There is a quickly increasing wealth of experimental data on so-called dusty plasmas i. e. ionized gases or usual plasmas that contain micron sized charged particles. Interest in these structures is driven both by their importance in many astrophysical as well as commercial situations. Among them are linear and nonlinear wave phenomena. We consider the influence of dust charge fluctuations on stability of the ion-acoustic waves when the stream of particles is present. It is assumed that all grains of dust have equal masses but charges are not constant in time-they may fluctuate in time. The dust charges are not really independent of the variations of the plasma potentials. All modes will influence the charging mechanism, and feedback will lead to several new interesting and unexpected phenomena. The charging of the grains depends on local plasma characteristics. If the waves disturb these characteristic, then charging of the grains is affected and the grain charge is modified, with a resulting feedback on the wave mode. In case considering here, when temperature of electrons is much greater then the temperature of the ions and temperature of electrons is not great enough for further ionization of the ions, we show that stability of the acoustic wave depends only one phenomenological coefficient.
It is shown that the grain mass fluctuation, which is due to the grain sputtering by the attracted ions, may be at the root of a new instability in infinite, unmagnetized and homogeneous dusty plasmas. The growth rate is determined in the framework of two plasma models, viz., a cold and electron depleted plasma, and a plasma where electrons and ions are taken Boltzmannian. This instability may affect the Jeans as well as the agglomeration instabilities.
In this paper we consider the influence of dust charge fluctuations on damping of the dust-ion-acoustic waves. Fluid approximation of longitudinal electrostatic waves in unmagnetized plasmas is considered. We show that for a weak acoustic wave the attenuation depends on a phenomenological charging coefficient.
Within the kinetic approach velocity and charge distributions of grains in stationary dusty plasmas are calculated and the relations between the effective temperatures of such distributions and plasma parameters are established. It is found that the effective temperature which determines the velocity grain distribution could be anomalously large due to the action of accelerating ionic bombarding force. The possibility to apply the results obtained to the explanation of the increasing grain temperature in the course of the Coulomb-crystal melting by reduction of the gas pressure is discussed. T…
The grains immersed in plasma get eroded by the ions falling onto them. As a consequence, they exhibit self-consistent mass fluctuations due to perturbations in the plasma charging currents. The grain mass is then a dynamical variable. The modifications in the plasma dielectric properties are investigated and new ultra-low frequency modes are shown to exist in the plasma.
It is well known that the form of grain size distribution strongly influences the linear dielectric response of a dusty plasma. In previous results [IEEE Trans. Plasma Sci. 29, 182 (2001)], it was shown that for a class of size distributions, there is an equivalence to a Lorentzian distribution of mono-sized particles. The electrostatic response to a slowly moving test charge, using a second order approximation can then be found [Phys. Lett. A 305, 79 (2002)]. It is also well known [Phys. Plasmas 10, 3484 (2003)] that the dynamical charging of grains in a dusty plasma enhances the shielding of…
We consider the influence of dust charge fluctuations on damping of the dust-ion-acoustic waves. It is assumed that all grains have equal masses but charges are not constant in time - they may fluctuate in time. The dust charges are not really independent of the variations in the plasma potentials. All modes will influence the charging mechanism, and feedback will lead to several new interesting and unexpected phenomena. The charging of the grains depends on local plasma characteristics. If the waves disturb these characteristic, then charging of the grains is affected and the grain charge is …
The influence of an inhomogeneous screened electric field on the charging of dust grains in a thermal dusty plasma is studied. The electric field of charged grains is considered within the cell approach, where the problem is reduced to a one-particle one. Within the model of quasichemical equilibrium, which is generalized to the case of an inhomogeneous screened electric field, we obtain the value of mean charge of dust grains, the distribution function of grains over charges, and the variance of this distribution. We also give the criterion of an inhomogeneity of the electric field and show t…
Within the approximation of dominant charging collisions the explicit microscopic calculations of the Fokker-Planck kinetic coefficients for highly-charged grains moving in plasma are performed. It is shown that due to ion absorption by grain the friction coefficient can be negative and the appropriate threshold value of the grain charge is found. The stationary solutions of the Fokker-Planck equation with the velocity dependent kinetic coefficient are obtained and the considerable deviation of such solutions from the Maxwellian distribution is established.
