N. N. Rao

DUST -ACOUSTIC WAVES IN DUSTY PLASMAS

New acoustic waves originating from a balance of dust particle inertia and plasma pressure are investigated. It is shown that these waves can propagate linearly as a normal mode in a dusty plasma, and non-linearly as supersonic solitons of either positive or negative electrostatic potential.

Relativistic nonlinear effects in plasmas

Abstract The purpose of this article is to present a review of the nonlinear effects associated with relativistic electron-mass variation and the ponderomotive force in unmagnetized as well as magnetized plasmas. Many high-frequency waves can become unstable with respect to the electron-mass modulation and the excitation of low-frequency density fluctuations. The nonlinear equations which govern the evolution of the modulationally unstable waves are derived. The phenomena of soliton formation, radiation collapse, and profile modification are investigated. Finite amplitude theories of the envelope solitons are reviewed. In a multidimensional situation, the electromagnetic waves can undergo self-focusing. The use of the variational methods allows one to calculate the nonlinear wavenumber and radius of the self-focused laser beams. Analytical solutions for the self-trapped radiation and the three-dimensional relativistic solitons are obtained. It is found that magnetized plasmas can support the propagation of new types of ultrarelativistic electromagnetic waves. The modulational instability of the latter is analyzed. Furthermore, it is shown that the relativistic ponderomotive force in a magnetized plasma can produce large amplitude field-aligned electrostatic potentials which can effectively accelerate particles to very high energies. Finally, we consider the nonlinear propagation of intense electromagnetic waves in electron-positron plasmas. Possible applications in inertial fusion, beat-wave particle accelerator, rf heating of magnetically confined plasmas, and pulsar radiation are pointed out.

Magnetoacoustic modes in a magnetized dusty plasma

The existence of various types of (fast) magnetoacoustic modes in different frequency regimes in a magnetized dusty plasma consisting of electrons, ions and dust particles is investigated. The analysis is carried out using an effective two-fluid MHD-like model which allows for the non-frozen motion of the component fluids. For frequencies much smaller than the dust particle gyro- frequency, we obtain a magnetoacoustic mode that is a generalization of the usual compressional fast hydromagnetic wave in an electron—ion plasma. In the higher-frequency regimes, we show the existence of two new types of modes called ‘Dust-magnetoacoustic waves’. Both modes are accompanied by compressional magnetic field and plasma number density perturbations, and are the electromagnetic generalizations of the dust-acoustic waves in an unmagnetized dusty plasma with thermal electrons and ions. For a two- component plasma, all three modes degenerate into the same fast magneto- acoustic wave found in the usual electron—ion plasmas. We also obtain another novel type of magneto-acoustic mode called a ‘dust—ion-magneto- acoustic wave’, which is an electromagnetic generalization of the dust—ion- acoustic wave. The dispersion relations as well as the frequency regimes for the existence of the various modes are explicitly obtained. An alternative derivation of the relevant governing equations using an approach similar to that employed in so-called ‘electron magnetohydrodynamics’ (EMHD) is also presented.

Coulomb crystallization in colloidal plasmas with streaming ions and dust grains

The test charge potential of a dust particle in dusty plasmas with equilibrium ion and dust particle drifts is presented. The possibility of Coulomb crystallization due to an attractive force between like polarity particulates is discussed.

Nonlinear dust-acoustic waves with dust charge fluctuations

Abstract Nonlinear dust-acoustic waves in an unmagnetized dusty plasma have been investigated by taking into account dust-grain charge perturbations. For small, but finite, amplitudes the waves are shown to be governed by a Boussinesq-like nonlinear equation coupled to the charge fluctuation equation. For unidirectional propagation, the equations reduce to a Korteweg-de Vries (K-dV) equation with a source term. At early times, localized solutions are found to be damped due to the dust charge fluctuations. Different limiting cases of the general equations are also discussed.

