Parametric instabilities and nucleation of coupled Langmuir and acoustic waves in a weakly-ionized plasma

A pair of coupled equations governing the nonlinear interaction between Langmuir and acoustic waves in partially-ionized plasmas are presented. Three-wave decay interactions, modulatinal instabilities, as well as the nucleation of coupled Langmuir and acoustic waves can then be studied. The results are of relevance to the lower part of the ionosphere, radio-frequency driven gas discharges, as well as the interstellar medium.     

Resistive instabilities in plasma

Instabilities produced by finite-resistivity effects in a plasma are of great interest in connection with research in fusion devices, solar flares, and geomagnetic substorms. We elucidate here the physical mechanism of this instability, and in particular, identify the tendencies in the system towards the instability and the tendencies opposing it, if any. As an illustration, we consider the example of the so-called gravitational interchange mode wherein a plasma with a statically stable vertical density gradient is situated in a vertical gravitational field and a sheared horizontal magnetic field. The physical picture developed here may be useful in sorting out phenomena that appear when more subtle properties of the resistive modes in a plasma are considered.     

Note on solar plasma irregularities and plasma instabilities

Observations of interplanetary scintillation of radio sources are used to estimate the size of plasma irregularities down to a distance of about 6 R from the Sun. This is compared with the values of the ion gyro-radius estimated for a range of distance from 1 AU to about 6 R from the Sun. The results of the calculations are discussed in the context of the hypothesis of plasma instability which is invoked to interpret the observations of the scattering of radio waves in the solar corona and of interplanetary scintillations.     

Proton-cyclotron instabilities in non-uniform loss-cone magnetospheric plasma

The waves, propagating nearly transverse to the ambient magnetic field, with frequencies near the harmonics of the proton-cyclotron frequency are studied in an inhomogeneous plasma with protons having loss-cone distributions. Three types of drift cyclotron instabilities have been studied: (i) non-flute instability; (ii) B-resonant instability; and (iii) non-resonant instability. Increases of loss-cone and density gradient increase the growth rates of all three instabilities. Increases in the positive temperature gradient and _t (ratio of thermal pressure of trapped protons to magnetic field pressure) have a stabilizing effect on the non-flute and non-resonant instabilities and a destabilizing effect on the B-resonant instability. The non-resonant instability has an interesting feature: a particular harmonic can be excited in two separate bands of unstable wave numbers. These instabilities can play an important role in the dynamics of the ring current and the inner edge of the plasma sheet region of the magnetosphere. The discrete turbulence generated by them would give rise to precipitation of protons on the auroral field lines, which may contribute to the excitation of diffuse aurora. These instabilities may be relevant to the observation of harmonic waves at 6R _E by Perrautet al. (1978).     

Electromagnetic instabilities in an anisotropic loss-cone plasma

A form of general dispersion relation for electromagnetic waves in a fully ionized anisotropic plasma with loss-cone that explicates the contribution of the loss-cone to the dispersion relation is developed. By initially ignoring effects due to anisotropy, it is shown by means of Nyquist diagram technique that an isotropic loss-cone distribution can be unstable to EM waves corresponding to the whistler mode (0<< _e ). The growth rate is then determined analytically for this distribution, assuming cyclotron resonance between the waves in the whistler mode and particles in the high energy tail of the velocity distribution. By including the effects of anisotropy, a general growth rate is obtained which is found to depend on the anisotropy, the size of the loss-cone, the softness of the energy spectrum, and the fraction of the particles which are resonant with the wave. For particular distributions the relative contributions of the anisotropy and of the loss-cone to the growth rate have been determined. It is seen that loss-cone effects, which depend on the size of the loss-cone as well as the softness of the energy spectrum, can be a significant factor in the determination of the growth rate. For the Lorentzian distribution, the half-width of unstable waves is considerably broadened and the growth rates are somewhat more severe as compared to a two-temperature Maxwellian. The threshold frequency is which confirms the presence of unstable EM waves in the magnetospheric plasma leading to turbulence.     

Parallel velocity shear instabilities in an inhomogeneous plasma

The stability of an inhomogeneous anisotropic plasma flowing along a straight magnetic field has been investigated. Both the flow velocity and the plasma density are spatially varying in a direction perpendicular to the magnetic field. The stability of an interface between an inhomogeneous anisotropic plasma flowing along the magnetic field and the non-conducting compressible gas of uniform density flowing parallel to the interface has also been discussed. The effect of gyroviscosity and inhomogeneity on the Kelvin-Helmholtz shear instability has been discussed in certain limiting situations.     

Kinetic theory of MHD instabilities in a nonuniform plasma

Most of the MHD instabilities originating from the nonuniformity of a plasma excite MHD surface wave. When the excited wave has a frequency _s which corresponds to the local shear Alfvén wave resonance (_s = k v _a (x), where v _a is the Alfvén speed and k is the wave number in the direction of the magnetic field), the surface wave resonantly mode converts to the kinetic Alfvén wave, the Alfvén wave having a perpendicular wavelength comparable to the ion gyroradius and being able to propagate across the magnetic field. We discuss various linear and nonlinear effects of this kinetic Alfvén wave on the plasma including particle acceleration and heating. A specific example for the case of a MHD Kelvin-Helmholtz instability is given.     

