Jeans-Buneman instability in a dusty plasma

A self consistent formulation of the Jeans instability of a dusty plasma with proper inclusion of charge dynamics is described. It is shown that charge fluctuations significantly affect the Jeans as well as the Buneman mode. For plasma particles (electrons and ions) in local thermal equilibrium, the Jeans lengthλ _J is given byλ _J≈λ _g F(R, ε, β/η), whereλ _g is the Debye length of the charged grains,R is the square of the ratio of the Jeans to the plasma frequency of the grains,ε is the square of the ratio of the Debye length of the grains and the plasma particles andβ/η is the ratio of the attachment to the decay frequency of the electronic charges to the grain surface. The functional form ofF is given in the text. Numerical investigation of the Jeans-Buneman mode for a two and three component plasma shows that the Jeans mode dominates atkλ _D≪1 (wherek is the wave number andλ _D is the Debye length of plasma particles), whereas atkλ _D≫1 only the Buneman mode operates. Charge fluctuations reduce the area of overlap of the two modes. Furthermore, in the absence of gravity, there exists a new, charge fluctuation induced unstable mode in a streaming dusty plasma. Astrophysical applications of the results are discussed.     

Thermal condensation mode in a dusty plasma

In the present work, the radiative condensation instability is investigated in the presence of dust charge fluctuations. We find that the charge variability of the grain reduces the growth rate of radiative mode only for fluctuation wavelength smaller or of the order of the Debye length and this reduction is not very large. Far from the Debye sphere, radiative mode can damp due to thermal conduction of electrons and ions     

Effects of dust-charge gradient and polarization forces on the waves and Jeans instability in strongly coupled dusty plasma

The effects of dust charge gradient (DCG) force and polarization force have been investigated on the properties of dust acoustic wave (DAW) and linear Jeans instability in strongly coupled dusty plasma. In the kinetic regime, DCG and polarization forces modify the DAW mode and couple with compressional viscoelastic wave mode. The Jeans instability criterion and critical wavenumber have been modified due to DCG force, polarization force and strong coupling effects. The results have been discussed in the warm photodisassociation region and in the laboratory complex plasmas. The strong correlation effect and the charge variation parameter stabilize the growth rate of Jeans instability. But, the polarization parameter stabilize the growth rate for positively charged dust grains and destabilize for negatively charged dust grains. The implications of charge gradient and polarization parameters are discussed for lower and higher charges in the laboratory complex plasma which decreases the growth of the propagating DAW.     

Effect of magnetic field and radiative condensation on the Jeans instability of dusty plasma with polarization force

The Jeans instability of self-gravitating dusty plasma with polarization force is investigated considering the effects of magnetic field, dust temperature and radiative condensation. The condition of Jeans instability and expression of critical Jeans wave number are obtained which depend upon polarization force and dust temperature but these are unaffected by the presence of magnetic field. The radiative heat-loss functions also modify the Jeans condition of instability and expression of critical Jeans wave number. It is observed that the polarization force and ratio of radiative heat-loss functions have destabilizing while magnetic field and dust temperature have stabilizing influence on the growth rate of Jeans instability.     

Nonlinear pulsational eigenmodes of a planar collisional dust molecular cloud with grain-charge fluctuation

We try to present a theoretical evolutionary model leading to the excitations of nonlinear pulsational eigenmodes in a planar (1D) collisional dust molecular cloud (DMC) on the Jeans scale. The basis of the adopted model is the Jeans assumption of self-gravitating homogeneous uniform medium for simplification. It is a self-gravitating multi-fluid consisting of the Boltzmann distributed warm electrons and ions, and the inertial cold dust grains with partial ionization. Dust-charge fluctuations, convections and all the possible collisions are included. The grain-charge behaves as a dynamical variable owing mainly to the attachment of the electrons and ions to the grain-surfaces randomly. The adopted technique is centered around a mathematical model based on new solitary spectral patterns within the hydrodynamic framework. The collective dynamics of the patterns is governed by driven Korteweg-de Vries (d-KdV) and Korteweg-de Vries (KdV) equations obtained by a standard multiscale analysis. Then, simplified analytical and numerical solutions are presented. The grain-charge fluctuation and collision processes play a key role in the DMC stability. The sensitive dependence of the eigenmode amplitudes on diverse relevant plasma parameters is discussed. The significance of the main results in astrophysical, laboratory and space environments are concisely summarized.     