The impacts of dust density inhomogeneity and dust size distribution (DSD) on linear dust acoustic (DA) wave propagation have been investigated theoretically in an inhomogeneous unmagnetized dusty plasma having powerlaw DSD. Two different types of wave modes, viz. slow and fast mode, are found to propagate in this inhomogeneous medium. It is shown that the linear dispersion characteristics of the DA waves are substantially affected by the DSD and density inhomogeneity. Also, it is found that the phase velocity increases with increasing dust density.
An investigation of dust-acoustic solitary waves in unmagnetized dusty plasma whose constituents are inertial charged dust grains, Boltzmannian electrons and nonthermal ions has been conducted. The pseudo potential as well as the reductive perturbation methods have been used in high and small amplitude limits. The existence of solitary waves of a positive as well as a negative potential is reported.
Nonlinear frequency response analysis is a widely used method for determining system dynamics in the presence of nonlinearities. In dusty plasmas, the plasma-grain interaction (e.g., grain charging fluctuations) can be characterized by a single particle nonlinear response analysis, while grain-grain nonlinear interactions can be determined by a multi-particle nonlinear response analysis. Here, a machine learning-based method to determine the equation of motion in the nonlinear response analysis for dust particles in plasmas is presented. Searching the parameter space in a Bayesian manner allow…
The void, which is a dust-free region inside the dust cloud in the plasma, results from a balance of the electrostatic force and the ion drag force on a dust particulate. The ion drag force having numerous forms, some of which are based on models whereas others are driven from first principles. To explain the generation of voids, Avinash et al.[K. Avinash, A. Bhattacharjee, and S. Hu, AIP.CP649, III ICPDP, (2002)p121]proposed a time-dependent nonlinear model that describes the void as a result of an instability. We augment this model by incorporating the grain drift and by replacing the ion-dr…
The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the inter--grain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the modulational instability of the carrier wave due to self--interaction. The stability profile depends explicitly on the form of the electric and magnetic fields in the plasma sheath. The long term evolut…
Expressions for the ion and electron thermal forces acting on a charged grain, suspended in a weakly ionized plasma subject to temperature gradients, are derived. The main emphasize is on the conditions pertinent to the investigations of complex (dusty) plasmas in gas discharges. Estimates show that for the electron temperature gradients $\sim {\mathcal O}$(eV/cm) typically encountered in laboratory gas discharges, the electron thermal force can become an important player among other forces acting on micron-size grains.
A radiofrequency glow discharge plasma, which is polluted with a certain number of dusty grains, is studied. In addition to various dusty plasma phenomena, several specific colloidal effects should be considered. We focus on radiometric forces, which are caused by inhomogeneous temperature distribution. Aside from thermophoresis, the role of temperature distribution in dusty plasmas is an open question. It is shown that inhomogeneous heating of the grain by ion flows results in a new photophoresis like force, which is specific for dusty discharges. This radiometric force can be observable unde…
Ground state structures of finite, cylindrically confined two-dimensional Yukawa systems composed of charged superparamagnetic dust grains in an external magnetic field are investigated numerically, using molecular dynamic simulations and lattice summation methods. The ground state configuration of the system is identified using, as an approximation, the experimentally obtained shape of the horizontal confinement potential in a classical single layer dusty plasma experiment with non-magnetic grains. Results are presented for the dependence of the number density and lattice parameters of the du…
An analytical model is presented for the description of nonlinear dust-ion-acoustic waves propagating in an unmagnetized, collisionless, three component plasma composed of electrons, ions and inertial dust grains. The formulation relies on a Lagrangean approach of the plasma fluid model. The modulational stability of the wave amplitude is investigated. Different types of localized envelope electrostatic excitations are shown to exist.
