Current-driven Ion-acoustic Instability Research Articles

A two-dimensional numerical study of ion-acoustic turbulence

We investigate the linear and nonlinear evolution of the current-driven ion-acoustic instability in a collisionless plasma via two-dimensional (2-D) Vlasov–Poisson numerical simulations. We initialise the system in a stable state and gradually drive it towards instability with an imposed, weak external electric field, thus avoiding physically unrealisable super-critical initial conditions. A comprehensive analysis of the nonlinear evolution of ion-acoustic turbulence (IAT) is presented, including the detailed characteristics of the evolution of the particles’ distribution functions, (2-D) wave spectrum and the resulting anomalous resistivity. Our findings reveal the dominance of 2-D quasi-linear effects around saturation, with nonlinear effects, such as particle trapping and nonlinear frequency shifts, becoming pronounced during the later stages of the system's nonlinear evolution. Remarkably, the Kadomtsev–Petviashvili (KP) spectrum is observed immediately after the saturation of the instability. Another crucial and noteworthy result is that no steady saturated nonlinear state is ever reached: strong ion heating suppresses the instability, which implies that the anomalous resistivity associated with IAT is transient and short-lived, challenging earlier theoretical results. Towards the conclusion of the simulation, electron-acoustic waves are triggered by the formation of a double layer and strong modifications to the particle distribution induced by IAT.

Linear theory of current driven ion acoustic instability at the distance 0.3 to 1 AU from the Sun

Several kinds of instabilities are often observed in the solar wind. We studied the linear theory of the current-driven electrostatic ion acoustic instability at frequencies near the ion cyclotron frequency at distances from the Sun over 0.3 to 1 AU. The properties of current driven electrostatic ion-acoustic instability are investigated. The instability parameters, such as angular wave frequency, the critical drift velocity and the growth rate are calculated. We used the dispersion relation in hot magnetized plasma to calculate the current driven ion acoustic instability properties. To determine the critical drift velocity and the growth rate a full numerical solution of the dispersion relation equation is carried out. Since the growth rate of instability depends on the wave normal angle, the drift velocity of the electron along the magnetic field and the ion thermal cyclotron radius, the calculation is carried out for ranging of the wave normal angles, drift velocities and ion thermal cyclotron radius. The results show that the growth rate of instability increases with increasing distance from the Sun. The growth rate of instability increases with decreasing the wave normal angle, but the critical drift velocity decreases with decreasing the wave normal angle.

Kinetic Theory of Ion Acoustic Waves Observed at Comet 67P/Churyumov–Gerasimenko

Abstract This work presents the resonance interaction of ion acoustic waves with the cometary plasma as observed at comet 67P/Churyumov–Gerasimenko. The plasma is comprised of cold, warm, and suprathermal electron populations and water ions such that the quasineutrality is satisfied. The cold electron population is found to play a dominant role in the damping of the waves, and its maximum Landau damping rate is observed when it is 2% of the total electron density in the system. It is determined that lowering the cold electron density supports the current-driven ion acoustic instability at a relatively lower drift speed of the warm and suprathermal electron species. In the absence of cold electrons, the wave phase speed does not change by populating the high-energy suprathermal electron species, therefore, the Landau damping rate of both warm and suprathermal electrons increases by increasing their respective densities. The growth rate of the current-driven ion acoustic instability decreases by elevating the concentration of suprathermal electrons in the case of drifting warm and stationary suprathermal electrons. In the case of stationary warm and drifting suprathermal electrons, the elevated density of suprathermal electron instead favors the instability.