Jeans stability of dusty space plasmas

The Jeans stability of dusty plasmas is re-considered. In contrast to a gas, a dusty plasma can support a plethora of wave modes each potentially able to impart to the dust particles the randomising energy necessary to avoid Jeans collapse on some length scale. Consequently, the analysis of the stability to Jeans collapse is many-fold more complex in a dusty plasma than it is for a charge-neutral gas. After recalling some of the fundamental ideas related to the ordinary Jeans instability in neutral gases, we extend the discussion to plasmas containing charged dust grains. Besides the usual Jeans criterion based upon thermal agitation, we consider two other ways of countering the gravitational collapse: (i) via the excitation of dust-acoustic modes and (ii) via a novel Alfvén-Jeans instability, where perturbations of the dust mass-loaded magnetic field counter the effects of self-gravitation. These two mechanisms yield different minimum threshold length scales for the onset of instability/condensation. It is pointed out that for the study of the Jeans instability produced by density enhancements induced in the plasma by the presence of normal wave modes, even more prohibitive plasma size constraints must necessarily be satisfied.     

Effect of polarization force on the Jeans instability of self-gravitating dusty plasma

The effect of polarization force acting on massive charged dust grains is investigated analytically on the Jeans instability of self-gravitating dusty plasma. The gravitational force acting on the massive negatively charged interstellar dust grains are considered in presence of both electrical and polarization forces. The basic equations of the problem are formulated and a general dispersion relation is obtained using plane wave approximation in low frequency wave mode. The effect of polarization force in the dispersion relation of the problem, condition of the Jeans instability and expression of the critical Jeans wave number is examined. The unstable growing modes due to self-gravitational force are studied in the situation when polarization force on the dust grain exceeds over the electrical force in magnitude. It is observed that the polarization force increases the growth rate of the system.     

Resistive drift instability and Rayleigh-Taylor instability in a dusty plasma

The resistive drift instability and the Rayleigh-Taylor instability are studied self-consistently in a magnetized inhomogeneous dusty plasma. The effect of grain charge fluctuations is taken into consideration. It is found that the presence of the dust grains in the plasma can significantly affect the resistive drift instability but less significantly the Rayleigh-Taylor instability. Further, the grain charge fluctuation has a tendency to stabilize both instabilities.     

Effects of long range Coulomb interaction on the Peierls instability

The Peierls instability is studied for a one-dimensional tight-binding model of conduction electrons in the half-filled case. The long range Coulomb interaction as well as the electron-phonon coupling are taken into account. It is found that the Peierls distortion is hindered by the long wavelength charge fluctuations due to the Coulomb interaction.     

Dust Alfven ordinary and cusp solitons and modulational instability in a self-gravitating magneto-radiative plasma

The effective one-fluid adiabatic magnetohydrodynamic (MHD) equations for a multicomponent plasma comprising of electrons, ions, and dust are used to investigate the nonlinear coupling of dust Alfven and dust acoustic waves in the presence of radiation pressure as well as the Jean’s term that arises in a self-gravitating plasma. In this context, the set of Zakharov equations are derived. The soliton solutions in the presence of radiation pressure and Jeans term are separately discussed. It is found that ordinary solitons are obtained in the absence of Jeans term whereas cusp solitons are found in the absence of radiation pressure. To the best of our knowledge, cusp solitons are obtained for the first time for a self-gravitating plasma with Jeans term for an electromagnetic wave in a dusty plasma. The modulational instability is also investigated in the presence of radiation pressure and Jeans term. It is found that the Jeans term drives the system modulationally unstable provided it dominates the dust acoustic and radiation pressure terms whereas the radiation pressure enhances the stability of the system. The relevance of the present investigation in the photodissociation region that separates the HII region from the dense molecular clouds is also pointed out.     