The standard nonlinear Schrödinger equation (NLSE) is one of the elegant equations to find the information about the modulational instability criteria of dust-ion-acoustic (DIA) waves (DIAWs) and associated DIA rogue waves (DIARWs) in a three-component dusty plasma medium having inertialess super-thermal kappa distributed electrons, and inertial warm positive ions and negative dust grains. It can be seen that under the consideration of inertial warm ions along with inertial negatively charged dust grains, the plasma system supports both fast and slow DIA modes. The charge state and number dens…
Instabilities of ion-acoustic waves in a dusty plasma with electron-drift, collisional, and dust charge fluctuations effects, have been investigated. The regimes are clearly marked out where the theory is applicable. The critical electron-drift velocity required to drive the instability is predicted. It is also shown that electron thermal conductivity and charged grains concentration enhance the growth of the ion-acoustic mode whereas ion-viscosity, ion-thermal conductivity, and dust charge fluctuations have a stabilizing effect.
The plasma is an ionized gas that responses collectively to any external (or internal) perturbations. Introducing micron-sized solid dust grains into plasma makes it more interesting. The solid grains acquire large negative charges on their surface and exhibits collective behavior similar to the ambient plasma medium. Some remarkable features of the charged dust grain medium (dusty plasma) allow us to use it as a model system to understand some complex phenomena at a microscopic level. In this perspective paper, the author highlights the role of dusty plasma experiments as a learning tool at u…
It is demonstrated that low frequency shear modes in a strongly coupled, inhomogeneous, dusty plasma can grow on account of an instability involving the dynamical charge fluctuations of the dust grains. The instability is driven by the gradient of the equilibrium dust charge density and is associated with the finite charging time of the dust grains. The present calculations, carried out in the generalized hydrodynamic viscoelastic formalism, also bring out important modifications in the threshold and growth rate of the instability due to collective effects associated with coupling to the compr…
Charges on the dust grains immersed in a plasma vary in time. We follow the hydrodynamic approach to obtain dispersion relations for some low frequency electrostatic modes, taking into account charge fluctuation on the dust. We have used the description of the one dimensional fully electromagnetic particle code. There exists one spatial dimension and three velocity components. This is usually referred to as a model. Our analysis shows that the presence of the dust grains causes different effects in different frequency regimes.
Star formation occurs in dark molecular regions where the number density of hydrogen nuclei, nH, exceeds 10^4 cc and the fractional ionization is 10^-7 or less. Dust grains with sizes ranging up to tenths of microns and perhaps down to tens of nanometers contain just under one percent of the mass. Recombination on grains is important for the removal of gas phase ions, which are produced by cosmic rays penetrating the dark regions. Collisions of neutrals with charged grains contribute significantly to the coupling of the magnetic field to the neutral gas. Consequently, the dynamics of the grain…
The dispersion relation of kinetic Alfvén wave in inertial regime is studied in a three component non-degenerate streaming plasma. A lin- ear dispersion relation using fluid- Vlasov equation for quantum plasma is also derived. The quantum correction CQ raised due to the insertion of Bohm potential in Vlasov model causes the suppression in the Alfven wave frequency and the growth rates of instability. A number of analytical expressions are derived for various modes of propagation. It is also found that many system parameters, i.e, streaming velocity, dust charge, num- ber density and quantum co…
It is shown that absorption of ions by the dust grain may reduce the effective translational temperature of the dust component below the ambient gas temperature.
