Kelvin-Helmholtz instability for a bounded plasma flow in a longitudinal magnetic field

Kelvin-Helmholtz MHD instability in a plane three-layer plasma is investigated. A general dispersion relation for the case of arbitrarily orientated magnetic fields and flow velocities in the layers is derived, and its solutions for a bounded plasma flow in a longitudinal magnetic field are studied numerically. Analysis of Kelvin-Helmholtz instability for different ion acoustic velocities shows that perturbations with wavelengths on the order of or longer than the flow thickness can grow in an arbitrary direction even at a zero temperature. Oscillations excited at small angles with respect to the magnetic field exist in a limited range of wavenumbers even without allowance for the finite width of the transition region between the flow and the ambient plasma. It is shown that, in a low-temperature plasma, solutions resulting in kink-like deformations of the plasma flow grow at a higher rate than those resulting in quasi-symmetric (sausage-like) deformations. The transverse structure of oscillatory-damped eigenmodes in a low-temperature plasma is analyzed. The results obtained are used to explain mechanisms for the excitation of ultra-low-frequency long-wavelength oscillations propagating along the magnetic field in the plasma sheet boundary layer of the Earth’s magnetotail penetrated by fast plasma flows.     

Pressure profiles of a plasma confined by the magnetic field of a ring current

Pressure profiles p(ψ) marginal with respect to convective instability in a toroidal tubular plasma confined by the magnetic field of an internal levitated ring current and external ring currents are studied as functions of the shape of the magnetic separatrix. Configurations are found in which the maximum plasma pressure in a finite-width layer near the plasma boundary decreases by two orders of magnitude at the expense of artificially raising the effective length (characterized by the integral ∮dl/B) of the magnetic field lines near the separatrix surface. It is shown that, in the case of a straight cylindrical tubular plasma, which is the limiting case of a toroidal configuration with an arbitrarily large aspect ratio, the sufficient condition for the plasma to be MHD stable against both convective and kink perturbations is satisfied for local values β≤0.4. __________ Translated from Fizika Plazmy, Vol. 26, No. 6, 2000, pp. 519–528. Original Russian Text Copyright ￠ 2000 by Popovich, Shafranov.     

Nonlinear dynamics of Kelvin-Helmholtz instability in a finite-width plasma flow

The nonlinear stage of Kelvin-Helmholtz (KH) instability in a finite-width plane-parallel plasma flow is analyzed. The analysis is performed by means of two-dimensional numerical simulations with the use of ideal magnetohydrodynamic equations describing isothermal plasma flows propagating along the magnetic field. The influence of the magnetic field strength, the plasma temperature, and the ratio of the flow width to the width of the transition layer on the formation of vortex layers and large-scale flow perturbations is investigated. It is shown that, if the wavelength of periodic perturbations is shorter than the flow width, the symmetric and antisymmetric modes develop in a qualitatively similar manner. For waves with wavelengths longer than the flow width, the development of such modes is very different due to the mutual influence of the flow boundaries. Analysis of the development of instability at different values of the Alfvén Mach number M _A shows that long-lived vortices with a characteristic scale length on the order of the flow width appear in a weak magnetic field for both symmetric and antisymmetric modes; however, the vortex geometries for these modes are different. In a strong magnetic field, M _A ～ 5, the phase of vortex decay for both types of modes occurs faster than in a weak field; however, in the case of an antisymmetric mode, large-scale perturbations of the flow boundary are retained for a longer time. Analysis of the evolution of the initial disturbance produced by an ensemble of random small perturbations (noise) at different plasma temperatures shows that, for a flow width comparable with the width of the transition region, the development of KH instability is always antisymmetric in character and leads to well-developed large-scale perturbations of the flow as a whole. For a cold plasma with C _S < 0.5U (where C _S is the speed of sound and U is the flow velocity), in contrast to hot plasma with C _S > 0.5U, the development of KH instability leads to the growth of the antisymmetric mode even if the flow width is much larger than the width of the transition region.     

Kelvin-Helmholtz instability in a bounded plasma flow

Kelvin-Helmholtz instability in a three-layer plane geometry is investigated theoretically. It is shown that, in a three-layer system (in contrast to the traditionally considered case in which instability develops at the boundary between two plasma flows), instability can develop at an arbitrary ratio of the plasma flow velocity to the ion-acoustic velocity. Perturbations with wavelengths on the order of the flow thickness or longer can increase even at a zero temperature. The system can also be unstable against long-wavelength perturbations if the flow velocity at one of the boundaries is lower than the sum of the Alfvén velocities in the flow and the ambient plasma. The possibility of applying the results obtained to interpret the experimental data acquired in the framework of the CLUSTER multisatellite project is discussed. It follows from these data that, in many cases, the propagation of an accelerated particle flow in the plasma-sheet boundary layer of the Earth’s magnetotail is accompanied by the generation of magnetic field oscillations propagating with a velocity on the order of the local Alfvén velocity.     

