Twisted electrostatic ion-cyclotron waves in dusty plasmas

Theoretical and experimental studies of low-frequency electrostatic waves in plasmas containing negatively charged dust grains are described. The presence of charged dust is shown to modify the properties of ion-acoustic waves and electrostatic ion-cyclotron waves through the quasineutrality condition even though the dust grains do not participate in the wave dynamics. If the dust dynamics is included in the analysis, new “dust modes” appear—dust acoustic and dust cyclotron modes. The results of laboratory experiments dealing with dust ion acoustic (DIA) waves and electrostatic dust ion cyclotron (EDIC) waves are shown. These modes are more easily excited in a plasma containing negatively charged dust. Finally, observations of dust acoustic (DA) waves are presented and measurements of the dispersion relation are compared with one obtained from fluid theory.

It is shown that finite amplitude electrostatic ion cyclotron (EIC) waves can parametrically decay into daughter EIC waves and kinetic Alfvén waves. Since the current associated with the latter is d.c. in the EIC time scale, it can linearly excite EIC waves when the amplitude of the Alfvén waves is sufficiently high. This provides a mechanism for the simultaneous existence of EIC and Alfvén fluctuations. Application of the theory in the auroral zone of the ionosphere is discussed.

A 50‐MHz Doppler radar interferometer and a 138‐MHz Doppler radar were operated from Kennedy Space Center to study 3‐m and 1‐m plasma waves associated with two shaped‐charged barium releases from Wallops Island, Virginia, on May 13, 1986. During the first release, interferometer and Doppler power spectral studies showed the existence of short‐lived (<2 s) coherent 3‐m and 1‐m waves centered near 30 Hz. The 3‐m waves were located about 100 km above the release on a magnetic field line in contact with the first release. No radar backscatter was observed by the radars during the second release. The coherent 30‐Hz radar echoes associated with the first barium release are very similar to some natural occurring auroral radar echoes that are believed to be generated by resistive current‐driven electrostatic ion cyclotron waves. A detailed linear dispersion analysis of electrostatic ion cyclotron (EIC) waves showed that only 3‐m O+ EIC waves were unstable for field‐aligned electron drifts greater than 0.7υthe at the altitude of 510 km in a multispecies (O+, NO+, or similarly O2+) ionospheric plasma. We interpret the 30‐Hz waves seen by the two radars far above the release as strong electrostatic ion cyclotron waves generated by intense field‐aligned currents associated with the barium stream acting like an MHD generator coupled to the ionosphere.

Emissions that appear to have been electrostatic ion cyclotron (EIC) waves have been observed at low altitude in the diffuse aurora by a sounding rocket payload. The rocket was launched from Poker Flat, Alaska, at ∼2030 MLT. The flight successively traversed ∼70 km of the diffuse aurora, a dark region, and a quiet 40 kR auroral arc. In the diffuse aurora, peaks were observed in the power spectrum of the electric field at frequencies near the hydrogen and oxygen ion cyclotron frequencies. Doppler shift and polarization analyses have been performed using EIC wave spectrum parameters derived from linear theory. Both analyses indicated that these emissions had properties consistent with those expected for H+ and O+ EIC waves. Taken together, the two analyses indicated that both emission bands were due to waves propagating both up and down the field line and eastward parallel to the poleward boundary of the diffuse aurora. The large local cold plasma density and resulting large Landau damping require that the source be local. Free energy for the waves was apparently available in the 5 µA/m² downward parallel current density which was inferred from the magnetometer data. The presence of the waves indicates that this current was being carried by less than 2% of the plasma, presumably in the form of a field aligned beam of electrons with energies of a few eV.