A simple minimally perturbative method is introduced which provides the ability to experimentally measure both the radial confining potential and the interaction potential between two individual dust particles, levitated in the sheath of a radio-frequency (RF) argon discharge. In this technique, a single dust particle is dropped into the plasma sheath to interact with a second individual dust particle already situated at the system's equilibrium point, without introducing any external perturbation. The resulting data is analyzed using a method employing a polynomial fit to the particle displac…
The structure of a discharge across a magnetic field in a dusty plasma is analysed. The dust macroparticles are negatively charged, but are unmagnetized because of their high mass. The electrons are highly magnetized, and the ions have intermediate magnetization. This results in different transport rates of the different species across the magnetic field. Depending on the size of the magnetic field, and the relative charge on the different species, the dust grains can be the dominant current carrier. The space charge clouds near the electrodes will then be determined by the relative mobility o…
We study the secondary electron emissions induced by the impact of electrons on dust grains and the resulting dust charging processes in the nonequilibrium dusty plasma with power-law distributions. We derive new expressions of the secondary emitted electron flux and the dust charging currents that are generalized by the power-law q-distributions, where the nonlinear core functions are numerically studied for the nonextensive parameter q. Our numerical analyses show that the power-law q-distribution of the primary electrons has a significant effect on the secondary emitted electron flux as wel…
The collective dynamics of annulus dusty plasma formed between a co-centric conducting (non-conducting) disk and ring configuration is studied in a strongly magnetized radio-frequency (rf) discharge. A superconducting electromagnet is used to introduce a homogeneous magnetic field to the dusty plasma medium. In absence of the magnetic field, dust grains exhibit thermal motion around their equilibrium position. The dust grains start to rotate in anticlockwise direction with increasing magnetic field (B $>$ 0.02 T), and the constant value of the angular frequency at various strengths of magnetic…
We examine linear dust acoustic waves (DAWs) in a dusty plasma with strongly correlated dust grains, and discuss possibility of a twisted DA vortex beam carrying orbital angular momentum (OAM). For our purposes, we use the Boltzmann distributed electron and ion density perturbations, the dust continuity and generalized viscoelastic dust momentum equations, and Poisson's equation to obtain a dispersion relation for the modified DAWs. The effects of the polarization force, strong dust couplings, and dust charge fluctuations on the DAW spectrum are examined. Furthermore, we demonstrate that the D…
In this paper, the collective dynamics of the large aspect ratio dusty plasma is studied over a wide range of discharge parameters. An inductively coupled diffused plasma, which creates an electrostatic trap to confine the negatively charged grains, is used to form a large volume (or large aspect ratio) dusty plasma at low pressure. For introducing the dust grains into the potential well, a unique technique using a secondary DC glow discharge plasma is employed. The dust dynamics is recorded in a 2-dimension (2D) plane at a given axial location. The dust fluid exhibits wave like behavior at lo…
The basic features of dust-acoustic (DA) waves (DAWs) in four component dusty plasma system (containing inertial cold and hot dust grains, inertialess non-extensive ions and electrons) have been theoretically investigated by deriving the nonlinear Schrödinger equation. The analytic analysis under consideration demonstrates two types of modes, namely, fast and slow DA modes. The unstable domain for the fast DA mode, which can be recognized by the critical wave number ($k_c$), gives rise to the DA rogue waves (DARWs). It is observed that the amplitude and width of the DARWs are significantly mod…
Dust particles immersed within a plasma environment, such as those found in planetary rings or cometary environments, will acquire an electric charge. If the ratio of interparticle potential energy to average kinetic energy is high enough the particles will form either a 'liquid' structure with short-range ordering or a crystalline structure with long-range ordering. Since their discovery in laboratory environments in 1994, such crystals have been the subject of a variety of experimental, theoretical, and numerical investigations. Laboratory experiments analyzing the behavior of dust grains in…
Motivated by experiments on the generation of streaming plasmas in high energy density facilities, industrial setups, and fundamental dusty plasma research the plasma polarization around a test charge in streaming plasmas is considered. The induced charge density distribution of plasma constituents is discussed for the subsonic, sonic, and supersonic regime. Also, it is shown that the plasma polarization in the vicinity of the test charge shows different scaling in subsonic and supersonic regimes.