The charge state of conducting fine-dispersed systems in an insulating matrix

The influence of fluctuations in the number of Fermi particles on the charge state of fine-dispersed metallic grains in an insulating matrix is investigated. It is suggested that the system of grains does not form a tunnel medium and that charge transfer between metallic elements of the composite occurs due to thermal excitations of electrons over barriers. As follows from a calculation of the grand partition function, the average charge of the ith grain is a nonlinear function of the potential V _i of the conductor.     

Streaming instability of a dusty plasma in the presence of mass and charge variation

We study the effect of the mass and charge dynamics on the collective behaviour of a dusty plasma. It is shown that the finite non-zero streaming velocity of the dust grains leads to a novel coupling of the dust mass fluctuation with other dynamic variables of the plasma and the grains. The mass fluctuations causes a collisionless dissipation and provides an alternate channel for the beam mode instability to occur. Physically the negative energy wave associated with the beam mode couples to the mass fluctuation induced dissipative medium to produce the instability. We conclude that the higher value of the ion mass density to the dust mass density ratio reduces the threshold value for the onset of the instability. Its application in the astrophysical context is discussed.     

Magnetogravitational instability of a rotating homogeneous gas cloud with radiation

Magnetogravitational instability of an infinite, homogeneous rotating hot plasma cloud associated with radiative processes has been studied with the help of relevant MHD equations using normal mode analysis. Rotation is taken parallel and perpendicular to the magnetic field for both, the longitudinal and transverse modes of propagation. The Jeans espression of instability is modified to give the stabilizing effect of radiation pressure. The stabilizing effect of magnetic field is observed only for transverse mode of propagation whereas rotation stabilizes only along the magnetic field for transverse mode. The stabilizing effect of rotation is comparatively more effective.D. S. Vaghela gratefully acknowledges the financial assistance for his minor research project given by University Grants Commission of India.     

Waves and instabilities in dark interstellar molecular clouds containing ferromagnetic dust grains

The propagation characteristics of magnetization waves, as well as the instabilities of sound waves in a self-gravitating dark interstellar molecular cloud containing ferromagnetic dust grains and baryonic gas clouds, have been theoretically investigated by including the dynamics of both ferromagnetic dust grains and baryonic gases. It has been shown that there exist two types of subsonic or supersonic (depending on the field strength of the magnetization) transverse magnetization waves, which can be regarded as counterparts of Alfvén waves (for the parallel propagation) and magnetosonic waves (for the perpendicular propagation) in a magnetoactive plasma. It has also been found that, in addition to the usual Jeans instability, the sound waves suffer a new type of instability, which is due to the combined effects of the baryonic gas dynamics and self-gravitational field in both weakly and highly collisional regimes.     

Fluctuations of the charge on a dust grain in a plasma

A dust grain in a plasma acquires an electric charge by collecting electron and ion currents. These currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value 〈Q〉. Electrons and ions are collected at random intervals and in a random sequence, with probabilities that depend on the grain's potential. We developed a model for these probabilities and implemented it in a numerical simulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain's charge. Electron emission from the grain is not included, although it could be added easily to our method. We obtained the power spectrum and the RMS fluctuation level, as well as the distribution function of the charge. Most of the power in the spectrum lies at frequencies much lower than 1/τ, the inverse charging time. The RMS fractional fluctuation level varies as 0.5 |〈N〉|^-1/2, where 〈N〉=〈Q〉/e is the average number of electron charges on the grain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can experience fluctuations to neutral and positive polarities, even in the absence of electron emission     

