Showing papers by "Steven Cowley published in 2001"

Structure of small-scale magnetic fields in the kinematic dynamo theory

Abstract: A weak fluctuating magnetic field embedded into a a turbulent conducting medium grows exponentially while its characteristic scale decays. In the interstellar medium and protogalactic plasmas, the magnetic Prandtl number is very large, so a broad spectrum of growing magnetic fluctuations is excited at small (subviscous) scales. The condition for the onset of nonlinear back reaction depends on the structure of the field lines. We study the statistical correlations that are set up in the field pattern and show that the magnetic-field lines possess a folding structure, where most of the scale decrease is due to the field variation across itself (rapid transverse direction reversals), while the scale of the field variation along itself stays approximately constant. Specifically, we find that, though both the magnetic energy and the mean-square curvature of the field lines grow exponentially, the field strength and the field-line curvature are anticorrelated, i.e., the curved field is relatively weak, while the growing field is relatively flat. The detailed analysis of the statistics of the curvature shows that it possesses a stationary limiting distribution with the bulk located at the values of curvature comparable to the characteristic wave number of the velocity field and a power tail extending to large values of curvature where it is eventually cut off by the resistive regularization. The regions of large curvature, therefore, occupy only a small fraction of the total volume of the system. Our theoretical results are corroborated by direct numerical simulations. The implication of the folding effect is that the advent of the Lorentz back reaction occurs when the magnetic energy approaches that of the smallest turbulent eddies. Our results also directly apply to the problem of statistical geometry of the material lines in a random flow.

Equilibrium and Stability of Prominence Flux Ropes

Abstract: Realistic models of solar prominence flux ropes are numerically constructed. The models are in 2.5 dimensions, including the effects of non-isothermal temperature, density and gravity, and pressure. Stability of the equilibria to pressure- and gravity-driven instabilities is numerically investigated, using the ballooning formalism of fusion plasma theory. The equilibrium models can become unstable to pressure- and gravity-driven modes at plasma parameters characteristic of prominences.

Poloidal rotation effects on a simulated resistive kink mode

Abstract: Through the principal use of the reduced magnetohydrodynamic version of the finite aspect ratio code [L. A. Charlton et al., J. Comput. Phys. 86, 270 (1990)], an m/n=1/1 resistive kink mode was poloidally rotated with the accompanying rotational shear. It was observed that the growth rate of this unstable mode can either decrease or increase as the applied equilibrium rotation is increased to near poloidal sonic speeds. Shear in the poloidal rotation profile is stabilizing, but only if the destabilizing effects of bulk rotation can be overcome. Therefore, the mode’s stability was sensitive to the location of the rotation’s peak relative to the eigenmode’s spatial extent. The destabilizing effects of bulk rotation are apparently a rotationally enhanced beta, and the stabilizing effects appear to be caused by exceeding a critical rotational shear spatially averaged over the eigenmode structure.

Local Gravitational Instability of Magnetized Shear Flows

Abstract: The effect of magnetic shear and shear flow on local gravitationally induced instabilities is investigated. A simple model is constructed allowing for an arbitrary entropy gradient and a shear plasma flow in the Boussinesq approximation. A transformation to shearing magnetic coordinates achieves a model with plasma flow along the magnetic field lines where the coordinate lines are coincident with the field lines. The solution for the normal modes of the system depends on two parameters: the Alfven Mach number of the plasma flow and the entropy gradient. The behavior of the unstable normal modes of this system is summarized by a stability diagram. Important characteristics of this stability diagram are the following: magnetic shear is stabilizing and the entropy gradient must exceed a threshold value for unstable mode growth to occur; flow acts to suppress mode growth in a substantially unstable regime as expected, yet near marginal stability it can lessen the stabilizing effect of magnetic shear and enhance the growth rates of the instability; and, as the Alfven Mach number approaches one, the instability is completely stabilized. Analytical work is presented supporting the characteristics of the stability diagram and illuminating the physical mechanisms controlling the behavior of the model. The implications of this work for astrophysical and fusion applications and the potential for future research extending the results to include compressibility are discussed.

The Nonlinear Turbulent Dynamo

Abstract: We simulate the evolution of an initially weak magnetic field in forced turbulence for a range of Prandtl numbers. The field grows exponentially with the Kulsrud-Anderson $k^{3/2}$ spectrum until the magnetic energy approaches the viscous-scale kinetic energy, where the magnetic forces then backreact on the velocity. Further growth proceeds more slowly until a saturated state is reached where the magnetic and kinetic energies are equal, and where the magnetic energy exists primarily at the resistive scale. We discuss the structure of this turbulence and the extrapolation of the results to astrophysically-large Prandtl numbers.

Local Buoyant Instability of Magnetized Shear Flows

Abstract: The effect of magnetic shear and shear flow on local buoyant instabilities is investigated. A simple model is constructed allowing for an arbitrary entropy gradient and a shear plasma flow in the Boussinesq approximation. A transformation to shearing magnetic coordinates achieves a model with plasma flow along the magnetic field lines where the coordinate lines are coincident with the field lines. The solution for the normal modes of the system depends on two parameters: the Alfven Mach number of the plasma flow and the entropy gradient. The behavior of the unstable normal modes of this system is summarized by a stability diagram. Important characteristics of this stability diagram are the following: magnetic shear is stabilizing, and the entropy gradient must exceed a threshold value for unstable mode growth to occur; flow acts to suppress mode growth in a substantially unstable regime as expected, yet near marginal stability it can lessen the stabilizing effect of magnetic shear and enhance the growth rates of the instability; and, as the Alfven Mach number approaches 1, the instability is completely stabilized. Analytical work is presented supporting the characteristics of the stability diagram and illuminating the physical mechanisms controlling the behavior of the model. A derivation of the stability criterion for the case without shear flow, asymptotic solutions in the limit that the Alfven Mach number approaches 1 and in the limit of zero growth rate, a complete WKB solution for large growth rates, an exactly soluble bounded straight field case, and energy conservation relations are all presented. The implications of this work for astrophysical and fusion applications and the potential for future research extending the results to include compressibility are discussed.

The Nonlinear Turbulent Dynamo

Abstract: We simulate the evolution of an initially weak magnetic field in forced turbulence for a range of Prandtl numbers The field grows exponentially with the Kulsrud-Anderson $k^{3/2}$ spectrum until the magnetic energy approaches the viscous-scale kinetic energy, where the magnetic forces then backreact on the velocity Further growth proceeds more slowly until a saturated state is reached where the magnetic and kinetic energies are equal, and where the magnetic energy exists primarily at the resistive scale We discuss the structure of this turbulence and the extrapolation of the results to astrophysically-large Prandtl numbers

The Nonlinear Turbulent Dynamo

Abstract: We simulate the evolution of an initially weak magnetic field in forced turbulence for a range of Prandtl numbers. The field grows exponentially with the Kulsrud-Anderson $k^{3/2}$ spectrum until the magnetic energy approaches the viscous-scale kinetic energy, where the magnetic forces then backreact on the velocity. Further growth proceeds more slowly until a saturated state is reached where the magnetic and kinetic energies are equal, and where the magnetic energy exists primarily at the resistive scale. We discuss the structure of this turbulence and the extrapolation of the results to astrophysically-large Prandtl numbers.