A comprehensive parametric study of plasma-grain interaction for non-Maxwellian streaming ions in steady-state employing particle-in-cell simulations is delineated. Instead of considering the inter-grain interaction potential to be the linear sum of isolated grain potentials, we incorporate the numerical advancement developed fully for grain shielding by including nonlinear contributions from the plasma and shadowing effect. The forces acting on grains versus inter-grain distance, streaming velocity of the ions, and impact of trapped ions density (number) are characterized for non- Maxwellian …
We present a fully nonlinear theory for dust acoustic (DA) shocks and DA solitary pulses in a strongly coupled dusty plasma, which have been recently observed experimentally by Heinrich et al. [Phys. Rev. Lett. 103, 115002 (2009)], Teng et al. [Phys. Rev. Lett. 103, 245005 (2009)], and Bandyopadhyay et al. [Phys. Rev. Lett. 101, 065006 (2008)]. For this purpose, we use a generalized hydrodynamic model for the strongly coupled dust grains, accounting for arbitrary large amplitude dust number density compressions and potential distributions associated with fully nonlinear nonstationary DA waves.…
Dusty plasma crystals have traditionally been observed and studied in radio frequency (RF) discharge plasmas and their formation in a DC glow discharge plasma remains experimentally challenging. We report the first ever observation of a stable dusty plasma Coulomb crystal in the cathode sheath region of a DC glow discharge plasma. The observations are made in the DPEx device where crystals of mono-disperse Melamine Formaldehyde grains are produced in the background of an Argon plasma. The crystalline nature of the structure is confirmed through a host of measurements that includes the radial p…
A two-dimensional dust crystal levitated in the sheath of a modified Gaseous Electronics Conference (GEC) reference cell is manipulated by heating or cooling the lower electrode. The dust charge is obtained from top-view pictures of the crystal using a previously developed analytical model. By assuming a simple force balance, and measuring the radial confining force, the vertical electric field profile in the sheath is reconstructed. The dust crystal is shown to levitate on the plasma side of the Bohm point. Finally, it is shown that the ion drag plays an important role in the vertical force b…
The paper reports on the dynamics of a 3-dimensional dusty plasma in a strong magnetic field. An electrostatic potential well created by a conducting or non-conducting ring in the rf discharge confines the charged dust particles. In the absence of the magnetic field, dust grains exhibit a thermal motion about their equilibrium position. As the magnetic field crosses a threshold value (B $>$ 0.02 T), the edge particles start to rotate and form a vortex in the vertical plane. At the same time, the central region particles either exhibit thermal motion or $\vec{E} \times \vec{B}$ motion in the ho…
In this paper we introduce an algebraic form of the dispersion relation for a non ideal inhomogeneous dusty plasma in order to improve drastically the calculation of the drift instability growth rate. This method makes use of the multipole approximation of the Z dispersion function, previously published, and valid for the entire range. A careful analysis of the solutions spectra of this kind of polynomial equation permits us to calculate easily the growth rate of the drift instability for the ion-dust and dust acoustic mode. The value of the parallel to magnetic field wavelength for which the …
A systematic numerical study of wake potential and ion density distribution of a single grain in streaming ions under the influence of the magnetic field applied along flow is presented. Strong magnetic field introduces ion focus depletion behind grain facilitating the entrance of electrons far away in the downstream towards the grain. It is shown that the magnetic field suppresses the amplitude of wake potential and modifies the ion density distribution substantially. The wake peak potential and position characteristics, and density distribution of plasma constituents in the presence of magne…
We study the nonlinear propagation of dust-ion acoustic (DIA) solitary waves in an unmagnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev-Petviashivili Burgers (KPB) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the KPB equation is obtained and its properties are analysed with different plasma nu…
A viscous dusty plasma containing Kappa distributed electrons, positive warm viscous ions and constant negatively charged dust grains with viscosity have been considered to study the modes of dust ion acoustic waves (DIAWs) theoretically and numerically. The derivations and basic features of shock and solitary waves with different plasma parameters like Mach number, finite temperature coefficient, unperturbed dust streaming velocity, kinematic viscosity of dust etc. of this DIAWs mode have been performed. Considering the dynamical equation from Korteweg de Vries(KdV) equation, a phase portrait…
Structural changes of self-organized vortices in Jupiter atmospheres such as Great Red Spot (GRS) and White Ovals are demonstrated using an electrostatically bounded charged dust cloud in an unbounded streaming plasma as the prototype for various driven-dissipative complex flow systems in nature. Using a 2D hydrodynamic model, the steady state flow solutions are obtained for the volumetrically driven dust cloud in a bounded domain of aspect-ratio of 1.5 relevant to the current size of GRS and a driving sheared ion flow similar to the part of zonal jets streaming through the GRS. These nonlinea…
