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Notes: The evolution of the Rayleigh–Taylor instability is studied using finite Larmor radius (FLR) magnetohydrodynamic (MHD) theory. Finite Larmor radius effects are introduced in the momentum equation through an anisotropic ion stress tensor. Roberts and Taylor [Phys. Rev. Lett. 3, 197 (1962)], using fluid theory, demonstrated that FLR effects can stabilize the Rayleigh–Taylor instability in the short-wavelength limit (kLn(very-much-greater-than)1, where k is the wave number and Ln is the density gradient scale length). In this paper a linear mode equation is derived that is valid for arbitrary kLn. Analytic solutions are presented in both the short-wavelength (kLn(very-much-greater-than)1) and long-wavelength (kLn(very-much-less-than)1) regimes, and numerical solutions are presented for the intermediate regime (kLn∼1). The long-wavelength modes are shown to be the most difficult to stabilize. More important, the nonlinear evolution of the Rayleigh–Taylor instability is studied using a newly developed two-dimensional (2-D) FLR MHD code. The FLR effects are shown to be a stabilizing influence on the Rayleigh–Taylor instability; the short-wavelength modes are the easiest to stabilize, consistent with linear theory. In the nonlinear regime, the FLR effects cause the "bubbles and spikes'' that develop because of the Rayleigh–Taylor instability to convect along the density gradient and to tilt. Applications of this model to space and laboratory plasma phenomena are discussed. © 1996 American Institute of Physics.

Notes: The dynamics of long-conduction-time (τc∼1 μs) plasma opening switches (POS) is studied using magnetohydrodynamic (MHD) theory, including the Hall term. Plasma switches with initial electron densities of ne=1014–1016 cm−3 are modeled; these densities are appropriate to recent experiments carried out at the Naval Research Laboratory using the Hawk generator (800 kA, 1.2 μs). The conduction times obtained from the simulation studies are in the range τc(approximately-equal-to)0.4–2.0 μs. The POS plasma is strongly redistributed by the penetrating magnetic field. As the field penetrates, it pushes the plasma both axially and radially (i.e., toward the anode and cathode). In the higher-density regime (ne(approximately-greater-than)1015 cm−3), Hall effects do not play a significant role. The magnetic field acts as a snowplow, sweeping up and compressing the plasma as it propagates through the POS plasma. In the lower-density regime (ne〈1015 cm−3), Hall effects become important in two ways: the conduction time is less than that expected from ideal MHD, and the POS plasma becomes unstable as the magnetic field penetrates, leading to finger-like density structures. The instability is the unmagnetized ion Rayleigh–Taylor instability and is driven by the magnetic force accelerating the plasma. The structuring of the plasma further decreases the conduction time and causes the penetrating magnetic field to have a relatively broad front in comparison to EMHD simulations (i.e., Vi=0). The simulation results are consistent with experimental data for conduction currents 300–800 kA.

Notes: The evolution of the Rayleigh–Taylor instability in a low β, two-dimensional plasma is studied using a hybrid code and a nonideal magnetohydrodynamic (MHD) code. The Rayleigh–Taylor instability was chosen as a test case because it is an important mixing process at boundary layers, and because it exhibits different behaviors in the conventional and nonideal limits. The nonideal MHD effects considered are the Hall term and finite Larmor radius (FLR) corrections. Three cases are considered in detail: conventional MHD, weak nonideal effects, and strong nonideal effects. In the conventional MHD regime the usual "bubble and spike" behavior of the Rayleigh–Taylor instability is observed. In the weak nonideal MHD regime long wavelength modes, reminiscent of the Kelvin–Helmholtz instability, dominate nonlinearly but very short wavelength filaments develop at the boundary interface. In the strong nonideal MHD regime, small-scale structures dominate and the boundary layer relaxes via a diffusion-like process rather than a large-scale nonlinear mixing process. In general, the hybrid and fluid simulations are in good agreement. The differences, both physical and numerical, are discussed. © 1998 American Institute of Physics.

Notes: Hall magnetohydrodynamic (MHD) theory has been used to understand and describe a variety of space and laboratory plasma phenomena. Generally speaking, the theory is applicable to phenomena occurring on length scales shorter than an ion inertial length and time scales shorter than an ion cyclotron period. The theory has been successfully applied to structuring of sub-Alfvénic plasma expansions, and to rapid magnetic field transport in plasma opening switches. An overview of the underlying physics associated with the Hall term, and a brief description of recent research on the application of Hall MHD theory to space and laboratory processes is presented. © 1995 American Institute of Physics.