The excitation of electrostatic ion cyclotron (EIC) waves is studied in a single-ended Q machine in a two-ion component plasma (Ca/sup +/ and K/sup +/). Over a large range of relative concentrations of Ca/sup +/ and K/sup +/ ions, two modes are excited with frequencies greater than the respective cyclotron frequencies of the ions. The results are discussed in terms of a fluid theory of electrostatic ion cyclotron waves in a two-ion component plasma.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Emissions that have properties consistent with electrostatic ion cyclotron (EIC) waves have been observed at low altitude in the diffuse aurora by a sounding rocket payload. Peaks were observed in the power spectrum of the electric field near the hydrogen and oxygen ion cyclotron frequencies. Doppler shift and polarization analyses have been performed using EIC wave parameters derived from linear theory. Both analyses indicated that these emissions had properties consistent with those expected for H+ and O+ EIC waves. The two analyses indicated that both emission bands were due to waves propagating eastward parallel to the poleward boundary of the diffuse aurora. The large local cold plasma density and resulting Landau damping require that the source be local. Magnetometer data indicated the presence of a downward parallel current density of 5μA/m². Sufficient free energy for the waves was available from this current, although the waves were observed frequently at altitudes where the ion‐neutral collision frequency exceeded the oxygen cyclotron frequency.

The nonlinear features of dust-acoustic waves (DAWs) propagating in a multicomponent, collisional, magnetized dusty plasma whose constituents are negative dust grains, superthermal ions, and electrons are investigated. The hydrodynamic fluid equations are reduced to a damped Zakharov–Kuznetsov (DZK) equation, using the reductive perturbation technique. The DZK equation is solved using both the generalized $$(G^{{\prime }}/G)$$ –expansion method and the Painleve analysis method. Each method gives a class of solutions. This indicates that these methods are sufficient to give all possible solutions of the DZK equation. These solutions successfully describe different kinds of nonlinear waves such as explosive, soliton, shocklike, periodical, and cnoidal waves. Additionally, the effects of different plasma parameters such as relative densities and temperatures as well as superthermality parameters of ions and electrons on the behavior of the obtained diverse waves are investigated. The relevance of the present investigation can be used to understand the cosmic dust-laden plasmas.

We have studied the instability of electrostatic ion-cyclotron waves in collisional magnetized two-ion component plasma (light positive K + ions and heavy positive Cs + ions). An ion beam propagating through collisional magnetized plasma containing electrons and two positive ion components drives electrostatic ion cyclotron (EIC) waves to instability via Cerenkov interaction. Analytical expressions & numerical calculations have been carried out for the frequency and growth rate of ion cyclotron waves for two EIC wave modes for existing experimental parameters, and it is found that the unstable mode frequency does not depend on electron collision frequency, while the growth rate is increased linearly with the electron collision frequency. Moreover, as the light ion concentration is increased, the frequency of the heavy ion mode moves closer to its gyrofrequency. Similarly, the frequency of the light ion mode approaches the light ion cyclotron frequency as the heavy ion concentration is increased. It is also found that the normalized unstable mode frequencies remains unchanged with electron collision frequencies, while the growth rate is increased linearly with the electron collision frequencies. In addition, the unstable mode frequencies are found to be dependent on the magnetic field strengths.

Theoretical models for Mach cones in magnetized dusty plasmas of Saturn’s rings are presented. Dispersion properties of different types of longitudinal and transverse waves (viz. dust–acoustic waves, fast and slow dust–magnetoacoustic waves) in magnetized dusty plasmas are presented. Numerical results are presented for Vd/Vp (> 1), which determines the existence of Mach cones as well as their opening angles [θ = sin-1(Vp/Vd)], where Vd is the dust boulder speed and Vp ( = ω/k) is the phase speed of short or long wavelength disturbances in magnetized dusty plasmas. It is found that short wavelength (in comparison with the ion gyroradius) modified dust–acoustic waves and long wavelength slow dust–magnetoacoustic waves (DMW) are viable candidates for the formation of Mach cones in the equatorial plane of Saturn’s rings. They should be observed by on board instruments of the CASSINI spacecraft that is supposed to enter Saturn’s orbit in July 2004.