A nonlinear single-mode structure in a plasma with anisotropic temperature

An exact solution is derived to the equations of vortex electron anisotropic hydrodynamics for a plasma that is unstable against the Weibel instability driven by the electron temperature anisotropy. This solution describes saturation of the Weibel instability in the single-mode regime with an arbitrary wavelength and corresponds to a standing helical wave of magnetic perturbations in which the amplitude of the generated magnetic field varies periodically over time. The longitudinal and transverse (with respect to the rotating anisotropy axis) plasma temperatures are subject to the same periodic variations. In this case, the maximum magnetic field energy can be on the order of the plasma thermal energy.

     

Resonant effect of the noncircular shape of the plasma surface on the dispersion properties of extraordinary azimuthal surface modes in magnetoactive waveguides

A theoretical study is made of the resonant effect of the shape of the cross section of the plasma column on the propagation of a packet of extraordinary electromagnetic waves with a zero axial wavenumber in a circular-cross-section cylindrical metal waveguide in an axial magnetic field. The waveguide is assumed to be partially filled with a plasma. The effect of the noncircular shape of the plasma cross section on the dispersion properties of surface eigenmodes propagating strictly transverse to the external magnetic field is investigated by the method of successive approximations for the case in which the angular period of the wave perturbations is twice the ripple period of the interface between the plasma and the dielectric. In this resonant case, the fields and eigenfrequencies of the eigenmodes are determined to second order in the small parameter describing the rippling of the plasma-dielectric interface.     

Electron-magnetohydrodynamic description of a steady-state current flow in a plasma with a three-dimensional localized density perturbation

The problem of a steady-state current flow through a localized density perturbation is analyzed in the framework of electron magnetohydrodynamics. It is examined how the degree of localization of such a flow depends on the plasma magnetization parameter and the geometric characteristics of the density perturbation. Corrections to the unperturbed current field are found by the iteration method. It is shown that the first-order correction to the current can be determined for an arbitrary perturbation. In the case of perfectly conducting plasma, the second-order correction can be found only for dipole perturbations, for which the integral change in the density is zero. In this case, the first-order correction to the current is localized, which makes possible the existence of the second-order correction. The finite plasma conductivity also assists current localization; therefore, for sufficiently small values of the plasma magnetization parameter, both first- and second-order steady-state corrections to the current can be obtained for any moderate plasma density perturbation.     

Azimuthally asymmetric eigenmodes of a magnetized plasma cylinder around a dielectric rod in a circular waveguide

The electrodynamics of a circular waveguide with a dielectric rod surrounded by a magnetized plasma layer is considered. A general dispersion relation for azimuthally asymmetric perturbations is derived, and its solutions describing slow waves—specifically, electromagnetic and plasma modes, as well as (and primarily) hybrid waves that combine the properties of both mode types—are investigated numerically. For the fundamental waveguide mode of the system—the HE₁₁ mode—the parameters of the plasma layer are determined at which the mode cannot be subject to Cherenkov interaction with a relativistic electron beam at a given frequency. For both waveguide and plasma modes, the radial profiles of the longitudinal components of the electric field and Poynting vector, the fractions of RF power carried within the dielectric and plasma regions and vacuum gap, and the coupling impedance are calculated as functions of the parameters of the plasma layer. The evolution of the field structure during the formation of asymmetric hybrid waves is traced. The results of calculating the dispersion and coupling impedance are analyzed as applied to an antenna-amplifier—a relativistic traveling-wave tube operating on the HE₁₁ mode of the dielectric rod: specifically, the implementability of the concept in the presence of a plasma at the rod surface is estimated, and the possible role of azimuthally asymmetric and symmetric plasma modes is examined.     

Experimental study of magnetized plasma rotation in crossed fields

Rotation of magnetized plasma between two coaxial electrodes in crossed electric and magnetic fields was studied experimentally. Three regimes of plasma rotation were observed. In the first regime, the radial electric field is created by a beam?plasma discharge due to the charging of the inner axial electrode by electrons, the outer electrode being grounded. Plasma rotation in this case is accompanied by strong high-frequency current oscillations detected by a Mach probe. When a negative voltage was applied to the coaxial electrodes, the second regime was observed, in which weakly perturbed quasi-stationary plasma rotation occurred at a relatively low radial current. The third regime of plasma rotation was observed upon a spontaneous disruption of the second regime. It is characterized by high currents of ~1 kA, sheared plasma rotation, and excitation of high-frequency perturbations.     