Notes: A comprehensive theoretical treatment of the linear stability of a sub-Alfvénic plasma expansion is developed. The analysis is similar to those performed for the lower-hybrid-drift instability and the drift cyclotron instability. In addition to the diamagnetic drift (Vdi) that drives these instabilities, the gravitational drift (Vg) caused by the deceleration of the plasma shell, and the Pedersen drift (VP) caused by ion–neutral collisions and neutral gas flow, are included. The emphasis of the paper is on the instability driven by the gravitational drift. The theory is fully kinetic and includes finite-beta effects (i.e., electromagnetic coupling and electron ∇B drift-wave resonances), collisional effects (electron–ion, electron–neutral, and ion–neutral collisions), and neutral gas flow, effects that have not been considered to date. The analysis is carried out in a slab geometry although the applications are to spherical expansions. The main conclusions are as follows. In the strong drift limit (Vg〉vi and Vdi∼vi, where vi is the ion thermal velocity) it is found that (1) finite-beta effects are stabilizing and reduce the wavelength of the maximum growth rate; (2) ion–neutral collisions are stabilizing and do not affect the wavelength of the maximum growth rate; (3) electron–neutral collisions are stabilizing and increase the wavelength of the maximum growth rate; (4) the gravitational drift driven mode maximizes the growth rate at longer wavelengths than the diamagnetic drift driven mode; (5) the Pedersen drift effectively reduces the gravitational drift, and is therefore a stabilizing influence; and (6) the instability splits into two modes for Te(very-much-greater-than)Ti in finite-beta plasmas: the lower-hybrid-drift instability at high frequencies and short wavelengths, and a gravitational mode at lower frequencies and longer wavelengths.In the weak drift regime (Vg〈vi and Vdi〈vi) it is found that (1) finite-beta effects are stabilizing and increase the wavelength of the maximum growth rate; (2) ion–neutral collisions are destabilizing and decrease the wavelength of the maximum growth rate; and (3) electron–ion and electron–neutral collisions are stabilizing, and increase the wavelength of the maximum growth rate. When the growth rate becomes less than the ion cyclotron instability (γ〈Ωi), the growth rate as a function of wave number "breaks up'' into a discrete set of modes which is associated with the coupling of the drift waves to ion cyclotron waves. These results are applied to the AMPTE magnetotail release [J. Geophys. Res. 92, 5777 (1987)], the Naval Research Laboratory laser experiment [Phys. Rev. Lett. 59, 2299 (1987)], and the upcoming CRRES GTO releases [D. Reasoner (private communication, 1989)].

Notes: A large ion Larmor radius plasma undergoes a particularly robust form of Rayleigh–Taylor instability when sub-Alfvénically expanding into a magnetic field. Results from an experimental study of this instability are reported and compared with theory, notably a magnetohydrodynamic (MHD) treatment that includes the Hall term, a generalized kinetic lower-hybrid drift theory, and with computer simulations. Many theoretical predictions are confirmed while several features remain unexplained. New and unusual features appear in the development of this instability. In the linear stage there is an onset criterion insensitive to the magnetic field, initial density clumping (versus interchange), linear growth rate much higher than in the "classic'' MHD regime, and dominant instability wavelength of order of the plasma density scale length. In the nonlinear limit free-streaming flutes, apparent splitting (bifurcation) of flutes, curling of flutes in the electron cyclotron sense, and a highly asymmetric expansion are found. Also examined is the effect on the instability of the following: an ambient background plasma (that adds collisionality and raises the expansion speed/Alfvén speed ratio), magnetic-field line tying, and expansion asymmetries (that promotes plasma cross-field jetting).

Notes: The nonlinear evolution of the unmagnetized ion Rayleigh–Taylor instability is investigated. A nonlinear state corresponding to localized clumps of high-density plasma is obtained analytically. The characteristic scale size of the clumps is given by Δ∼D(gLn)−1/2, where g is the gravitational acceleration, Ln is the density gradient scale length, and D is a diffusion coefficient associated with the short-scale dissipation processes in the system. It is shown numerically that this nonlinear state may be both accessible and stable.

Notes: A magnetized, inhomogeneous, partially ionized gas is theoretically shown to be unstable to an interchange instability. The source of free energy for the instability is the cross-field current. The instability is caused by neutral drag dynamics, and is therefore critically dependent upon charged particle–neutral collisions ναn. The growth rate is largest in the strongly coupled regime, i.e., ω(very-much-less-than)νin, νni, and is given by γ(approximately-equal-to)(εme/mi)1/2(1+ε)−1kyVd, where ky is the wave number, Vd=(cT/eB)[∂ ln(ni0)/∂x] is the diamagnetic drift velocity, T=Te+Ti, and ε=mnnn/mini [m is the mass and n the density of the ions (i) and neutrals (n)]. The growth rate is a maximum when ε=1, which corresponds to νin=νni.

Notes: A set of one-fluid, modified magnetohydrodynamic (MHD) equations is developed that describes magnetized plasmas for which the relevant scale lengths are intermediate between the electron and ion Larmor radii, and the relevant time scales are intermediate between the electron and ion cyclotron frequencies. It is shown that the momentum equation is the same as that of conventional MHD but that the evolution of the magnetic field is strongly affected. The implications of the modified MHD system on the "frozen-in'' theorem, magnetosonic waves, Alfvén waves, and the interchange instability are examined.

Notes: A sheared, relative ion–neutral flow can generate a magnetic field in an unmagnetized, weakly ionized plasma. The field generation term is ∂B/∂t=(mec/e)∇×νen(Vi−Vn) where νen is the electron–neutral collision frequency, Vi is the ion fluid velocity, and Vn is the neutral fluid velocity. The time period over which the field grows is limited by diffusion, convection, or collisional relaxation of the relative drift. Since the field generation term scales as νen/Ωe relative to the other terms in the field induction equation, the maximum field generated is found from Ωe(approximately-equal-to)few νen so that Bmax(approximately-equal-to)few (mec/e)νen. Both analytical and numerical results are presented. The computational results are based upon a two-dimensional (2-D) magnetohydrodynamic (MHD) code which includes the following terms: ion–neutral drag, gravity, resistivity, recombination, the Hall term, and the shear-driven source term. The theory is applied to the generation of magnetic fields in an unmagnetized planetary ionosphere, such as Venus, and to cometary plasmas.