Ion Plasma Oscillations Research Articles

Role of electron temperature at extremely low density in negative positive ion plasma

It is pointed out that the role of electrons in the dynamics of pair ion and negative positive ion plasmas cannot be neglected even at extremely low density of electrons, i.e., ne0n+0≪mem+ (where nj0 is the background density of jth species and mj is the mass of the particles of the j-species while j = e, +, −) because electron thermal velocity is almost always larger than thermal velocities of ions, i.e., vT± ≪ vTe. An analysis of electrostatic waves in unmagnetized negative positive ion electron (NPIE) and pair ion electron (PIE) plasmas is presented for the case ωpe ≪ ωp+ (where ωpj=(4πnj0e2mj)1/2 is the plasma oscillation frequency corresponding to j-species). The electron dynamics contribute to electrostatic perturbations at ion plasma oscillation time scale at longer wavelengths for λDe2k2<1 where λDe=(Te4πne0)1/2 is the electron Debye length. On the other hand, the electron plasma wave turns into thermal wave when the conditions ωpe ≪ ωp± and 1≪λDe2k2 hold simultaneously and ion acoustic wave approaches the sum of ion plasma oscillation frequencies of positive and negative ions. The only electrostatic normal mode of such a plasma is the ion plasma wave corresponding to longer wavelengths, which also includes the contribution of electrons. The electron thermal wave is separated from plasma oscillations and electron time scale disappears with respect to electrostatic perturbations. Similar situation also occurs in plasmas having negatively charged dust particles. To elaborate these points, the analytical results are applied to the two experiments with NPIE and PIE plasmas.

Stimulated scattering instability in a relativistic plasma

We study the stimulated scattering instabilities of an intense linearly polarized electromagnetic wave (EMW) in a relativistic plasma with degenerate electrons. Starting from a relativistic hydrodynamic model and the Maxwell's equations, we derive coupled nonlinear equations for low-frequency electron and ion plasma oscillations that are driven by the EMW's ponderomotive force. The nonlinear dispersion relations are then obtained from the coupled nonlinear equations which reveal stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), and modulational instabilities (MIs) of EMWs. It is shown that the thermal pressure of ions and the relativistic degenerate pressure of electrons significantly modify the characteristics of SRS, SBS, and MIs.

Nonlinear response and bistability of driven ion acoustic waves

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

Nonlinear oscillations of coalescing magnetic flux ropes.

An analytical model of highly nonlinear oscillations occurring during a coalescence of two magnetic flux ropes, based upon two-fluid hydrodynamics, is developed. The model accounts for the effect of electric charge separation, and describes perpendicular oscillations of the current sheet formed by the coalescence. The oscillation period is determined by the current sheet thickness, the plasma parameter β, and the oscillation amplitude. The oscillation periods are typically greater or about the ion plasma oscillation period. In the nonlinear regime, the oscillations of the ion and electron concentrations have a shape of a narrow symmetric spikes.

Jeans self gravitational instability of strongly coupled quantum plasma

The Jeans self-gravitational instability is studied for quantum plasma composed of weakly coupled degenerate electron fluid and non-degenerate strongly coupled ion fluid. The formulation for such system is done on the basis of two fluid theory. The dynamics of weakly coupled degenerate electron fluid is governed by inertialess momentum equation. The quantum forces associated with the quantum diffraction effects and the quantum statistical effects act on the degenerate electron fluid. The strong correlation effects of ion are embedded in generalized viscoelastic momentum equation including the viscoelasticity and shear viscosities of ion fluid. The general dispersion relation is obtained using the normal mode analysis technique for the two regimes of propagation, i.e., hydrodynamic and kinetic regimes. The Jeans condition of self-gravitational instability is also obtained for both regimes, in the hydrodynamic regime it is observed to be affected by the ion plasma oscillations and quantum parameter while in the kinetic regime in addition to ion plasma oscillations and quantum parameter, it is also affected by the ion velocity which is modified by the viscosity generated compressional effects. The Jeans critical wave number and corresponding critical mass are also obtained for strongly coupled quantum plasma for both regimes.