In this paper, by comparing the time scales associated with the velocity relaxation and correlation time of the random force due to dust charge fluctuations, memory effects in the velocity relaxation of an isolated dust particle exposed to the random force due to dust charge fluctuations are considered, and the velocity relaxation process of the dust particle is considered as a non-Markovian stochastic process. Considering memory effects in the velocity relaxation process of the dust particle yields a retarded friction force, which is introduced by a memory kernel in the fractional Langevin eq…
A rigorous theoretical investigation is made to study the characteristics of dust-acoustic (DA) waves (DAWs) in an electron depleted unmagnetized opposite polarity dusty plasma system that contains super-thermal ($κ$-distributed) ions, mobile positively and negatively charged dust grains for the first time. The reductive perturbation method is employed to obtain the NLSE to explore the modulational instability (MI) conditions for DAWs as well as the formation and characteristics of gigantic rogue waves. The nonlinear and dispersion properties of the dusty plasma medium are the prime reasons be…
The theoretical description of complex (dusty) plasmas requires multiscale concepts that adequately incorporate the correlated interplay of streaming electrons and ions, neutrals, and dust grains. Knowing the effective dust-dust interaction, the multiscale problem can be effectively reduced to a one-component plasma model of the dust subsystem. The goal of the present publication is a systematic evaluation of the electrostatic potential distribution around a dust grain in the presence of a streaming plasma environment by means of two complementary approaches: (i) a high precision computation o…
The nonlinear propagation of small but finite amplitude dust ion-acoustic waves (DIAWs) in an ion-beam driven plasma with Boltzmannian electrons, positive ions and stationary charged dust grains, is studied by using the standard reductive perturbation technique (RPT). It is shown that there exist two critical values $(γ_{c1}$ and $γ_{c2})$ of ion-beam to ion phase speed ratio $(γ)$, beyond which the beam generated solitons are not possible. The effects of the parameters, namely $γ$, the ratio of the ion-beam to plasma ion density $(μ_{i})$, the dust to ion density ratio $(μ_{d})$ as well as th…
A 2D hydrodynamical model is developed and analyzed for the steady state of a driven-dissipative dust clouds confined in an azimuthally symmetric toroidal system which is in dynamic equilibrium with background unbounded streaming plasma. Its numerical solution not only confirms the analytical structure of the driven dust vortex flow in linear limit as reported in previous analysis, but also shows how the dust vortices are strongly affected by the nonlinear convection of the flow itself. Effects of various system parameters including external driving field and Reynolds number (Re) are investiga…
Dust Dynamics Simulations utilizing a dynamical screening approach are performed to study the effect of ion-streaming on the self-organized structures in a three-dimensional spherically confined complex (dusty) plasma. Varying the Mach number M - the ratio of ion drift velocity to the sound velocity, the simulations reproduce the experimentally observed cluster configurations in the two limiting cases: at M=0 strongly correlated crystalline structures consisting of nested spherical shells (Yukawa balls) and, for M\geq1, flow-aligned dust chains, respectively. In addition, our simulations revea…
Collective response of the plasma medium is well known and has been explored extensively in several contexts. The single particle response is typically treated as collisional interactions leading to dissipative effects. In this manuscript a 2D molecular dynamics (MD) simulation of dusty plasma with Yukawa interactions amidst dust grains have been considered in a strongly coupled regime. It has been shown that disturbances induced in the crystal by introducing highly charged particle elicit both collective and single particle responses. The single particle collisional interaction often generate…
A new method called `Configurational Temperature' is introduced in the context of dusty plasma, where the temperature of the dust particles, submerged in the plasma, can be measured directly from the positional information of the individual dust particles and the interaction potential between the dust grains. This method does not require the velocity information of individual particles which is a key parameter to measure the dust temperature in the conventional method. The technique is initially tested using two dimensional OpenMP parallel Molecular Dynamics and Monte-Carlo simulation and then…
The nature of long-range interactions between dust grains in plasma is discussed. The dust grain interaction potential within a cell model of dusty plasma is introduced. The attractive part of intergrain potential is described by multipole interaction between two electro-neutral cells. This allowed us to draw an analogy with molecular liquids where the attraction between molecules is determined by dispersion forces. The main ideas of the fluctuation theory for electrostatic field in a cell model are formulated, and the dominating contribution to the attractive part of intergrain potential is o…
We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any fluid wave. The wave itself can be quite general--sound waves, magnetosonic waves, epicyclic oscillations, and Brunt-Väisälä oscillations each generate instabilities, for example. We derive a simple expression for the growth rates of these "resonant drag instabilities" (RDI). This expression (i) illustrates why such instabilities are so virulent and generic…