Numerical study of the two-species Vlasov–Ampère system: Energy-conserving schemes and the current-driven ion-acoustic instability

In this paper, we propose energy-conserving Eulerian solvers for the two-species Vlasov–Ampère (VA) system and apply the methods to simulate current-driven ion-acoustic instability. The two-species VA systems are of practical importance in applications, and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy.The main goal of this paper is to generalize our previous work for the single-species VA system [9] and Vlasov–Maxwell (VM) system [8] to the two-species case. The methodologies proposed involve careful design of temporal discretization and the use of the discontinuous Galerkin (DG) spatial discretizations. We show that the energy-conserving time discretizations for single-species equations [9,8] can also work for the two-species case if extended properly. Compared to other high order schemes, we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size, making them very attractive for long time simulations. We benchmark our algorithms on a test example to check the one-species limit, and the current-driven ion-acoustic instability. To simulate the current-driven ion-acoustic instability, a slight modification for the implicit method is necessary to fully decouple the split equations. This is achieved by a Gauss–Seidel type iteration technique. Numerical results verified the conservation and performance of our methods. Finally, we remark that the schemes in this paper can be readily extended to applications when the models take more general form, such as the multi-species VM equations.

Ion temperature anisotropy effects on the dispersion relation and threshold conditions of a sheared current-driven electrostatic ion-acoustic instability with applications to the collisional high-latitude F-region

Plasma instabilities play a important role in producing small-scale irregularities in the ionosphere. In particular, current-driven electrostatic ion-acoustic (CDEIA) instabilities contribute to high-latitude F-region electrodynamics. Ion temperature anisotropies with enhanced perpendicular temperature often exist in the high-latitude F-region. In addition to temperature anisotropies, ion velocity shears are observed near auroral arc edges, sometimes coexisting with thermal ion upflow processes and field-aligned currents (FAC). We investigated whether ion temperature anisotropy lowers the threshold conditions required for the onset of sheared CDEIA instabilities. We generalised a dispersion relation to include ion thermal anisotropy, finite Larmor radius corrections and collisions. We derived new fluid-like analytical expressions for the threshold conditions required for instability that depend explicitly on ion temperature anisotropy. We studied how the instability threshold conditions vary as a function of the wave vector direction in both fluid and kinetic regimes. We found that, despite the dampening effect of collisions on ion-acoustic waves, ion temperature anisotropy lowers in some cases the threshold drift requirements for a large range of oblique wave vector angles. More importantly, realistic ion temperature anisotropies contribute to reducing the instability threshold velocity shears that are associated with small drift thresholds, for modes propagating almost perpendicularly to the geomagnetic field. Small shear thresholds that seem to be sustainable in the ionospheric F-region are obtained for low-frequency waves. Such instabilities could play a role in the direct generation of field-aligned irregularities in the collisional F-region that could be observed with the Super Dual Auroral Radar Network (SuperDARN) array of high-frequency radars. These modes would be very sensitive to the radar probing direction since they are restricted to very narrow angular intervals. The ion temperature anisotropy is an important parameter that needs to be considered in the studies of sheared and collisional CDEIA waves and instabilities in the high-latitude F-region.

Nonlinear current-driven ion-acoustic instability driven by phase-space structures

The nonlinear stability of current-driven ion-acoustic waves in collisionless electron–ion plasmas is analyzed. Seminal simulations from the 1980s are revisited. Accurate numerical treatment shows that subcritical instabilities do not grow from an ensemble of waves, except very close to marginal stability and for large initial amplitudes. Further from marginal stability, one isolated phase-space structure can drive subcritical instabilities by stirring the phase-space in its wake. Phase-space turbulence, which includes many structures, is much more efficient than an ensemble of waves or an isolated hole for driving subcritically particle redistribution, turbulent heating and anomalous resistivity. Phase-space jets are observed in subcritical simulations.