Electrostatic Ion Cyclotron and Ion Plasma Waves in a Symmetric Pair-Ion Plasma Cylinder

Complicated wave behavior observed in the cylindrical pair-ion (fullerene) experiments by Oohara and co-workers are now identified to be low harmonic ion cyclotron waves combined with ion plasma oscillations inherent to kinetic theory. The electrostatic dispersion equation derived is based on an approximation for the current from the exact solutions of the characteristic cylindrical geometry form of the Vlasov plasma equation in a uniform magnetized plasma cylinder surrounded by a larger metal boundary outside a vacuum gap, which thus differs from that in unbounded plasmas. Positive and negative ions, differing only in the sign of their charge, respond to a potential in the same time scale and cooperate to reflect the enhanced kinetic orbital behaviors to the macroscopic propagation characteristics. In addition, the experimental value of the Larmor radius (comparable to the discharge radius but small enough to make the analytic approximation useful) makes higher harmonic ion cyclotron effects both observable and calculable with the appropriate approximation for the kinetic theory.

Nonlinear multiplicative ion-plasma oscillations

Equations of self-consistent ion dynamics in plasma are solved by the method of separation of variables. New solutions describing nonlinear multiplicative ion-plasma oscillations are found. These oscillations are periodic in coordinate and time and have constant amplitude.

Verification of particle simulation of radio frequency waves in fusion plasmas

Radio frequency (RF) waves can provide heating, current and flow drive, as well as instability control for steady state operations of fusion experiments. A particle simulation model has been developed in this work to provide a first-principles tool for studying the RF nonlinear interactions with plasmas. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic equation. This model has been implemented in a global gyrokinetic toroidal code using real electron-to-ion mass ratio. To verify the model, linear simulations of ion plasma oscillation, ion Bernstein wave, and lower hybrid wave are carried out in cylindrical geometry and found to agree well with analytic predictions.

Stimulated scattering of electromagnetic waves carrying orbital angular momentum in quantum plasmas

We investigate stimulated scattering instabilities of coherent circularly polarized electromagnetic (CPEM) waves carrying orbital angular momentum (OAM) in dense quantum plasmas with degenerate electrons and nondegenerate ions. For this purpose, we employ the coupled equations for the CPEM wave vector potential and the driven (by the ponderomotive force of the CPEM waves) equations for the electron and ion plasma oscillations. The electrons are significantly affected by the quantum forces (viz., the quantum statistical pressure, the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron spin), which are included in the framework of the quantum hydrodynamical description of the electrons. Furthermore, our investigation of the stimulated Brillouin instability of coherent CPEM waves uses the generalized ion momentum equation that includes strong ion coupling effects. The nonlinear equations for the coupled CPEM and quantum plasma waves are then analyzed to obtain nonlinear dispersion relations which exhibit stimulated Raman, stimulated Brillouin, and modulational instabilities of CPEM waves carrying OAM. The present results are useful for understanding the origin of scattered light off low-frequency density fluctuations in high-energy density plasmas where quantum effects are eminent.

A theoretical and simulation study of the contact discontinuities based on a Vlasov simulation code

[1] Contact discontinuity (CD) is the simplest solution that can be obtained from the magnetohydrodynamics (MHD) Rankine-Hugoniot jump conditions. Due to the limitations of the previous kinetic simulation models, the stability of the CD has become a controversial issue in the past 10 years. The stability of the CD is reexamined analytically and numerically. Our theoretical analysis shows that the electron temperature profile and the ion temperature profile must be out of phase across the CD if the CD structure is to be stable in the electron time scale and with zero electron heat flux on either side of the CD. Both a newly developed fourth-order implicit electrostatic Vlasov simulation code and an electromagnetic finite-size particle code are used to examine the stability and the electrostatic nature of the CD structure. Our theoretical prediction is verified by both simulations. Our results of Vlasov simulation also indicate that a simulation with initial electron temperature profile and ion temperature profile varying in phase across the CD will undergo very transient changes in the electron time scale but will relax into a quasi-steady CD structure within a few ion plasma oscillation periods if a real ion-electron mass ratio is used in the simulation and if the boundary conditions allow nonzero heat flux to be presented at the boundaries of the simulation box. The simulation results of this study indicate that the Vlasov simulation is a powerful tool to study nonlinear phenomena with nonperiodic boundary conditions and with nonzero heat flux at the boundaries of the simulation box.

