The Non-Linear Growth of the Magnetic Rayleigh-Taylor Instability

This work examines the effect of the embedded magnetic field strength on the non-linear development of the magnetic Rayleigh-Taylor Instability (RTI) (with a field-aligned interface) in an ideal gas close to the incompressible limit in three dimensions. Numerical experiments are conducted in a domain sufficiently large so as to allow the predicted critical modes to develop in a physically realistic manner. The ratio between gravity, which drives the instability in this case (as well as in several of the corresponding observations), and magnetic field strength is taken up to a ratio which accurately reflects that of observed astrophysical plasma, in order to allow comparison between the results of the simulations and the observational data which served as inspiration for this work. This study finds reduced non-linear growth of the rising bubbles of the RTI for stronger magnetic fields, and that this is directly due to the change in magnetic field strength, rather than the indirect effect of altering characteristic length scales with respect to domain size. By examining the growth of the falling spikes, the growth rate appears to be enhanced for the strongest magnetic field strengths, suggesting that rather than affecting the development of the system as a whole, increased magnetic field strengths in fact introduce an asymmetry to the system. Further investigation of this effect also revealed that the greater this asymmetry, the less efficiently the gravitational energy is released. By better understanding the under-studied regime of such a major phenomenon in astrophysics, deeper explanations for observations may be sought, and this work illustrates that the strength of magnetic fields in astrophysical plasmas influences observed RTI in subtle and complex ways.Comment: Accepted for publication by A&A. 10 pages, 9 figure

A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets

We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal non-dissipative case is studied up to the equivalent of 2048^3 grid points for one of these flows. The temporal evolution of the logarithmic decrements, delta, of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of delta, the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind.Comment: 8 pages, 4 figure

The Magnetic Rayleigh-Taylor Instability in Three Dimensions

We study the magnetic Rayleigh-Taylor instability in three dimensions, with focus on the nonlinear structure and evolution that results from different initial field configurations. We study strong fields in the sense that the critical wavelength l_c at which perturbations along the field are stable is a large fraction of the size of the computational domain. We consider magnetic fields which are initially parallel to the interface, but have a variety of configurations, including uniform everywhere, uniform in the light fluid only, and fields which change direction at the interface. Strong magnetic fields do not suppress instability, in fact by inhibiting secondary shear instabilities, they reduce mixing between the heavy and light fluid, and cause the rate of growth of bubbles and fingers to increase in comparison to hydrodynamics. Fields parallel to, but whose direction changes at, the interface produce long, isolated fingers separated by the critical wavelength l_c, which may be relevant to the morphology of the optical filaments in the Crab nebula.Comment: 14 pages, 9 pages, accepted by Ap

Nonlinear Evolution of the Magnetohydrodynamic Rayleigh-Taylor Instability

We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional MHD simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact discontinuity perpendicular to the effective gravity g, with a uniform magnetic field B parallel to the interface. Modes parallel to the field with wavelengths smaller than l_c = [B B/(d_h - d_l) g] are suppressed (where d_h and d_l are the densities of the heavy and light fluids respectively), whereas modes perpendicular to B are unaffected. We study strong fields with l_c varying between 0.01 and 0.36 of the horizontal extent of the computational domain. Even a weak field produces tension forces on small scales that are significant enough to reduce shear (as measured by the distribution of the amplitude of vorticity), which in turn reduces the mixing between fluids, and increases the rate at which bubbles and finger are displaced from the interface compared to the purely hydrodynamic case. For strong fields, the highly anisotropic nature of unstable modes produces ropes and filaments. However, at late time flow along field lines produces large scale bubbles. The kinetic and magnetic energies transverse to gravity remain in rough equipartition and increase as t^4 at early times. The growth deviates from this form once the magnetic energy in the vertical field becomes larger than the energy in the initial field. We comment on the implications of our results to Z-pinch experiments, and a variety of astrophysical systems.Comment: 25 pages, accepted by Physics of Fluids, online version of journal has high resolution figure

Influence of turbulence on the dynamo threshold

We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold. When the noise is at small (resp. large) scale, the dynamo threshold is decreased (resp. increased). For a large scale noise, a finite correlation time reinforces this effect

The Surface Topography of a Magnetic Fluid -- a Quantitative Comparison between Experiment and Numerical Simulation

The normal field instability in magnetic liquids is investigated experimentally by means of a radioscopic technique which allows a precise measurement of the surface topography. The dependence of the topography on the magnetic field is compared to results obtained by numerical simulations via the finite element method. Quantitative agreement has been found for the critical field of the instability, the scaling of the pattern amplitude and the detailed shape of the magnetic spikes. The fundamental Fourier mode approximates the shape to within 10% accuracy for a range of up to 40% of the bifurcation parameter of this subcritical bifurcation. The measured control parameter dependence of the wavenumber differs qualitatively from analytical predictions obtained by minimization of the free energy.Comment: 21 pages, 16 figures; corrected typos, added reference to Kuznetsov and Spector(1976), S.J. Fortune(1995) and Harkins&Jordan (1930). Figures revise

Magnetic properties of colloidal suspensions of interacting magnetic particles

We review equilibrium thermodynamic properties of systems of magnetic particles like ferrofluids in which dipolar interactions play an important role. The review is focussed on two subjects: ({\em i}) the magnetization with the initial magnetic susceptibility as a special case and ({\em ii}) the phase transition behavior. Here the condensation ("gas/liquid") transition in the subsystem of the suspended particles is treated as well as the isotropic/ferromagnetic transition to a state with spontaneously generated long--range magnetic order.Comment: Review. 62 pages, 4 figure