A relativistic theory of plasma cut-offs

It is pointed out that at frequencies near the plasma cut-off frequencies, the corrections to wave refractive indices in a cold plasmaN ₀due to the contribution of ions and relativistic effects can be of the same order of magnitude or greater thanN ₀. Expressions for wave refractive indicesN taking into account these corrections are derived in a limiting case |N| I. It is shown that the increase in cut-off frequencies due to effects of ions is negligibly small unless the electron plasma frequency is well below the electron gyrofrequency. The decrease of the cut-off frequencies due to relativistic effects is significant ( 1%) only in a rather hot plasma (T _e 1 keV), which may be observed in a plasma sheet region of the Earth's magnetosphere and in astrophysical conditions. These effects appear to be particularly important in a strongly anisotropic plasma (the electron perpendicular temperature is noticeably greater than the parallel one).     

Waves in a one-dimensional magnetized relativistic pair plasma

Normal modes of a one-dimensional relativistically streaming electron–positron plasma in a superstrong magnetic field are considered, taking into account possible different bulk velocities and thermal effects. This physical picture corresponds to the plasma present on the open field lines of rotating neutron stars where the observed radio emission is generated. Various cases are considered: relativistic and non-relativistic relative streaming of cold components, and relativistically hot distributions. A distinction between superluminous and subluminous waves (which can be excited by the Cherenkov effect) is clearly stated. In the low-frequency regime the Cherenkov and cyclotron two-stream instabilities occur. Polarization of the quasi-transverse modes changes from circular for the propagation along magnetic field lines to linear for angles of propagation larger than some critical angle that depends on the relative velocity of the plasma components.     

Low-frequency waves in asymmetric magnetized relativistic pair plasma

The properties of waves in a pulsar magnetosphere are considered in the most general case of a non-neutral, current-carrying pair plasma with arbitrary distribution functions for electrons and positrons. General dispersion relations are derived for a strong but finite magnetic field, including gyrotropic terms caused by the deviations from quasi-neutrality and the relative streaming of electrons and positrons. It is shown how the ellipticity of the wave polarization depends on the plasma parameters and angle of propagation. Two examples of plasma distributions are analysed numerically: a waterbag distribution and a piecewise distribution that models the numerical result for pair cascades. A possible application to the interpretation of the observed circular polarization of some pulsars is discussed.     

Electromagnetic wave instability in a relativistic electron-positron-ion plasma

By employing the anisotropic plasma distribution function, the stability of circularly polarized electromagnetic (EM) waves is studied in a relativistically hot electron-positron-ion (e-p-i) plasma, investigating two specific scenarios. First, linear dispersion relations associated with the transverse EM waves are analyzed in different possible frequency regimes. The expression of the aperiodic hydrodynamic instability is obtained and numerically the transverse EM modes are shown to grow exponentially. Secondly, we have found that the transverse electromagnetic wave interact with a collisionless anisotropic e-p-i plasma and damp through the nonlinear Landau damping phenomena. Taking the effects of the latter into consideration, a kinetic nonlinear Schrödinger equation is derived with local and nonlocal nonlinearities, computing the damping rates. The present work should be helpful to understand the linear and nonlinear properties of the intense EM waves in hot relativistically astrophysical plasmas, e.g., pulsars, black holes, neutron stars, etc.     

Ion acoustic soliton in relativistic degenerate electron-positron-ion plasma

Large amplitude ion-acoustic (IA) soliton in a fully relativistic plasma consisting of relativistic cold ions and relativistic degenerate electrons and positrons are investigated. It is shown that the features of IA soliton are strengthened increasingly with relativistic effects. The relativistic degeneracy of electrons and positrons acts in opposite way on the properties of the IA soliton. The latter becomes more flatten in the first case and narrower in the second one.     

Interstellar turbulent magnetic field generation by plasma instabilities

The maximum magnetic field strength generated by Weibel-type plasma instabilities is estimated for typical conditions in the interstellar medium. The relevant kinetic dispersion relations are evaluated by conducting a parameter study both for Maxwellian and for suprathermal particle distributions showing that micro Gauss magnetic fields can be generated. It is shown that, depending on the streaming velocity and the plasma temperatures, either the longitudinal or a transverse instability will be dominant. In the presence of an ambient magnetic field, the filamentation instability is typically suppressed while the two-stream and the classic Weibel instability are retained.     

Ion-acoustic solitary waves in a fully relativistic ion-electron-positron plasma

A fully and coherent relativistic fluid model derived from the covariant formulation of relativistic fluid equations is used to study ion-acoustic solitary waves in a fully relativistic ion-electron-positron plasma. This approach has the characteristic to be consistent with the relativistic principle and consequently leads to a more general set of equations valid for fully relativistic plasmas with arbitrary Lorentz relativistic factor. Our results may be relevant to cosmic relativistic double- layers and relativistic plasma structures involving energetic plasma flows that may occur in space plasmas. Furthermore, they may complement and provide new insights into recently published results (G. Lu et al. in Astrophys. Space Sci., doi:, 2010).     

Strong electromagnetic waves in a magnetized relativistic electron-positron plasma

It is shown that in a strongly magnetized relativistic electron-positron plasma, strongly localized large amplitude circularly polarized electromagnetic wave pulses exist. The localization is due to relativistic mass variation as well as ponderomotive force effects. Three types of pulses are found analytically: the sharply spiked pulse in a strongly magnetized cold plasma, the smooth pulse in a week magnetized warm plasma, and the moderately spiked pulse for a weakly magnetized cold plasma. The physical mechanisms giving rise to these pulses are distinct for each case. Possible implications of our investigation to pulsar radiation are discussed.