Fast oscillatory behavior of the excited xenon density in the discharge cells of a plasma display panel

Fast oscillation of the excited xenon density occurs universally after an electrical discharge in the cells of a plasma display panel. A theoretical model based on ion plasma oscillation simulates this oscillatory behavior of the excited xenon density reasonably well. The magnitude and lifetime of the excited xenon density in a metastable state depend highly on the electrode configuration. Particularly, T-type electrodes provide better generation and confinement of excited xenon atoms for an abundant emission of 173 nm ultraviolet light at a high level of efficiency.

Oblique Ion Two‐Stream Instability in the Foot Region of a Collisionless Shock

The electrostatic behavior of a collisionless plasma in the foot region of high Mach number perpendicular shocks is investigated through a two-dimensional linear analysis and electrostatic particle-in-cell (PIC) simulations. The simulations are double periodic and taken as a proxy for the situation in the foot region. The linear analysis for relatively cold unmagnetized plasmas with a reflected proton beam shows that the obliquely propagating Buneman instability is strongly excited. We also found that when the electron temperature is much higher than the proton temperature, the most unstable mode is the highly obliquely propagating ion two-stream instability excited through the resonance between ion plasma oscillations of the background protons and of the beam protons, rather than the ion acoustic instability that is dominant for parallel propagation. To investigate nonlinear behavior of the ion two-stream instability, we have made PIC simulations for the shock foot region in which the initial state satisfies the Buneman instability condition. In the first phase, electrostatic waves grow two-dimensionally by the Buneman instability to heat electrons. In the second phase, highly oblique ion two-stream instability grows to heat mainly ions. This result is in contrast to previous studies based on one-dimensional simulations, for which the ion acoustic instability further heats electrons. The present result implies that the overheating problem of electrons for shocks in supernova remnants is resolved by considering the ion two-stream instability propagating highly obliquely to the shock normal and that multidimensional analysis is crucial to understand the particle heating and acceleration processes in shocks.

Localized plasmons in quantum plasmas

We consider the nonlinear interactions between finite amplitude electron and ion plasma oscillations in a fermionic quantum plasma. Accounting for the quantum statistical electron pressure and the quantum Bohm potential, we derive a set of coupled nonlinear equations that govern the dynamics of modulated electron plasma oscillations (EPOs) in the presence of the nonlinear ion oscillations (NLIOs). We numerically study stationary solutions of our coupled nonlinear equations. We find that the quantum parameter H (equal to the ratio between the plasmonic and electron Fermi energy densities) introduces new features to the electron density and electric potential humps of localized NLIOs in the absence of EPOs. Furthermore, the nonlinear coupling between the EPOs and NLIOs gives rise to a new class of envelope solitons composed of bell shaped electric field envelope of the EPOs, which are trapped in the electron density hole (and an associated negative oscillatory electric potential) that is produced by the ponderomotive force of the EPOs. The knowledge of the localized plasmonic structures is of immense value for interpreting experimental observations in dense quantum plasmas.

Stimulated scattering instabilities of electromagnetic waves in an ultracold quantum plasma

The nonlinear interaction between a large-amplitude electromagnetic wave (EMW) and low-frequency electron and ion plasma oscillations in a quantum plasma is considered. By using the Maxwell equations and the quantum hydrodynamic equations, a system of equations, which shows the nonlinear couplings between the EMWs and the electrostatic plasma oscillations, is derived. The nonlinear mode coupled equations are then Fourier analyzed to obtain the dispersion relation which exhibits decay and modulational instabilities. The relevance of such an investigation of stimulated scattering of light off plasmons in ultracold quantum plasmas is noted.