Low-frequency waves in magnetized dusty plasmas

A systematic analysis of low-frequency waves such as hydromagnetic and acoustic waves in a magnetized dusty plasma containing electrons, ions and dust particles is presented. Starting with the three-fluid equations and the Maxwell equations, we derive, retaining finite ion mass, an effective two-fluid model incorporating deviations from the frozen-in-fluid approximation for the ion and electron fluid motions. We show that normal modes exist in two widely separated frequency regimes. In addition to obtaining hydromagnetic waves that are generalizations of the usual Alfven and magneto-acoustic modes in a two-component electron–ion plasma, we demonstrate the existence of a new class of magneto-acoustic waves (both fast and slow type) called ‘dustmagneto-acoustic waves’. These modes have qualitatively different dependences on the equilibrium parameters such as density, magnetic field and temperature when compared with the usual magneto-acoustic waves. The new modes arise owing to finite ion mass (compared with the dust-particle mass), leading to an effective inertial resistivity that inhibits the ion (as well as the electron) fluid from being frozen to the magnetic field lines. The fast branch of the dust-magneto-acoustic waves is shown to be the electromagnetic generalization of the electrostatic dust-acoustic wave recently obtained in unmagnetized dusty plasmas. In the two-component limit the new modes degenerate into the usual type of magneto-acoustic waves. Dispersion relations for various other modes are also presented.

Dust–Coulomb waves in dense dusty plasmas

Dusty plasmas can be considered as tenuous, dilute or dense when the dust fugacity parameter f≡4πnd0λD2R∼NDR/λD satisfies f≪1, ∼1, or ≫1, where nd0, λD and R denote, respectively, the dust number density, the plasma Debye length and the dust grain size (radius), and ND=nd0λD3 is the dust plasma parameter. Dense dusty plasmas are shown to support a new kind of ultra low-frequency electrostatic dust mode which may be called the “Dust–Coulomb Wave” (DCW). In contrast to the dust–acoustic wave (DAW) and the dust–lattice wave (DLW) which exist even for constant grain charge, DCWs are accompanied by dust charge as well as number density perturbations which are proportional to each other. For frequencies much smaller than the grain charging frequency, DCWs propagate as normal modes with the phase speed CDC≡qd0/mdR, where qd0 (md) is the charge (mass) of the dust grains. In the long wavelength limit, the DCW phase speed is much smaller than that of DAW (CDA), and scales as ∼CDA/f. Thus, for a given wave number, t...

Linear and nonlinear dust-acoustic waves in inhomogeneous dusty plasmas

The propagation of linear, as well as nonlinear, dust-acoustic waves in inhomogeneous dusty plasmas consisting of electrons, ions, and charged dust particles is investigated. It is shown that the amplitude of the dust-acoustic waves is affected by the presence of the dust density inhomogeneity. Amplitudes of the linear and nonlinear dust-acoustic waves decrease (increase) as the waves propagate in the direction of increasing (decreasing) density. The wave amplitude is inversely proportional to the square root of the dust particle’s density for the linear dust-acoustic waves. In the nonlinear case, to the lowest order and for the cold dust species, the wave amplitude is found to be directly proportional to nd0−1/4. Various special cases are explicitly considered, and comparison with the corresponding results for the usual two-component electron-ion plasmas is also carried out.

Modified Korteweg-De Vries equation for spatially inhomogeneous plasmas

The problem of propagation of ion-acoustic KdV solitons in weakly, spatially inhomogeneous plasmas is considered taking into account self-consistently the zeroth-order velocity and the potential existing in the system due to the presence of the inhomogeneity. An explicit soliton solution of the modified KdV equation is obtained.

Strong electromagnetic pulses in magnetized plasmas

Circularly polarized intense electromagnetic waves along an external magnetic field can nonlinearly produce large amplitude field‐aligned electrostatic potentials. The relevant two‐fluid equations together with Maxwell’s equations (incorporating the departures from the quasineutrality condition) are shown to be integrable when the radiation pressure dominates over the plasma pressure. The parameter regimes for the existence of large amplitude localized solutions in a magnetoplasma are explicitly obtained through an analysis of the energy integral. The small amplitude limits are also discussed.