Despite the importance of the magnetorotational instability (MRI) as a fundamental mechanism for angular momentum transport in magnetized accretion disks, it has yet to be demonstrated in the laboratory. A liquid sodium ! dynamo experiment at the New Mexico Institute of Mining and Technology provides an ideal environment to study the MRI in a rotating metal annulus (Couette flow). A local stability analysis is performed as a function of shear, magnetic field strength, magnetic Reynolds number, and turbulent Prandtl number. The latter takes into account the minimum turbulence induced by the formation of an Ekman layer against the rigidly rotating end walls of a cylindrical vessel. Stability conditions are presented, and unstable conditions for the sodium experiment are compared with another proposed MRI experiment with liquid gallium. Because of the relatively large magnetic Reynolds number achievable in the sodium experiment, it should be possible to observe the excitation of the MRI for a wide range of wavenumbers and to further observe the transition to the turbulent state.

A new formulation is presented for the implicit moment method applied to the time-dependent relativistic Vlasov-Maxwell system. The new approach is based on a specific formulation of the implicit moment method that allows us to retain the same formalism that is valid in the classical case despite the formidable complication introduced by the nonlinear nature of the relativistic equations of motion. To demonstrate the validity of the new formulation, an implicit finite difference algorithm is developed to solve the Maxwell’s equations and equations of motion. A number of benchmark problems are run: two stream instability, ion acoustic wave damping, Weibel instability, and Poynting flux acceleration. The numerical results are all in agreement with analytical solutions.

We derive analytic formulas for the radiation power output when electrons are accelerated by a relativistic comoving kinetic Poynting flux, and validate these analytic results with Particle-In-Cell simulations. We also derive analytically the critical frequency of the radiation spectrum. Potential astrophysical applications of these results are discussed. A quantitative model of gamma-ray bursts based on the breakout of kinetic Poynting flux is presented.

The stability of nonaxisymmetric perturbations in differentially rotating astrophysical accretion disks is analyzed by fully incorporating the properties of shear flows. We verify the presence of discrete unstable eigenmodes with complex and pure imaginary eigenvalues, without any artificial disk edge boundaries, unlike Ogilvie & Pringle(1996)'s claim. By developing the mathematical theory of a non-self-adjoint system, we investigate the nonlocal behavior of eigenmodes in the vicinity of Alfvén singularities at ω D = ±ω A , where ω D is the Doppler-shifted wave frequency and ω A = k v A is the Alfvén frequency. The structure of the spectrum of discrete eigenmodes is discussed and the magnetic field and wavenumber dependence of the growth rate are obtained. Exponentially growing modes are present even in a region where the local dispersion relation theory claims to have stable eigenvalues. The velocity field created by an eigenmode is obtained, which explains the anomalous angular momentum transport in the nonlinear stage of this stability.

All experiments, which have been proposed so far to model the magnetorotational instability (MRI) in the laboratory, involve a Couette flow of liquid metals in a rotating annulus. All liquid metals have small magnetic Prandtl numbers, Pm, of about 10^{-6} (the ratio of kinematic viscosity to magnetic diffusivity). With plasmas both large and small Pm are achievable by varying the temperature and the density of plasma. Compressibility and fast rotation of the plasma result in radial stratification of the equilibrium plasma density. Evolution of perturbations in radially stratified viscous and resistive plasma permeated by an axial uniform magnetic field is considered. The differential rotation of the plasma is induced by the ExB drift in applied radial electric field. Global unstable eigenmodes are calculated by our newly developed matrix code. The plasma is shown to be MRI unstable for parameters easily achievable in experimental setup.Comment: 6 pages, 2 figures; to be published in the Proceedings of the 3d Workshop on Non-Neutral Plasmas, July 2003, Santa Fe, US