Instability Of Acoustic Waves Research Articles

Instability analysis and face‐to‐face collision of dust acoustic waves in dusty plasmas: Perspective Jupiter environment

AbstractThe collisionless unmagnetized five components dusty plasmas have been considered to study the significance of the face‐to‐face collision of single‐ and multi‐solitons, phase shifts due to face‐to‐face collision, and instability of the dust acoustic waves in Jupiter's environment. To study the consequence of face‐to‐face collision extended Poincaré–Lighthill–Kuo method is used to derive the two‐sided nonlinear Korteweg–De Vries (KdV) equation. Besides, to investigate the dust acoustic wave's instability, the nonlinear Schrödinger equation has been derived following the procedure of Slathia et al. The multi‐soliton solutions are determined by employing the Hirota bilinear method. The concerned parameters in the issue play a crucial role in the phase shift (generated by the face‐to‐face collision); the collisional process of single‐, double‐, triple‐, and quadruple‐soliton; and the generation of dust acoustic solitons. Furthermore, the plasma parameters are crucial in the formation of dark solitons and envelop shocks.

Modulational instability of dust-ion acoustic waves in generalized (r, q) distributed electron dissipative plasmas

The modulational instability of the dust-ion acoustic waves in a dissipative dusty plasma system containing warm ions, generalized ( r , q ) distributed electrons, and immobile dust grains has been studied. The Krylov–Bogoliubov–Mitropolsky (KBM) perturbation method is employed to analyze the amplitude modulation of a monochromatic plane wave through the derivation of a nonlinear Schrödinger equation. This equation is solved analytically to determine the modulational instability region, and the corresponding dissipative rogue wave solution is obtained. The effects of various system parameters, such as the kinematic viscosity of the ions (υ), the wavenumber (k), the ion to electron temperature ratio ( σ i ), the unperturbed ion to electron density ratio (γ) as well as the electron distribution parameters: r and q, are investigated. The dependence of the amplitude of dissipated rogue waves on υ is discussed. It is found that various system parameters have significant effects on the features of dissipated rogue waves. The present investigation can be relevance to the electrostatic rogue structures in various cosmic dust-laden plasmas such as Saturn's F-ring.

Dust-ion acoustic rogue waves in six-component dusty plasma

In this work, we investigate the modulational instability of finite amplitude dust-ion acoustic nonlinear waves in a six-component cometary dusty plasma. Such plasma system is composed of Oxygen ion-pair, negative dust particles, kappa distributed light ions of Hydrogen, solar electrons and cometary electrons of the comet tail. By employing the standard reductive perturbation technique, a nonlinear Schrödinger-type equation is obtained. This equation governs the investigation of the modulational instability of finite amplitude dust-ion acoustic nonlinear waves. Our analysis shows two parametric domains, where the dust-ion acoustic waves are modulationally stable and unstable depending on the plasma configurational parameters. Within the unstable domain, rogue waves could be generated due to the nonlinear and dispersion properties of plasma system. The effects of some relevant plasma parameters on the profile of rogue waves are studied. The obtained results might be useful for better understanding the modulational instability of nonlinear plasma waves and formation of dust-ion acoustic rogue waves in space plasmas.

Absolute instability of acoustic wave in semiconductor plasma: relativistic effects

Present paper reports the impact of relativistic effects on the acoustic wave instability in the semiconductor plasma medium. The classical hydrodynamic model has been used to derive dispersion relation of acoustic wave. A close inspection of dispersion relation inclusive of the relativistic effects admits the possibility of propagation of four modes in the laser semiconductor plasma system under study. Analysis of all these modes has been done quantitatively as well as qualitatively as a function of laser pump field intensity and doping concentration of the medium. The subsequent numerical analysis is made with n-InSb at 77 K duly irradiated by a 1.06 µm Nd:YAG laser. Applied laser intensity is well below the damage threshold of the InSb crystal. The phase profile of observed modes confirms the existence of two co-propagating and two contra-propagating modes. The phase speed of I and IV modes are found to be augmented, whereas II and III modes are found to modify the gain profile of all the modes effectively. It is found that the propagation and amplification characteristics of all the modes get modified when relativistic effects are taken into account. It is found that proper selection of laser pump field intensity and carrier density plays a significant role in the favourable propagation and gain characteristics of the acoustic wave in the semiconductor plasma medium.

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.