A Twenty-Year Review of Time-Delay Feedback Control and Recent Developments

The delayed feedback control (DFC) method has been invented in 1992 (this year is a 20th anniversary). Following the original paper by Pyragas [Phys. Lett. A, 170, 421, 1992], more than 1500 papers devoted or related to the DFC have been published. Many different modifications of the algorithm have been proposed, and significant achievements are attained in the theory of the DFC. Although this theory is non-trivial, currently the mechanism of the DFC action is rather well understood, and the main limitations of the algorithm are established. The DFC has been successfully implemented in a number of experimental systems of different physical nature. The aim of this talk is to present a brief review of important modifications of the DFC algorithm, significant theoretical results and experimental implementations attained during the past twenty years. The recent results concerning adaptive modifications of the DFC and analytical achievements based on phase reduction of time-delay systems will be discussed as well. 1. Brief review of experimental and theoretical results The DFC algorithm [1] is a simple, robust, and efficient method to stabilize unstable periodic orbits (UPOs) in chaotic systems. Nowadays, it becomes one of the most popular methods in the chaos control research [2]. The method allows a noninvasive stabilization of UPOs of dynamical systems in the sense that the control force vanishes when the target state is reached. The DFC algorithm is reference-free and makes use of a control signal K∆s(t) obtained from the difference ∆s(t) = s(t) − s(t − τ) between the current state s(t) of the system and the state of the system s(t−τ) delayed by one-period τ of the target orbit. The UPO may become stable under the appropriate choice of feedback strength K. Note that only the stability properties of the orbit are changed, while the orbit itself and its period remain unaltered. The controlled system can be treated as a black box, since the method does not require any exact knowledge of either the form of the periodic orbit or the system’s equations. The method is particularly appealing for experimentalists, since one does not need to know anything about the target orbit beyond its period τ. The DFC algorithm is notably superior to other control methods in fast dynamical systems, since it does not require any realtime computer processing. Successful implementation of the DFC algorithm has been attained in diverse experimental systems, including electronic chaotic oscillators, mechanical pendulums, lasers, gas discharge systems, a current-driven ion acoustic instability, a chaotic Taylor-Couette flow, chemical systems, high-power ferromagnetic resonance, helicopter rotor blades, and a cardiac system. (cf. [3] for review up to 2006). An important practical application of the DFC algorithm has been recently demonstrated by Yamasue et al. [4]. The authors have successfully implemented the DFC method in an atomic force microscope and managed to stabilize cantilever oscillations. As a result, they remove artifacts on a surface image. Another interesting application of the DFC for the analysis of bifurcations of periodic states in experimental systems has been recently considered in Ref. [5]. A reach variety of modifications of the DFC has been suggested in order to improve its performance (cf. [3]). Here we mention only the most important modification known as an extended DFC (EDFC), which has been introduced in Ref. [6]. The authors improved an original DFC scheme by using an information from many previous states of the system. The EDFC scheme achieves stabilization of UPOs with a greater degree of instability [7, 8]. The theory of DFC is difficult because the delayed feedback induces an infinite number of degrees of freedom. Even linear analysis of such systems is complicated due to the infinite number of Floquet exponents characterizing the stability of controlled orbits. Nevertheless, some analytical approaches have been developed in vicinity to various bifurcations of periodic orbits, such as the period doubling bifurcation [9, 10], the subcritical Hopf bifurcation [11, 12, 13] and the Nejmark-Sacker (discrete Hopf) bifurcation [14]. In 1997 Nakajima [15, 9] proved the so-called odd number limitation, which states that any UPOs with an odd number of real Floquet multipliers greater than unity can never be stabilized by any DFC technique. This limitation has been commonly accepted and intensively discussed in the literature. However, in 2007, Fiedler at al [16] have shown by a simple example that this limitation does not hold in general for autonomous systems (note that for non-autonomous systems it remains valid in general). Recently, a modified (corrected) proof of the limitation for autonomous systems has been presented by Hooton and 2012 International Symposium on Nonlinear Theory and its Applications NOLTA2012, Palma, Majorca, Spain, October 22-26, 2012

Low frequency electrostatic waves in weakly inhomogeneous magnetoplasma modeled by Lorentzian (kappa) distributions

