Threshold Condition For Instability Research Articles

Electromagnetic proton cyclotron ring instability: Threshold and saturation

This paper describes a theoretical and computational study of the threshold and saturation conditions of the electromagnetic proton cyclotron ring instability. The initial proton velocity distribution is modeled as a Maxwellian in the direction parallel to the ambient magnetic field and as a relatively cold ring in the plane perpendicular to the field. Linear Vlasov theory and one‐dimensional hybrid simulations are used to examine and confirm previously derived scaling laws for the maximum instability growth rate and maximum value of the fluctuating magnetic field energy density. Linear theory yields a new instability threshold condition relating the dimensionless ring perpendicular speed and the dimensionless ring parallel temperature. Simulation results show that cessation of fluctuation growth is due to the heating of the ring protons in the parallel direction and to the reduction of the perpendicular kinetic energy of the ring; at saturation these parameters typically lie near values predicted by a linear threshold condition. The threshold condition is predicted to provide an upper bound for proton ring kinetic energies observed in space plasmas.

Hot proton anisotropies and cool proton temperatures in the outer magnetosphere

The hot protons of the outer magnetosphere typically exhibit a temperature anisotropy such that T⊥/T∥ > 1, where perpendicular and parallel symbols denote directions relative to the background magnetic field. If this anisotropy is sufficiently large, the electromagnetic proton cyclotron anisotropy instability may be excited. This instability is studied using linear Vlasov theory and one‐dimensional hybrid simulations for a homogeneous plasma model representative of conditions in the outer magnetosphere with a hot anisotropic proton component (denoted by subscript h) and a cool, initially isotropic proton component (subscript c). Linear theory yields an instability threshold condition on the hot proton temperature anisotropy whereas the simulations imply an upper bound on T⊥h/T∥h; both the threshold and the upper bound have similar scalings with the maximum growth rate γm, the parallel β of the hot component, β∥h, and the relative density of the hot component nh/ne. An analysis of plasma observations from the Los Alamos magnetospheric plasma analyzer (MPA) in geosynchronous orbit finds that the maximum value of the hot proton temperature anisotropy approximately satisfies the predicted scalings with β∥h and nh/ne and yields the proportionality factor that quantifies this upper bound. The simulations are also used to examine the heating of the cool protons by the proton cyclotron instability. The simulations yield a scaling for the dimensionless late‐time cool proton average temperature Tc/T∥h as (nh/ne)/β∥h0.5. Analysis of MPA data shows that the observed values of Tc/T∥h have similar scalings and again yield the proportionality factor which quantifies this relationship.

Landau-fluid simulation of laser filamentation

The Landau-fluid model is a recently introduced fluid-moment closure scheme [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)] that was designed to include kinetic dissipative effects like Landau damping in fluid calculations. The fluid-moment hierarchy is terminated by assuming linear relationships among the retained moments in Fourier-transform space, with coefficients determined by matching the plasma response to that obtained from a kinetic analysis. This paper generalizes the technique to the full range of ion and electron collisionality and applies it to a new fluid simulation code constructed to study laser filamentation in underdense plasmas [Berger et al., Phys. Fluids B 5, 2243 (1993)]. By matching the ion-acoustic complex frequency derived from the fluid model with that predicted by collisional, Fokker–Planck, and kinetic analyses, the specific heat ratio, thermal conductivity coefficient, and viscosity coefficient for ions and the thermal conductivity coefficient for electrons are determined as functions of the wave number k. For frequencies much less than the pump frequency this leads to a fourth-order polynomial dispersion relation whose spectrum includes damped ion-acoustic waves as well as filamentation modes whose stability depends on the pump strength. An analytic instability threshold condition on the laser intensity is derived from which the relative importance of ponderomotive and thermal drives can be assessed. Expressions for the linear susceptibilities in the presence of a finite-amplitude pump are also given, which might prove useful for understanding spectral linewidths for Thomson scattering.