Temporal Instability of Acoustic Wave in a Semiconductor Plasma Medium under Momentum Mismatched Condition

Temporal instability of acoustic wave is investigated in an infinite semiconductor plasma using classical hydrodynamic approach. We consider a homogeneous semiconductor placed in an external magnetic field. Dispersion and gain characteristics of acoustic wave generated in a piezoelectric semiconductor plasma medium with momentum mismatched situation are examined. Numerical analysis of qualitative nature of the four available modes infers that an endurable momentum mismatch modifies the spectra of acoustic wave significantly. Influence of pump field and doping profile on the dispersion and gain characteristics of all possible modes in the medium has been studied and reported. The result infers that the pump field and carrier density play significant roles as control parameters for the favourable propagation and gain characteristics of the acoustic wave in the medium. Presence of momentum mismatch is found to enhance the phase speed of highly unstable modes. These results may pave way to generate squeezed states, useful in optical communication system having operational wavelengths compatible with the spatial scales under consideration.

Modulational instability of dust-ion acoustic waves in the presence of generalized (r, q) distributed electrons

We have investigated the modulational instability (MI) of dust-ion acoustic waves in a dusty plasma model containing warm ions fluid, generalized (r, q) distributed electrons, and immobile dust grains. Using the Krylov-Bogoliubov-Mitropolsky method, the amplitude modulation of a monochromatic plane wave is analyzed through derivation of a nonlinear Schrödinger equation. The MI condition is calculated. Moreover, the effects of the plasma parameters such as the ion-to-electron temperature ratio, the wavenumber, and the unperturbed dust-to-electron number density ratio as well as the electron distribution dual parameters (r, q) are discussed. Our investigations have shown that the unstable region is bounded by two stable regions, i.e., two critical wavenumbers [kcl(lower) and kch(higher)] are found. The applications of the present theoretical study are briefly discussed in space physics whether positive or negative dust grains are enclosed.

Modulational instability of acoustic waves in a dusty plasma with nonthermal electrons and trapped ions

Abstract In the present work, employing the nonlinear field equations of a hot dusty plasma in the presence of nonthermal electrons and trapped ions, we studied the amplitude modulation of nonlinear waves in such a plasma medium by use of the reductive perturbation method and obtained the modified nonlinear Schrodinger equation. The modulational instability (MI) was investigated and the effects of the proportion of the fast electrons (α), the trapping parameter (b) and the plasma parameters such as the dust-ion temperature ratio (σd), the partial unperturbed electron to dust density (δ), and the ion-electron temperature ratio (σi) on it was discussed. For the investigation of modulational instability problems three parameters P/Q, Kmax and Γmax play the central role. The variations of these parameters with the wave number k and the other physical parameters are discussed and the possibility of occurence of modulational instability is indicated.

Two stream ion acoustic wave instability in warm dense plasmas

In this study we investigate the two-ion stream instability of plasma with a generalized Fermi-Dirac equation of state (EoS) for electron fluid. We use a hydrodynamic set of evolution equations for electron-ion plasma in order to obtain the linearized set of equations from which the dispersion relation of the plasma is obtained in the presence of ion acoustic wave instability. It is remarked that changes in the electron plasma fluid parameters such as the chemical potential and electron fluid temperature have fundamental effects on the growth rate of ion acoustic waves instability. It is however found that the plasma degeneracy has rather more significant effect on the two stream instability phenomenon. The generalized equation of state of electrons used in this research is valid for a wide density-temperature regimes of plasmas relevant to both laboratory as well as astrophysical environments including high-energy density fusion plasmas and fully degenerate compact stellar plasmas. We believe that using such a wide scope of plasma EoS provides a broader view of underlying physical mechanisms in plasma dynamics and instabilities and better understanding of astrophysical harsh plasma environments.

Impact of Relativistic Electron Beam on Hole Acoustic Instability in Quantum Semiconductor Plasmas

Abstract We studied the influence of the classical relativistic beam of electrons on the hole acoustic wave (HAW) instability exciting in the semiconductor quantum plasmas. We conducted this study by using the quantum-hydrodynamic model of dense plasmas, incorporating the quantum effects of semiconductor plasma species which include degeneracy pressure, exchange-correlation potential and Bohm potential. Analysis of the quantum characteristics of semiconductor plasma species along with relativistic effect of beam electrons on the dispersion relation of the HAW is given in detail qualitatively and quantitatively by plotting them numerically. It is worth mentioning that the relativistic electron beam (REB) stabilises the HAWs exciting in semiconductor (GaAs) degenerate plasma.

