. The topological constraint imposed by helicity‐conserving reconnection is discussed. It is found numerically that helicity‐conserving reconnection causes the initial X‐point structure of the loop to change to Y points, with current sheets at the separatrices encompassing the Y points. Implications for observations are discussed.

Four‐field model for dispersive field‐line resonances: Effects of coupling between shear‐Alfvén and slow modes

A new theoretical model is proposed for dispersive field-line resonances in collisionless magnetospheric plasmas on the basis of reduced four-field equations. The model improves upon the predictive capabilities of earlier two-field models. In particular, due to the coupling of the shear-Alfven mode to the slow mode in the four-field system, it is now possible to account for the observed low frequencies of field-line resonances. Furthermore, parallel electric fields can be large without requiring the field-aligned current density to be unrealistically large. Qualitative implications for recent FAST and ground-based observations are discussed.

HIGH-LUNDQUIST NUMBER SCALING IN THREE-DIMENSIONAL SIMULATIONS OF PARKER'S MODEL OF CORONAL HEATING

Parkers model is one of the most discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results in a two-dimensional (2D) version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state. Our numerical work has now been extended to 3D by means of large-scale numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal heating rates. Simulations are done for different values of the Lundquist number to determine scaling. In the high-Lundquist number limit, the coronal heating rate obtained so far is consistent with a trend that is independent of the Lundquist number, as predicted by previous analysis as well as 2D simulations. In the same limit the average magnetic energy built up by the random footpoint motion tends to have a much weaker dependence on the Lundquist number than that in the 2D simulations, due to the formation of strong current layers and subsequent disruption when the equilibrium becomes unstable. We will present scaling analysis showing that when the dissipation time is comparable or larger than the correlation time of the random footpoint motion, the heating rate tends to become independent of Lundquist number, and that the magnetic energy production is also reduced significantly.