Kinetic theory of acoustic wave in pair-ion plasmas

A theoretical analysis of the ion acoustic wave in pair-ion plasmas is presented using a kinetic model. It is shown that a small concentration of electrons in pair-ion plasmas can break down the quasineutrality in perturbed systems because the electron Debye length can become very large. In the limit 1⪡λDe2k2 (where λDe is the electron Debye length), the damping is reduced and hence the acoustic wave can be easily excited. The real frequency of acoustic wave can be larger than the ion plasma oscillation frequency in this case. But the decreasing number density of electrons can increase the Landau damping significantly in the limit λDe2k2⪡1. The results are discussed in comparison with the recent experimental and theoretical findings. It is pointed out that this investigation can be very useful for further research on pair-ion plasmas.

Graphical analysis of electron inertia induced acoustic instability

Recently, the practical significance of the asymptotic limit of me∕mi→0 for electron density distribution has been judged in a two-component plasma system with drifting ions. It is reported that in the presence of drifting ions with drift speed exceeding the ion acoustic wave speed, the electron inertial delay effect facilitates the resonance coupling of the usual fluid ion acoustic mode with the ion-beam mode. In this contribution the same instability is analyzed by graphical and numerical methods. This is to note that the obtained dispersion relation differs from those of the other known normal modes of low frequency ion plasma oscillations and waves. This is due to consideration of electron inertial delay in derivation of the dispersion relation of the ion acoustic wave fluctuations. Numerical calculations of the dispersion relation and wave energy are carried out to depict the graphical appearance of poles and positive-negative enegy modes. It is found that the electron inertia induced ion acoustic wave instability arises out of linear resonance coupling between the negative and positive energy modes. Characterization of the resonance nature of the instability in Mach number space for different wave numbers of the ion acoustic mode is presented.

Investigation of low-frequency waves in plasma-filled microwave oscillators

The excitation of microwave oscillations by an electron beam in a hybrid plasma waveguide—a slow-wave structure (a sequence of inductively coupled resonators) with a plasma-filled transport channel—is studied both experimentally and theoretically. It is shown that the governing role in the generation of microwaves and their transmission to a feeder line is played by the spatial and temporal plasma-density variations associated with low-frequency ion plasma oscillations. The microwave pressure gives rise to low-frequency plasma oscillations with a rise time shorter than their period. This nonlinear mechanism for the excitation of low-frequency oscillations has a threshold in terms of the microwave power. The unsteady character of the spatial distribution of the plasma density results in intermittent microwave generation and shortens the duration of microwave pulses.

Velocity shear-induced effects on electrostatic ion perturbations

Linear evolution of electrostatic perturbations in an unmagnetized electron–ion plasma shear flow is studied. New physical effects, arising due to the non-normality of linear dynamics are disclosed. A new class of nonperiodic collective mode with vortical motion of ions, characterized by intense energy exchange with the mean flow, is found. It is also shown that the velocity shear induces extraction of the mean flow energy by ion-sound waves and that during the shear-induced evolution the ion-sound waves turn eventually into ion plasma oscillations.

Comment on the thermoelectric term

It is shown that the thermoelectric term which appears as a source of fluctuating magnetic field B1 in unmagnetized nonuniform plasmas in the limit ωpe≪ω≪ωpe [where ωpi(ωpe) are ion (electron) plasma oscillation frequencies, respectively] is of smaller order. Therefore, the thermoelectric term does not seem to contribute to magnetic fluctuations linearly. The theory of magnetic field generation based on ion dynamics predicts the same order of magnitude of B1 which is experimentally observed.

Observation of spontaneously excited chaos-like ion plasma oscillations

An oscillation which behaves quite similarly to chaos under some conditions is observed to exist among ion plasma oscillations spontaneously excited in an ion beam–plasma system. There are two different states of the system, the ‘‘silent’’ and ‘‘chaotic’’ states, sensitively depending on the value of a direct current (DC) voltage VB, which determines the beam energy and is adopted as a control parameter here. In the chaotic state, a spontaneously excited ion plasma oscillation is observed to become chaotic. Here, the correlation dimension for the oscillation in the chaotic state is calculated to be 1.64±0.22. The result shows that an attractor for the oscillation has a low degree of freedom and a noninteger dimension.