Magnetorotational instability of a weakly ionized accretion disk with vertical and azimuthal magnetic fields

Magnetorotational instability of a weakly ionized accretion disk with an admixture of charged dust grains in a magnetic field with the axial and toroidal components is analyzed. The dispersion relation for perturbations perpendicular to the disk plane is derived with allowance for both the Hall current and the finite transverse plasma conductivity. It is shown that dust grains play an important role in the disk magnetic dynamics. Due to the effect of dust grains, the Hall current can reverse its direction as compared to the case of electron-ion plasma. As a result, the instability threshold shifts toward the short-wavelength range. Under certain conditions, electromagnetic fluctuations of any length can become unstable. It is established that the instability criterion for waves of any scale length is satisfied within a finite interval of the density ratio between the dust and electron plasma components. The width of this interval and the instability growth rate as functions of the plasma parameters and the configuration of the magnetic field in the disk are analyzed.     

Electromagnetic radiation from a plasma slab during the development of Weibel instability

Electromagnetic radiation from an anisotropic plasma slab formed by ionization of matter in the field of a high-power femtosecond pulse is studied. It is shown that the growth of initial field perturbations in the course of Weibel instability is accompanied by the generation of nonmonochromatic radiation with a characteristic frequency on the order of the instability growth rate. It is found that perturbations with characteristic scale lengths less than or on the order of the ratio of the speed of light to the Langmuir frequency are excited and radiated most efficiently, provided that the slab is thicker than this ratio.     

On the growth rate of aperiodic instability in plasma with an anisotropic bi-Maxwellian electron velocity distribution

The growth rate of aperiodic instability of transverse and longitudinal-transverse electromagnetic field perturbations in plasma with an anisotropic bi-Maxwellian electron velocity distribution is studied. The boundaries of the instability domains in wave vector space are found, and the growth rates of field perturbations with configurations different from that corresponding to the maximum growth rate are determined.     

Kelvin-Helmholtz instability of a cylindrical plasma flow with an arbitrary temperature

The dispersion relation for Kelvin-Helmholtz magnetohydrodynamic instability of a cylindrical plasma flow in a longitudinal magnetic field is studied with allowance for plasma compressibility. Stability of the system in a wide range of plasma parameters is thoroughly analyzed in the incompressible plasma approximation. Using the results obtained, a diagram of the system stability is constructed in terms of the magnetic field and the ratio between the plasma densities in the flow and the ambient space. It is shown by numerically solving the dispersion relation for the case of a compressible plasma that perturbations with scale lengths on the order of the flow diameter and larger can develop even at a zero temperature. For low ion-sound velocities, c _S ²/U ₀² < 0.25, the growth rate of the axisymmetric mode with m = 0 is much smaller than that of non-axisymmetric modes. It is shown that, in an incompressible plasma, the eigenmodes are damped monotonically with distance from the flow. In plasma with a finite temperature, the character of damping is oscillatory; in this case, the lower the plasma temperature, the larger the distance at which the ambient plasma is perturbed.     

Stability of Alfvén modes in a collisionless anisotropic plasma confined by a highly curved magnetic field

The stability of Alfvén modes in a collisionless plasma with an anisotropic pressure in a highly curved magnetic field is studied. A linearized equation for describing longitudinally nonuniform MHD perturbations with frequencies below the bounce frequency is derived. In this equation, the perturbations of longitudinal and transverse pressures are calculated using a collisionless kinetic equation. It is shown that longitudinal fluxes of the transverse and longitudinal plasma energies give rise to pressure perturbations different from those in the Chew-Goldberger-Low collisionless hydrodynamics. The corresponding energy principle is constructed. A stability criterion for Alfvén modes is obtained and is found to be more stringent than that in the Chew-Gold-berger-Low model.     

MHD plasma stabilization in a chain of axisymmetric adiabatic open mirror cells

Conditions for convective plasma instability in a chain of axisymmetric adiabatic mirror cells with different signs of magnetic field curvature are analyzed. The boundaries of the region that can be occupied by a stable hollow plasma in a system of two connected cells—a nonparaxial simple mirror cell and a semicusp—are determined, as well as the interval of allowed values of the ratio between the pressures in the cells. Because of the large magnetic field curvature in the component cells, the safety factor that is achieved at both—external and internal—plasma boundaries in accordance with the average min-B principle can be high. It is assumed that the unperturbed pressure in each cell is almost isotropic, in which case the mirror ratio should necessarily be large. A key role in the stability of the plasma is played by its compressibility. A comparison is made between the conditions for complete plasma stabilization against arbitrary perturbations and the conditions for stability of individual cells against the global mode. The stability of the cells against the global mode is sufficient, but not necessary, for stabilizing the chain. The analysis is done by using orthogonal coordinates associated with the unperturbed magnetic field (flux variables). Numerical simulations were carried out for nonparaxial cells from a certain three-parameter family.     