Microinstabilities driven by non-thermal plasma in the high-latitude F-region

Threshold conditions for the ion cyclotron instability, due to a distorted ion velocity distribution in the auroral F-region ionosphere, and the quasilinear evolution of the distribution function, are investigated. It is found that the critical value of the ion drift parameter D∗ for the resonant ion species is between 1.3 and 1.4 in most cases, becoming considerably larger only if the fractional concentration of the resonant species is less than about 20 % or if the field-parallel ion temperature for the non-resonant species is low compared with the resonant species. Also, the threshold is independent of the degree of distortion of the non-resonant ion velocity distribution. Velocity space diffusion driven by ion cyclotron waves becomes important if the ratio of the electrostatic energy and the ion thermal energy (the weak turbulence parameter) is of the order of 10 −6 Δk | (m −1) or more, where Δk | is the width of the wave spectrum in k |. The steady state velocity distribution function for a given value of parallel velocity lies between two extremes: the Raman et al. -type distribution with a large positive slope in field-perpendicular velocity ( ν ⊥) and a distribution function with the positive slope replaced by a plateau of the size Δν ⊥ ∼ 3.8 Ω i k ⊥ , where Ω i is the resonant ion (angular) gyrofrequency and k ⊥ the perpendicular wavenumber which dominates the spectrum.

Velocity shear and fluctuations in the auroral regions of the ionosphere

The theory of collisional electrostatic modes that are driven unstable by a sheared field‐aligned ion flow velocity (i.e., Vi0 = V0(x)ez, B0 = B0ez) is presented. The instability threshold condition is |dV0/dx| > 2(1 + Ti/Te)νin, where νin is the ion‐neutral collision frequency, the characteristic longitudinal wavelengths λ∥ > λe, λe being the electron collision mean free path, and the transverse wavelengths λ⊥ > 21/2πρi, ρi being the ion gyroradius. The linearly unstable modes can account for fluctuations with transverse wavelengths ranging from a kilometer to several meters for only a moderate amount of shear (in the parallel velocity). Thus the instability provides a direct means of exciting almost the entire range of the observed (Basu et al., 1988) subkilometer scale irregularities in the auroral F region. The quasi‐linear analysis presented here shows that an effective viscosity describing momentum transport in the x direction can be derived in the presence of the shear‐driven fluctuations. The spatial profiles of the excited modes are evaluated from the solution of the appropriate dispersion equation. A model is proposed to describe the nonlinear evolution of the instability while ensuring that the characteristics of the turbulent fluctuation spectra resulting from it are consistent with those of the observed spectra.

Threshold conditions for hydrodynamic instabilities in two-frequency nematics

Electrohydrodynamic equations for a layer of nematic material with planar homogeneous alignment are given for alternating applied voltage, for the case of small deformations. Conditions for hydrodynamic instabilities are studied firstly for the case of a positive dielectric anisotropy in a small wavevector-expansion, and secondly numerically for two-frequency nematic materials in which the conductivity originates from orientational relaxation of polar molecules. It is found that, except for some cases of negative conductivity anisotropy the static Frederiks deformation can only be overtaken by a finite-(non-zero) wavevector dynamic instability. In two-frequency materials instabilities hardly occur over a frequency range of more than a factor of two. Best conditions are a high amplitude of the relaxation process and large negative dielectric anisotropy at high frequencies Traitement des equations electrohydrodynamiques pour une couche de nematique en configuration planaire, dans le cas de petites deformations. Conditions pour une instabilite hydrodynamique dans le cas d'une anisotropie dielectrique positive sous la forme d'un developpement en petits vecteurs d'onde et dans le cas de nematiques a deux frequences

Scaling of the beam‐plasma discharge

It is shown that the scaling observed in a recent experiment of the beam‐plasma discharge is consistent with the assumption that triggering occurs when an instability threshold condition is exceeded for electron plasma waves with ω ≈ ωe, the electron plasma frequency.