Results are presented of a particle simulation study of the electrostatic ion-cyclotron (EIC) instability driven by a parallel ion beam. The results of this simulation study demonstrate the nonlinear consequences of nonresonant EIC waves destabilized by an ion beam parallel to the magnetic field for the case of a large beam velocity. As a consequence of the instability, it is shown that the beam ions are heated strongly in the perpendicular direction and suffer a strong anomalous friction via EIC waves which leads to the beam slowing down. Simulation results indicate that the anomalous slowing down of beam ions by EIC waves is much larger than that from the classical electron-drag, and the perpendicular collision frequency measured from perpendicular beam heating is as large as that from Bohm diffusion. It is concluded that the ion beam driven EIC wave is a viable mechanism for the transfer of ion parallel beam energy to the ion perpendicular energy.

The nonlinear dynamics of dust-acoustic waves (DAWs) in a six-component magnetized cometary dusty plasma comprising cold oxygen ions, kappa-distributed hot hydrogen ions, hot solar electrons, cold cometary photoelectrons and negatively charged dust grains are theoretically investigated. Using the reductive perturbation method (RPM), a modified Korteweg–de Vries (mKdV) equation is derived to explore dust-acoustic solitary structures via Sagdeev pseudo-potential analysis. The modulation instability (MI) of DAWs is examined by transforming the mKdV into a nonlinear Schrödinger equation (NLSE), enabling the study of both bright and dark envelope solitons and various breather modes (Akhmediev, Kuznetsov-Ma and Peregrine or rogue wave). The influence of plasma parameters on the formation and evolution of these structures is systematically analyzed. A dynamical system approach to the NLSE reveals finite and supernonlinear DAWs through phase plane analysis. Additionally, the introduction of a weak external periodic force demonstrates multistability in the wave dynamics. These results provide important insights into the nonlinear excitation and stability of magnetosonic DAWs in cometary dusty plasma.

A summary of recent experimental work performed by our group at the University of Iowa on current-driven dust ion acoustic (DIA) and dust acoustic (DA) waves is given. A discussion of relevant theoretical work is also included.

For the critical values of the parameters q and V, the work (Samanta et al. in Phys. Plasma 20:022111, 2013b) is unable to describe the nonlinear wave features in magnetized dusty plasma with superthermal electrons. To describe the nonlinear wave features for critical values of the parameters q and V, we extend the work (Samanta et al. in Phys. Plasma 20:022111, 2013b). To extend the work, we derive the modified Kadomtsev-Petviashvili (MKP) equation for dust ion acoustic waves in a magnetized dusty plasma with q-nonextensive velocity distributed electrons by considering higher order coefficients of ϵ. By applying the bifurcation theory of planar dynamical systems to this MKP equation, the existence of solitary wave solutions of both types rarefactive and compressive, periodic travelling wave solutions and kink and anti-kink wave solutions is proved. Three exact solutions of these above waves are determined. The present study could be helpful for understanding the nonlinear travelling waves propagating in mercury, solar wind, Saturn and in magnetosphere of the Earth.

Associated with the large heat conduction in the solar wind is a skewing of the ion and electron distribution functions. It is shown that this collisional skewing of the electron distribution function can linearly excite collisionless ion-acoustic, electrostatic ion cyclotron, magnetoacoustic, and ion cyclotron waves in the steady-state solar wind even though the net equilibrium current parallel to B is zero. The initial growth rates for these unstable waves are derived, and the effectiveness of the wave-particle interactions in heating the ions and in altering the thermal and electrical conductivities is discussed.

The coupling of electrostatic ion cyclotron and ion acoustic waves is examined in three component magnetized plasma consisting of electrons, protons, and alpha particles. In the theoretical model relevant to solar wind plasma, electrons are assumed to be superthermal with kappa distribution and protons as well as alpha particles follow the fluid dynamical equations. A general linear dispersion relation is derived for such a plasma system which is analyzed both analytically and numerically. For parallel propagation, electrostatic ion cyclotron (proton and helium cyclotron) and ion acoustic (slow and fast) modes are decoupled. For oblique propagation, coupling between the cyclotron and acoustic modes occurs. Furthermore, when the angle of propagation is increased, the separation between acoustic and cyclotron modes increases which is an indication of weaker coupling at large angle of propagation. For perpendicular propagation, only cyclotron modes are observed. The effect of various parameters such as number density and temperature of alpha particles and superthermality on dispersion characteristics is examined in details. The coupling between various modes occurs for small values of wavenumber.