Ram K. Varma

Convective cells in nonuniform dusty plasmas

It is shown that purely damped convective cell modes acquire a real frequency in the presence of static charged dust grains in a nonuniform magnetized dusty plasma. The frequency of the two‐dimensional mode is induced by the plasma density gradient and corresponds to charge density waves arising out of the plasma non‐neutrality. The dynamics of weakly interacting finite‐frequency convective cell modes is governed by the generalized Navier–Stokes equation. The presence of the new term arising from the dust inhomogeneity in the latter provides the possibility of a two‐dimensional dipolar vortex solution in dusty plasmas.

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.

Charged particle trajectories in a magnetic field on a curved space-time

In this paper we have studied the motion of charged particles in a dipole magnetic field on the Schwarzscbild background geometry. A detailed analysis has been made in the equatorial plane through the study of the effective potential curves. In the case of positive canonical angular momentum the effective potential has two maxima and two minima giving rise to a well-defined potential well rear the event horizon. This feature of the effective potential categorises the particle orbits into four classes, depending on their energies. (i) Particles, coming from infinity with energy less than the absolute maximum ofVeff, would scatter away after being turned away by the magnetic field. (ii) Whereas those with energies higher than this would go into the central star seeing no barrier. (iii) Particles initially located within the potential well are naturally trapped, and they execute Larmor motion in bound gyrating orbits. (iv) and those with initial positions corresponding to the extrema ofVeff follow circular orbits which are stable for non-relativistic particles and unstable for relativistic ones. We have also considered the case of negative canonical angular momentum and found that no trapping in bound orbits occur for this case.In the case when particles are not confined to the equatorial plane we have found that the particles execute oscillatory motion between two mirror points if the magnetic field is sufficiently high, but would continuously fall towards the event horizon otherwise.

A theory for Langmuir solitons

A systematic and self-consistent analysis of the problem of Langmuir solitons in the entire range of Mach numbers (0 < M < 1) has been presented. A coupled set of nonlinear equations for the amplitude of the modulated, high-frequency Langmuir waves and the associated low-frequency ion waves is derived without using the charge neutrality condition or any a priori ordering schemes. A technique has been developed for obtaining analytic solutions of these equations where any arbitrary degree of ion nonlinearity consistent with the nonlinearity retained in the Langmuir field can be taken into account self-consistently. A class of solutions with non-zero Langmuir field intensity at the centre (ξ=0) are found for intermediate values of the Mach number. Using these solutions, a smooth transition from single-hump solitons to the double-hump solitons with respect to the Mach number has been established through the definitions of critical and cut-off Mach numbers. Further, under appropriate limiting conditions, various solutions discussed by other authors are obtained. Sagdeev potential analyses of the solutions for the Langmuir field as well as the ion field are carried out. These analyses confirm the transition from single-hump solitons to the double-hump solitons with respect to the Mach number. The existence of many-hump solitons for higher-order nonlinearities in the low-frequency ion wave potential has been conjectured. The method of solution developed here can be applied to similar equations in other fields.

Classical and macroquantum dynamics of charged particles in a magnetic field

Abstract The investigations relating to the dynamics of charged particles in a magnetic field carried out over more than 40 years have been reviewed with special reference to the problem of nonadiabaticity due to field inhomogeneity, and time dependence. A detailed overview is presented of the standard approaches to one of the main problems namely the determination of the residence times of charged particles in an adiabatic magnetic trap which involves nonadiabaticity in a crucial way. In a major departure from the standard approach, a new paradigm described here as “macroquantum dynamics” was advanced by the author to address the problem of residence times. The evolution and development of this new paradigm is next presented as the main focus of the review. This consists of a probability amplitude Schrodinger-like formalism for the classical macrodomain, which has been shown to be a description of the system in the correspondence limit of large Landau quantum numbers. It is demonstrated that this represents a remarkable persistence of matter wave behaviour well into the classical macrodomain, leading to unexpected experimental consequences. Experimental results confirming some of the spectacular predictions of this formalism are presented. These refer to the existence of macroscopic matter wave interference phenomena and the observation of the curl-free vector potential a la Aharonov–Bohm in the macrodomain. The problem of the nonadiabatic leakage of particles from an adiabatic trap takes the appearance here of the quantum-like tunneling of the adiabatic potential. The multiplicity of residence times predicted by the set of Schrodinger-like equations have been well confirmed by experiments. A critical comparison is finally presented of the classical vs. macroquantum description of the system in the macrodomain. The new paradigm thus represents an entirely new and unexpected manifestation of quantum dynamics in the classical macrodomain.

Drift‐Alfvén vortices

The solitary vortex solution is shown to exist for the set of nonlinear equations describing low‐frequency fluid motion in a magnetized plasma.

Localization of circularly polarized intense electromagnetic waves in relativistic plasmas

Localization of a circularly polarized, high‐intensity electromagnetic field in a relativistic, unmagnetized plasma is considered. A new class of double‐hump electromagnetic soliton solutions having nonzero high‐frequency field intensity at the center is found for subsonic as well as supersonic velocities. For subsonic velocities, these solitons are found to be accompanied by density dips whereas supersonic solitons are associated with density humps. Parameter regions for the existence of different types of electromagnetic solitons are obtained explicitly. A few limiting cases of the general solutions obtained in the present theory are also discussed.

Theory of sonic-langmur solitons

Abstract A general, self-consistent treatment for the problem of sonic-Langmuir solitons has been presented. A method is developed to solve the coupled set of nonlinear equations which allows the system to be solved to any arbitrary degree of ion nonlinearity consistent with the nonlinearities retained in the Langmuir field and for any value of the Mach number. A new class of solutions are found for the intermediate value of the Mach number. Smooth transition from single-hump solution to the double-hump solution is shown to exist with respect to the Mach number.

Fluid equations for a dusty plasma with dust charge and mass distribution interacting with neutral dust through dust grain charging and secondary emission

A set of fluid equations is obtained for a dusty plasma, with dust charge and mass distributions, interacting with ambient neutral dust through inelastic collision processes involving dust grain charging and discharging and secondary electron emission from the dust grains. These are obtained as appropriate moments of the Boltzmann–Vlasov equations for the positively and negatively charged dust components, neutral dust component, electrons, and ions. Also obtained are the charge and mass moments of these equations, which bring out a new term involving the charge dispersion in the equation for the phase space charge density. The inelastic collision process involving dust grain charging and discharging and secondary electron emission provides a coupling between the positive and negatively charged dust components and the neutral dust component. The source/sink terms in the equations of continuity, momentum balance, and heat equations then are the proper terms obtained systematically from the Boltzmann–Vlasov ...

Formation of kinetic Alfvén vortices

Abstract Formation of kinetic Alfven vortices is considered. Previously derived Alfven vortex solutions are improved.