Stability and transition of the driven magnetohydrodynamic sheet pinch

The stability and transition properties of a bounded, current carrying magnetofluid are explored, using the hydrodynamic theory developed for plane shear flows as a guide. A driven magnetohydrodynamic sheet pinch equilibrium is employed. A sixth order, complex eigenvalue equation which governs the normal modes of small oscillations is derived, and solved numerically by the Chebyshev tau method. Eigenfunctions are shown, as well as the curve of neutral stability. The locus of critical Lundquist numbers has the form of a hyperbola. The nonlinear stability of a primary disturbance of the system is considered. For regions in parameter space close to criticality, a nonlinear stability equation of the Landau type is derived. These regions are characterized by low values of the Lundquist numbers, in contrast with the inviscid, highly conducting limit considered by Rutherford (1973). Amplitude phase planes for these disturbances are exhibited. The full set of two dimensional magnetohydrodynamic equations is solved numerically by a semi-implicit, mixed Fourier pseudospectral-finite difference algorithm. Both linear and random perturbations of the system are followed numerically into the nonlinear regime. Current sheets and deflection currents are nonlinear structures found to be significant to the evolution of the system. A secondary instability mechanism, the dynamic rupturing of the current density sheet, is also observed

Numerical simulation of the compressible Orszag-Tang vortex 2. Supersonic flow

The numerical investigation of the Orszag-Tang vortex system in compressible magnetofluids will consider initial conditions with embedded supersonic regions. The simulations have initial average Mach numbers 1.0 and 1.5 and beta 10/3 with Lundquist numbers 50, 100, or 200. The behavior of the system differs significantly from that found previously for the incompressible and subsonic analogs. Shocks form at the downstream boundaries of the embedded supersonic regions outside the central magnetic X-point and produce strong local current sheets which dissipate appreciable magnetic energy. Reconnection at the central X-point, which dominates the incompressible and subsonic systems, peaks later and has a smaller impact as M increases from 0.6 to 1.5. Similarly, correlation between the momentum and magnetic field begins significant growth later than in subsonic and incompressible flows. The shocks bound large compression regions, which dominate the wavenumber spectra of autocorrelations in mass density, velocity, and magnetic field

Numerical simulation of solar coronal magnetic fields

Many aspects of solar activity are believed to be due to the stressing of the coronal magnetic field by footpoint motions at the photosphere. The results are presented of a fully spectral numerical simulation which is the first 3-D time dependent simulation of footpoint stressing in a geometry appropriate for the corona. An arcade is considered that is initially current-free and impose a smooth footpoint motion that produces a twist in the field of approx 2 pi. The footprints were fixed and the evolution was followed until the field relaxes to another current-free state. No evidence was seen for any instability, either ideal or resistive and no evidence for current sheet formation. The most striking feature of the evolution is that in response to photospheric motions, the field expands rapidly upward to minimize the stress. The expansion has two important effects. First, it suppresses the development of dips in the field that could support dense, cool material. For the motions assumed, the magnetic field does not develop a geometry suitable for prominence formation. Second, the expansion inhibits ideal instabilities such as kinking. The results indicate that simple stearing of a single arcade is unlikely to lead to solar activity such as flares or prominences. Effects are discussed that might possibly lead to such activity

Modeling the Galactic Center Nonthermal Filaments as Magnetized Wake

We simulate the Galactic Center nonthermal filaments as magnetized wakes formed dynamically from amplification of a weak (tens of $\mu$G) global magnetic field through the interaction of molecular clouds with a Galactic Center wind. One of the key issues in this cometary model is the stability of the filament against dynamical disruption. Here we show 2-dimensional MHD simulations for interstellar conditions that are appropriate for the Galactic Center. The structures eventually disrupt through a shear driven nonlinear instability but maintain coherence for lengths up to 100 times their width as observed. The final instability, which destroys the filament through shredding and plasmoid formation, grows quickly in space (and time) and leads to an abrupt end to the structure, in accord with observations. As a by-product, the simulation shows that emission should peak well downstream from the cloud-wind interaction site.Comment: postscript file, 7 figs (included); Accepted for publication in ApJ (Part 1

Plasmoid Formation and Acceleration in the Solar Streamer Belt

The dynamical behavior of a configuration consisting of a plane fluid wake flowing in a current sheet embedded in a plasma sheet that is denser than its surroundings is discussed. This configuration is a useful model for a number of structures of astrophysical interest, such as solar coronal streamers, cometary tails, the Earth's magnetotail and Galactic center nonthermal filaments. In this paper, the results are applied to the study of the formation and initial motion of the plasma density enhancements observed by the Large-Angle Spectrometric Coronagraph (LASCO) instrument onboard the Solar and Heliospheric Observatory (SOHO) spacecraft. It is found that beyond the helmet cusp of a coronal streamer, the magnetized wake configuration is resistively unstable, that a traveling magnetic island develops at the center of the streamer, and that density enhancements occur within the magnetic islands. As the massive magnetic island travels outward, both its speed and width increase. The island passively traces the acceleration of the inner part of the wake. The values of the acceleration and density contrasts are in good agreement with LASCO observations

PLASMOID FORMATION AND ACCELERATION IN THE SOLAR STREAMER BELT

ABSTRACT The dynamical behavior of a conÐguration consisting of a plane Ñuid wake Ñowing in a current sheet embedded in a plasma sheet that is denser than its surroundings is discussed. This conÐguration is a useful model for a number of structures of astrophysical interest, such as solar coronal streamers, cometary tails, the EarthÏs magnetotail and Galactic center nonthermal Ðlaments. In this paper, the results are applied to the study of the formation and initial motion of the plasma density enhancements observed by the Large-Angle Spectrometric Coronagraph (LASCO) instrument onboard the Solar and Heliospheric Observatory (SOHO) spacecraft. It is found that beyond the helmet cusp of a coronal streamer, the magnetized wake conÐguration is resistively unstable, that a traveling magnetic island develops at the center of the streamer, and that density enhancements occur within the magnetic islands. As the massive magnetic island travels outward, both its speed and width increase. The island passively traces the acceleration of the inner part of the wake. The values of the acceleration and density contrasts are in good agreement with LASCO observations

Modeling the Galactic Center Nonthermal Filaments as Magnetized Wakes

We simulate the Galactic Center nonthermal filaments as magnetized wakes formed dynamically from amplification of a weak (tens of µG) global magnetic field through the interaction of molecular clouds with a Galactic Center wind. One of the key issues in this cometary model is the stability of the filament against dynamical disruption. Here we show 2-dimensional MHD simulations for interstellar conditions that are appropriate for the Galactic Center. The structures eventually disrupt through a shear driven nonlinear instability but maintain coherence for lengths up to 100 times their width as observed. The final instability, which destroys the filament through shredding and plasmoid–2– formation, grows quickly in space (and time) and leads to an abrupt end to the structure, in accord with observations. As a by-product, the simulation shows that emission should peak well downstream from the cloud-wind interaction site. Subject headings: Galaxy:Center — nonthermal emission 1