Absorption optical bistability in semiconductors under the action of an external electric field

The conditions for the realization of absorption optical bistability under the simultaneous action of two (radiative and nonradiative) mechanisms of recombination of free charge carriers are investigated. It is shown that, in the diffusion mechanism of stream of free electrons from the beam axis, the temperature dependence of radiative recombination does not expand the temperature range of the thermostat in which the optical bistability occurs. A scheme is proposed with application of an external transverse electric field, which makes it possible to realize absorption optical bistability at any ambient temperature. An important advantage of this scheme is the conservation of the state of a bistable system after the action of a light pulse and a significant decrease in the energy spent on cooling of the medium.     

Peierls-Fröhlich instability and Kohn anomaly

A mathematical basis is given to the Peierls-Fröhlich instability and the Kohn anomaly. The techniques and ideas are based on the recently developed mathematical theory of quantum fluctuations and response theory. We prove that there exists a unique resonant one-mode interaction between electrons and phonons which is responsible for the Peierls-Fröhlich instability and the phase transition in the Mattis-Langer model. We prove also that the softening of this phonon mode at the critical temperature (Kohn anomaly) is a consequence of the critical slowing down of the dynamics of the lattice distortion fluctuations. It is the result of the linear dependence of two fluctuation operators corresponding to the frozen charge density wave and the distortion order parameter.     

Modified jeans instability for dust grains in a plasma

An investigation of the properties of linear stability is conducted for a system consisting of particles having mass m and charge q, interacting through the gravitational and electrostatic force (Jeans instability). However, in light of recent works showing that dust particles in a plasma can have a Lennard-Jones-like shielding potential, a new set of equations has been derived, where the electrostatic interaction among the dust particles is Lennard-Jones-like instead of Coulomb-like. A new condition for the gravitational instability is derived, showing a broader spectrum of unstable modes with faster growth rates.     

Radiative recombination of ions and nuclei in electron cooling systems

Experimental data on rates for the radiative recombination of nuclei (from helium to uranium) and various ions in interaction with an electron beam in electron cooling systems are reviewed. An analysis of the experimental data has yielded the dependence of the radiative recombination rate on the relative electron energy appreciably differently than the theoretical models obtained earlier by H. Kramers and R. Schuch. In addition, it is shown that the radiative recombination rate of nuclei in the experiment depends on the transverse electron energy as T _?? ^?0.82 ,which is also different from the results of the calculations by the theoretical model proposed by M. Bell and J. Bell. Experimental data on the cooling of ions in intermediate charge states are analyzed and the dependence of the radiative recombination rate on the charge state of the ion (electron-shell configuration) is shown. For some ion charge states, the rate of the process is of a resonance character. Loss to radiative recombination in the electron cooling system of the NICA Booster is evaluated for the Au³²⁺, Au³³⁺, Au⁵⁰⁺, and Au⁵¹⁺ ion beams. Limitations imposed on the Au79+ beam lifetime by radiative recombination in the electron cooling system of the NICA Collider are analyzed. Possible ways to decrease the radiative recombination rate of nuclei by selecting the parameters of the electron cooling system for the NICA Collider are proposed.     

Measurement of the charging of individual dust grains in a plasma

An experiment is described for investigating the charging of dust grains in a plasma. The apparatus is a double plasma device into which single dust grains are dropped from the top. The dust charge is detected and measured by a sensitive electrometer attached to a Faraday cup on the bottom. Experiments with electrons from the emissive filaments but without plasma indicate that the grains charge to approximately the filament potential for filament bias voltages smaller in absolute value than -70 V. The charge is of order 10⁶ electrons for SiC grains 30-150 μm in diameter. At higher bias voltage the charge is reduced due to secondary emission. The charge on grains increases with grain size and is nearly independent of the filament emission current. With plasma in the device, the grains charge both positively and negatively