Ions shear flow and electron field-aligned current produce ion acoustic waves in the oxygen-hydrogen ionospheric plasma

It is pointed out that the ion acoustic waves (IAWs) are excited either by field-aligned shear flows or electron parallel current in oxygen-hydrogen (O-H) plasma of upper ionosphere. The purely growing D'Angelo instability becomes ion acoustic wave instability in the presence of second kind of ions within the framework of multi-fluid plasma model. On the other hand, kinetic theory is used to show that the growth rate of current driven ion acoustic wave overcomes the ion Landau damping. Out of four real roots corresponding to negative shear flow, the two roots can become unstable. Thus, ion acoustic waves at different but very low real frequencies appear in O-H plasma of ionosphere due to parallel shear flow and current, which is in agreement with satellite observations.

Modulational instability of electrostatic waves in a magnetized dusty plasma with kappa distributed electrons

The modulational instability of dust-ion acoustic wave (DIAW) and dust-ion cyclotron wave (DICW) is investigated in a magnetized plasma containing static dust particles. The static dust particles can be positively or negatively charged, while ions are taken to be dynamic and inertialess electrons follow the kappa distribution in a magnetized dusty plasma. The nonlinear Schrödinger equation is derived to study the amplitude modulation of obliquely propagating electrostatic waves in a magnetized dusty plasma using the Krylov-Bogoliubov-Mitropolsky method. The dispersive and nonlinear coefficients, i.e., P and Q of nonlinear Schrödinger equation, are obtained which depend on the dust charge concentration, the magnetic field intensity, dust charge polarity, angle of wave propagation, and spectral index kappa for the nonthermal electrons. The modulationally stable and unstable regions of DIAW and DICW are investigated numerically, and the illustration of contour plots of product PQ with wave propagation angle θ and critical wave number kc is also presented. It is found that DIAW and DICW become modulationally unstable at low values of wave number k for negatively charged dust particles in comparison with positively charged dust particles or without dust particles case in a magnetized plasma. The stable region for DIAW, whose wave frequency now depends also on wave propagation angle in a magnetized plasma, is found to be increased in comparison with the unmagnetized plasma case. The observations and existence of positively and negatively charged dust particles in different regions of space plasmas and in laboratory experiments are also pointed out.

Ion acoustic wave instabilities and nonlinear structures associated with field-aligned flows in the F-region ionosphere

It is shown that the inhomogeneous field-aligned flow of heavier ions into the stationary plasma of the upper ionosphere produces very low frequency (of the order of a few Hz) electrostatic unstable ion acoustic waves (IAWs). This instability is an oscillatory instability unlike D'Angelo's purely growing mode. The growth rate of the ion acoustic wave (IAW) corresponding to heavier ions is due to shear flow and is larger than the ion Landau damping. However, the ion acoustic waves corresponding to non-flowing lighter ions are Landau damped. It is found that even if D'Angelo's instability condition is satisfied, the unstable mode develops its real frequency in this coupled system. Hence, the shear flow of one type of ions in a bi-ion plasma system produces ion acoustic wave activity. If the density non-uniformity is taken into account, then the drift wave becomes unstable. The coupled nonlinear equations for stationary ions “a,” flowing ions “b,” and inertialess electrons are also solved using the small amplitude limit. The solutions predict the existence of the order of a few kilometers electric field structures in the form of solitons and vortices, which is in agreement with the satellite observations.

Weakly dissipative dust-ion acoustic wave modulation

The modulational instability of dust-ion acoustic (DIA) waves in an unmagnetized dusty plasma is investigated in the presence of weak dissipations arising due to the low rates (compared to the ion oscillation frequency) of ionization recombination and ion loss. Based on the multiple space and time scales perturbation, a new modified nonlinear Schrödinger equation governing the evolution of modulated DIA waves is derived with a linear damping term. It is shown that the combined action of all dissipative mechanisms due to collisions between particles reveals the permitted maximum time for the occurrence of the modulational instability. The influence on the modulational instability regions of relevant physical parameters such as ion temperature, dust concentration, ionization, recombination and ion loss is numerically examined. It is also found that the recombination frequency controls the instability growth rate, whereas recombination and ion loss make the instability regions wider.