On the parametric dependences of the beam‐plasma‐discharge at low pressures and magnetic field strengths

An explanation for the relationship between the critical current and the physical parameters observed in recent experiments on beam‐plasma‐discharge at low pressures and magnetic fields is proposed. The observed relationship is reproduced by combining the threshold condition for electrostatic instability in a magnetized, bounded beam‐plasma system and the balance equation for the rate of plasma production and that of loss through the ends. It is found that the principal scaling of the threshold criterion with variations in the magnetic field is determined by the variations in the radius of the beam‐plasma system.

Space-time evolution of nonlinear three-wave interactions. II. Interaction in an inhomogeneous medium

The effects of dephasing due to spatial inhomogenelty on the space-time evolution (two-dimensional steady state) of nonlinear three-wave interactions are described. After summarizing previous work on the inhomogeneous-medium three-wave equations, the authors describe an inverse scattering transform for these equations. They then use this transform along with numerical integration of the equations to determine the effects of inhomogeneity on the nonlinear evolution of decay, backscatter, and explosive interactions. The effects include modified threshold conditions for explosive instabilities and modified conditions for optimal energy transfer in two-pump interactions. Energy transfer in both absolute and convective decay interactions in an inhomogeneous medium is found to plateau and then decrease with increasing pump width, in striking contrast to homogeneous-medium interactions. A suppression of the nonlinear modulation in stimulated backscatter is described. A time-asymptotic solution for the spatial profiles of daughter waves is given for the absolute instability.

The effect of the gradient drift term on type 1 electrojet irregularities

We hypothesize that type 1 VHF radar echoes can only be observed when the electrojet plasma is linearly unstable at half the radar wavelength and that further, for reasons not yet understood, the phase velocity of the unstable waves always corresponds to the threshold conditions for instability, even when the destabilizing forces (electron drift and plasma density gradient) exceed the threshold. This phase velocity, which produces the Doppler shift of the radar echoes, is usually close to the ion acoustic velocity of the medium but can differ from it to some extent because of the effect of the density gradient. This difference can be positive or negative, is proportional to λ², and can be substantial at night, when the vertical density gradients in the equatorial E region are large and variable. Nighttime equatorial radar observations do seem to indicate considerable variability in the type 1 velocity. These effects may also be important in explaining auroral radar observations.

Anomalous Heating of Dense Plasma by Laser Radiation

The enhanced heating of plasmas by laser radiation is discussed in this report. A systematic investigation of threshold conditions for instabilities is described and contributions of various instabilities to the anomalous dissipation are compared. Special attention is paid to dense plasmas for which Coulomb collisions are essential.

Chemical and hydrodynamic stability of an interface with an autocatalytic reaction

An autocatalytic reaction of the trimolecular type is assumed to take place at the interface of two immiscible fluids. By coupling the chemical rate equations with the surface hydrodynamic equations, the authors obtain the threshold conditions for chemical and hydrodynamic instability.

A Plasma Instability Induced by Electron-Hole Generation in Impact Ionization

Existence of a new kind of plasma density instability, caused by the dependence of the plasma generation rate on the electric field, is predicted, and lower frequency oscillations believed due to it have been observed experimentally. The observed oscillations, induced by shunting the plasma with an external capacitance, are damped and of frequency 2∼10 Mc/sec in n-InSb at 77°K. The electron-hole generation rate has been calculated from the observations and is found to vary approximately as the eighth power of the electric field, with values from about 106 to 108 sec−1 for electric fields between 2.3 and 4.0×104 V/m. When a small external transverse magnetic field was applied, the generation rate increased, but obeyed the identical relationship as a function of electric field as observed in zero magnetic field. Evaluation of the threshold conditions for instability indicates that the microwave radiation observed from an impact-ionization plasma in InSb can be the result of this density instability.