Linear dispersion relations for electrostatic waves in spatially inhomogeneous, current-carrying anisotropic plasma, where the equilibrium particle velocity distributions are modeled by various Lorentzian (kappa) distributions and by well-known bi-Maxwellian distribution, are presented. Spatial inhomogeneities, assumed to be weak, include density gradients, temperature gradients, and gradients (shear) in the parallel (to the ambient magnetic field) flow velocities associated with the current. In order to illustrate the distinguishing features of the kappa distributions, stability properties of the low frequency (lower than ion cyclotron frequency) and long perpendicular wavelength (longer than ion gyroradius) modes are studied in detail, and the results are contrasted with those for the bi-Maxwellian distribution. Specific attention is given to the drift waves, the current-driven ion-acoustic waves in the presence of velocity shear, the velocity shear-driven ion-acoustic modes, and the ion temperature-gradient driven modes. Growth rates of the drift wave instability and the current-driven ion-acoustic instability are reduced from their values for bi-Maxwellian distribution due to larger ion Landau damping rates associated with the kappa distributions. For the same reason, excitation conditions for these two instabilities are more stringent in the case of the kappa distributions. Growth rates of the velocity shear-driven ion-acoustic instability and the ion temperature-gradient driven instability are reduced from their values for bi-Maxwellian distribution as a consequence of the reduced adiabatic response of the electrons to the electrostatic potential perturbation. Frequencies of the drift waves and the ion-acoustic waves are also reduced in kappa-distribution plasmas due to the reduced adiabatic response of the electrons.

An assessment of how a combination of shears, field-aligned currents and collisions affect F-region ionospheric instabilities

Abstract.We present an in depth study of the fluid limit of a kinetically derived collisional, current-driven instability that includes shears in the field-aligned currents as well as collisions. We show how the theory presented here generalizes other theories, including the collisionless current-driven electrostatic ion acoustic instability and its sheared collisionless version. We offer a low-frequency generalization of the zero frequency ion shear driven instability by minimizing the relative drift magnitude as well as the shears themselves. We discuss the implication of our theoretical framework both for strongly field-aligned modes and modes where the wavevectors have arbitrary angles with respect to the ambient magnetic field. We discuss the results in terms of F-region irregularity observations of coherent echoes by ionospheric radars.

Dynamical behavior of the motions associated with the nonlinear periodic regime in a laboratory plasma subject to delayed feedback

Time-delayed feedback is applied to the motions associated with the nonlinear periodic regime generated due to current-driven ion acoustic instability; this is a typical instability in a laboratory plasma, and the dynamical behavior is experimentally investigated using delayed feedback. A time-delayed autosynchronization method is applied. When delayed feedback is applied to the nonlinear periodic orbit, the periodic state changes to various motions depending on the control parameters, namely, the arbitrary time delay and the proportionality constant. Lyapunov exponents are calculated in order to examine the dynamical behavior.

Theory of the anomalous resistivity of a randomly inhomogeneous plasma

The effect of random density inhomogeneities on the anomalous plasma resistivity caused by a current-driven ion acoustic instability is considered. It is shown that, under certain conditions, dissipation due to the plasma inhomogeneity can be more efficient than that due to nonlinear effects. The scenario under consideration can occur in the low-density corona of a high-density Z-pinch.

Dynamical control of the chaotic state of the current-driven ion acoustic instability in a laboratory plasma using delayed feedback

Controlling chaos caused by the current-driven ion acoustic instability is attempted using delayed feedback, i.e., the time-delay auto synchronization (TDAS) method introduced by Pyragas [Phys. Lett. A 170, 421 (1992)] with flexibility. When the control parameter of the system Vm is increased, the current-driven ion acoustic instability is excited, and then, the system demonstrates chaotic oscillation in a certain range of the parameter. When the electronic circuit to control chaos based on the TDAS method is applied to the chaotic regime, the chaotic orbit changes to a periodic one maintaining the instability, that is, the chaotic state caused by the current-driven ion acoustic instability is well controlled using the TDAS method. Furthermore, it is shown that controlling chaos can be achieved when the delay time τ is chosen to be close to a fundamental frequency of the unstable periodic orbit embedding in the chaotic system.

Observation of Synchronization of Two Chaotic Oscillators in Plasma

The dynamical behavior of two coupled chaotic oscillators caused by current-driven ion acoustic instability is experimentally studied. It is found that when two oscillators are interacting with the mediation of a central mesh grid, and the DC potential applied to either of the two oscillators is varied gradually while maintaining coupling, the two oscillators synchronize in a certain region.