Publisher's Note: “Modulational instability of electrostatic acoustic waves in an electron-hole semiconductor quantum plasma” [Phys. Plasmas 21, 022107 (2014)

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Effects of superthermal electrons and negatively (positively) charged dust grains on dust-ion acoustic wave modulation

The modulational instability of dust-ion acoustic (DIA) waves is studied in an unmagnetized dusty plasma comprising arbitrarily charged dust particles, adiabatic fluid ions, and electrons satisfying a kappa (κ) distribution. By using the multiple space and time scales perturbation, a nonlinear Schrodinger (NLS) equation is derived, and then the existence along with the stability of wave packets are discussed in the parameter space of two oppositely charged dust and ion temperature over a range of values of electron superthermality. It is found that the transition from stable dark solitons to unstable bright ones shifts to the smaller wavelength regions in a way that depends on the increase of superthermality index κ. In this case, a narrower range (in spatial extension) of the envelope solitons is observed. It is also found that the instability growth rate reduces, due to the electron superthemality. Furthermore, positive dust concentration enhances the instability region, whereas more populations of negative dust grains may control or suppress one.

Modulational instability of electrostatic acoustic waves in an electron-hole semiconductor quantum plasma

The modulational instability of quantum electrostatic acoustic waves in electron-hole quantum semiconductor plasmas is investigated using the quantum hydrodynamic model, from which a modified nonlinear Schrodinger equation with damping effects is derived using the reductive perturbation method. Here, we consider the combined effects of quantum recoil, quantum degenerate pressures, as well as the exchange-correlation effect standing for the electrons (holes) spin. The modulational instability for different semiconductors (GaAs, GaSb, and InP) is discussed. The collision between electron (hole) and phonon is also investigated. The permitted maximum time for modulational instability and the damping features of quantum envelope solitary wave are all determined by the collision. The approximate solitary solution with damping effects is presented in weak collision limit. The damping properties were discussed by numerical method.

Modulational instability of electron-acoustic waves in magnetized plasma in presence of excess superthermal electrons

Modulational instability of finite amplitude electron-acoustic waves along external magnetic field is investigated in plasma composed of inertial cold electrons, hot inertialess superthermal electrons and stationary ions. Reductive perturbation technique is used to derive the three-dimensional nonlinear Schrodinger equation which governs the slow modulation of electron acoustic wave packets. Accounting for effects of hot electron to cold electron number density ratio (α), normalized electron-cyclotron frequency (ω c ) as well as the electron superthermal parameter (κ e ) new regimes for modulational instability of electron acoustic waves are obtained and analyzed. The presence of superthermal electrons modifies conditions for modulational instability to occur, as well as associated threshold and growth rate. Concentration of superthermal electrons (i.e., the deviation from a Maxwellian electron distribution) may control or even suppress modulational instability. In contrast to one-dimensional unmagnetized plasmas, instability growth rate is shown to suppress increasing values of k.

Multi-dimensional instability of multi-ion acoustic solitary waves in a degenerate magnetized plasma

The multi-dimensional instability of obliquely propagating multi-ion acoustic (MIA) solitary structures was studied theoretically by the small-k (long wavelength plane wave) perturbation expansion technique in an ultra-relativistic degenerate magnetized plasma, which consists of inertia less electrons, inertial ions and stationary arbitrarily charged heavy ions. The Zakharov–Kuznetsov equation is derived by the reductive perturbation method and its solitary wave solution is analyzed. The basic properties of small but finite-amplitude MIA solitary waves have been modified significantly by the combined effects of the degenerate electron number density, heavy ion number density, external magnetic field and obliqueness. The underlying physics of the MIA solitary waves, which are relevant to space plasma situations, and the basic features, such as amplitude, width and growth rate, are briefly discussed.

Mathematical model for the initiation of intense acoustic vibrations in a ramjet ejector combustor and their suppression by resonators

A mathematical model is constructed to describe the mechanism of intense acoustic vibrations in a ramjet ejector combustor based on the instability of natural acoustic vibrations in the combustor due to jet exhaust. The feedback necessary for the onset of instability of acoustic waves is taken to be their interaction with the unsteady gas motion induced by the vortex sheet from the trailing edges of the combustor. An algorithm for suppressing intense acoustic vibrations in the combustor using resonators is developed. The obtained theoretical results are compared with the results of experimental studies.