Large-scale perturbations due to a small-scale instability in a finite-conductivity plasma

By considering kink modes in a plasma cylinder in a strong axial magnetic field as an example, it is demonstrated that, because of the finite plasma conductivity (the finite longitudinal plasma permittivity ?_∥), large-scale perturbations can grow with time due to a small-scale instability that develops near a certain magnetic surface.     

Rayleigh-Taylor instability in quantum magnetized viscous plasma

Quantum effects on Rayleigh-Taylor instability of stratified viscous plasmas layer under the influence of vertical magnetic field are investigated. By linearly solving the viscous QMHD equations into normal mode, a forth-order ordinary differential equation is obtained to describe the velocity perturbation. Then the growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes. The results show that, the presence of vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration for viscous plasma, which is greater than that of inviscous plasma.     

Optical biosensors for real-time measurement of analytes in blood plasma

The preparation of assemblies consisting of multiple molecular layers of bovine serum albumin (BSA), monoclonal antibodies against horseradish peroxidase (anti-HRP), and monoclonal antibodies against methotrexate (anti-MTT), as well as interaction of the assemblies with human blood plasma were observed using a grating coupler and Young interferometer (YI). The assemblies could be arranged according to decreasing amounts of nonspecific deposits bound irreversibly to them from blood plasma as follows-an adsorbed antibody monolayer saturated with adsorbed BSA, antibody multilayers linked with polycations, antibodies covalently immobilized on a BSA layer densely crosslinked with glutaraldehyde (GA), slightly crosslinked BSA double layer, slightly crosslinked antibody double layers. The occurrence of human serum albumin (HSA), human fibrinogen (Fg), IgG, and IgM in the plasma deposits was studied by binding the respective antibodies. IgG, IgM, and Fg were detected in plasma deposits on the immobilized assemblies while the composition of a plasma deposit on the unmodified sensor surface reflected roughly the plasma composition containing mainly adsorbed HSA and Fg. A crosslinked anti-HRP double layer was immobilized on a waveguiding branch of YI and a similar anti-MTT double layer was immobilized on the other branch. The sensor response to blood plasma was fairly decreased owing to a compensation of the respective optical changes in the two branches, in which a similar non-specific adsorption took place. The addition of HRP or MTT to plasma induced specific responses of the corresponding branches.     

Wall plasma in a wideband dielectric cherenkov maser

Results are reported of experimental investigations that have revealed the presence of a plasma in the interaction region of a model wideband relativistic microwave amplifier—a dielectric Cherenkov maser. The electrodynamic properties of a hybrid system—a waveguide with an annular dielectric liner and a plasma layer adjacent to its inner wall—are analyzed. Experiments with a high-current accelerator have revealed that the power of the emitted microwaves at the output of the system increases strongly when an external microwave source at different frequencies in the X-band is switched on. However, this effect was found to be hard to reproduce. Indirect evidence is obtained of the fact that, during the transport of an electron beam and under the action of the signal from a high-power pulsed magnetron, the plasma in the system is created at the surface of the dielectric. In the model of a cold magnetized plasma, a dispersion relation is derived for axisymmetric waves in a system with a wall plasma layer. The spectra of the waveguide and plasma modes in the system and the transverse structure of their electromagnetic fields are investigated thoroughly as functions of the plasma density and layer thickness. It is shown that even a very thin layer of a high-density plasma results in a large frequency shift of the dispersion curve of the waveguide mode, in which case the coupling impedance at a fixed frequency decreases sharply. On the other hand, a layer of a moderately dense plasma increases the coupling impedance for the waveguide mode. It is established that, in a configuration with a wall plasma layer, the longitudinal component of the electric field of a plasma mode whose power flux in the dielectric is of a volumetric nature reverses direction across the layer.     

Numerical simulations of ion and electron transport in a low-temperature dusty plasma

Charged particle transport and kinetic processes in a low-temperature dusty plasma are numerically simulated. Dust grains are represented as spheres with a given radius. The self-consistent electric field in the plasma surrounding a charged dust grain is calculated taking into account the perturbations of plasma quasineutrality near the grains. It is shown that applying an external electric field leads to a rearrangement of the plasma space charge and a break of the spherical symmetry of the electron and ion density distributions around the grain. The mutual influence of two identical charged dust grains is considered, and the energy of the electrostatic interaction between the grains is calculated. It is shown that this energy has a minimum at a certain finite distance between the grains.