Controlling chaos in the current-driven ion acoustic instability

Control of intermittent chaos caused by the current-driven ion acoustic instability is attempted and the controlling mechanism is investigated. When a small negative dc voltage is applied to the chaotic system as a perturbation, the system changes from a chaotic state to a periodic state while maintaining the instability, indicating that the chaotic state caused by the ion acoustic instability is well controlled by applying a small negative dc voltage. A hysteresis structure is observed on the V–I curve of the mesh grid to which the negative dc voltage to control is applied. Furthermore, when a negative dc voltage is applied to the state which shows a laminar structure existing under same experimental conditions, the system becomes chaotic via a bifurcation. Driven-chaos is excited when a negative dc voltage is applied to the laminar state. Applying a small negative dc voltage leads to controlling intermittent chaos while exciting driven-chaos.

Low frequency oscillations in a plasma with spatially variable field-aligned flow

The effects of a transverse gradient in the plasma flow velocity parallel to the ambient magnetic field are analyzed. A transverse velocity gradient in the parallel ion flow, even in small magnitude, can increase the parallel phase speed of the ion-acoustic waves sufficiently to reduce ion Landau damping. This results in a significantly lower threshold current for the current driven ion acoustic instability. Ion flow gradients can also give rise to a new class of ion cyclotron waves via inverse cyclotron damping. A broadband wave spectrum with multiple cyclotron harmonics is possible. A combination of the multiple cyclotron harmonic waves can result in spiky electric field structures with their peaks separated by an ion cyclotron period. A spatial gradient in the parallel electron flow is also considered but it is found to play a minimal role in the low frequency regime. Relevance of these to natural plasma environments is discussed.

Current-driven dust ion-acoustic instability in a collisional dusty plasma with charge fluctuations

The extended fluid analysis of the excitation of dust ion-acoustic waves (DIAWs) in a collisional dusty plasma [Merlino, IEEE Trans. Plasma Sci. 25, 60 (1997)] is reconsidered to include self-consistently the fluctuations in the charges of the dust grains, which liberate or capture electrons and protons. The numerical results show that the dust charge fluctuations can have a significant influence on the excitation of the DIAW and may deeply modify its nonlinear features.

Non-Maxwellian shape of electron distribution function in ion acoustic turbulence

In a DC discharge plasma system, in which two meshes are installed, the current-driven ion acoustic instability is excited when a de potential V/sub m/ is applied to one of them. When the instability fully grows, the system reaches a very turbulence state, the so-called ion acoustic turbulence. The experimental measurement of energy distribution function of electrons in ion acoustic turbulence measured by the Langmuir probe shows a non-Maxwellian nature along with electron heating.

Control of Intermittent Chaos Caused by Applying a Pulse

The control of intermittent chaos caused by the current-driven ion acoustic instability is attempted. It is found that when a positive pulse is applied to one of two mesh grids which are installed in a plasma, the instability is suddenly suppressed. On the other hand, when a negative pulse is applied, the system changes from chaotic orbits to periodic orbits while maintaining the instability, showing that the chaotic state caused by the instability is well controlled by applying a negative pulse.

On the realization of the current-driven dust ion-acoustic instability

The current-driven dust ion-acoustic instability in a collisional dusty plasma is studied. The effects of dust-charge variation, electron and ion capture by the dust grains, as well as various dissipative mechanisms leading to the changes of the particles momenta, are taken into account. It is shown that the threshold for the excitation of the dust ion-acoustic waves can be high because of the large dissipation rate induced by the dusts.

Current-driven dust ion-acoustic instability in a collisional dusty plasma with a variable charge

The analysis of the excitation of the dust ion-acoustic (DIA) waves in a collisional dusty plasma by Merlino [IEEE Trans. Plasma Sci. 25, 60 (1997)] has been extended to include the dust charge fluctuations. A damping term arises in the growth rate. It is due to the grain charge variations.