arXiv subjects

Padma Kant Shukla

Publications and source records attributed to Padma Kant Shukla.

14 recordsLinked to original sources

arXiv2012

Novel Attractive Force Between Ions in Quantum Plasmas

We report new attractive force between ions that are shielded by degenerate electrons in quantum plasmas. Specifically, we show that the electric potential around an isolated ion has a hard core negative part that resembles the Lennard-Jones (LJ)-type potential. Physically, the new electric potential is attributed to the consideration of the quantum statistical pressure, the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron-1/2 spin within the framework of the quantum hydrodynamical description of quantum plasmas. The shape of the attractive potential is determined by the ratio between the Bohr radius and the Wigner-Seitz radius of degenerate electrons. The existence of the hard core negative potential will be responsible for the attraction of ions forming lattices and atoms/molecules, as well as for critical points and phase transitions in quantum plasmas at nanoscales.

physics.plasm-ph↗

arXiv2012

Relativistic X-Ray Free Electron Lasers in the Quantum Regime

We present a nonlinear theory for relativistic X-ray free electron lasers in the quantum regime, using a collective Klein-Gordon (KG) equation (for relativistic electrons), which is coupled with the Maxwell-Poisson equations for the electromagnetic and electrostatic fields. In our model, an intense electromagnetic wave is used as a wiggler which interacts with a relativistic electron beam to produce coherent tunable radiation. The KG-Maxwell-Poisson model is used to derive a general nonlinear dispersion relation for parametric instabilities in three-space-dimensions, including an arbitrarily large amplitude electromagnetic wiggler field. The nonlinear dispersion relation reveals the importance of quantum recoil effects and oblique scattering of the radiation that can be tuned by varying the beam energy.

physics.plasm-ph↗

arXiv2009

Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation

On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schrödinger equation and a one-dimensional (1D) nonlinear Schrödinger equation, constrained by a variational condition for the controlling potential. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.

cond-mat.quant-gas↗

arXiv2009

Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method

We present a class of three-dimensional solitary waves solutions of the Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensates (BECs). By imposing an external controlling potential, a desired time-dependent shape of the localized BEC excitation is obtained. The stability of some obtained localized solutions is checked by solving the time-dependent GP equation numerically with analytic solutions as initial conditions. The analytic solutions can be used to design external potentials to control the localized BECs in experiment.

nlin.SI↗

arXiv2009

Some mathematical aspects in determining the 3D controlled solutions of the Gross-Pitaevskii equation

The possibility of the decomposition of the three dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schrödinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, solutions of the 3D controlled GPE can be constructed from the solutions of a 2D linear Schrödinger equation (transverse component of the GPE) coupled with a 1D nonlinear Schrödinger equation (longitudinal component of the GPE). Such a decomposition, called the 'controlling potential method' (CPM), allows one to cast the above solutions in the form of the product of the solutions of the transverse and the longitudinal components of the GPE. The coupling between these two equations is the functional of both the transverse and the longitudinal profiles. The analysis shows that the CPM is based on the variational principle that sets up a condition on the controlling potential well, and whose physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control operation.

nlin.SI↗

arXiv2009

Quantum and classical dynamics of Langmuir wave packets

The quantum Zakharov system in three-spatial dimensions and an associated Lagrangian description, as well as its basic conservation laws are derived. In the adiabatic and semiclassical case, the quantum Zakharov system reduces to a quantum modified vector nonlinear Schrödinger (NLS) equation for the envelope electric field. The Lagrangian structure for the resulting vector NLS equation is used to investigate the time-dependence of the Gaussian shaped localized solutions, via the Rayleigh-Ritz variational method. The formal classical limit is considered in detail. The quantum corrections are shown to prevent the collapse of localized Langmuir envelope fields, in both two and three-spatial dimensions. Moreover, the quantum terms can produce an oscillatory behavior of the width of the approximate Gaussian solutions. The variational method is shown to preserve the essential conservation laws of the quantum modified vector NLS equation.

physics.plasm-ph↗

arXiv2004

Nonlinear theory of dust lattice mode coupling in dust crystals

Quasi-crystals formed by charged mesoscopic dust grains (dust lattices), observed since hardly a decade ago, are an exciting paradigm of a nonlinear chain. In laboratory discharge experiments, these quasi-lattices are formed spontaneously in the sheath region near a negative electrode, usually at a levitated horizontal equilibrium configuration where gravity is balanced by an electric field. It is long known (and experimentally confirmed) that dust-lattices support linear oscillations, in the longitudinal (acoustic mode) as well as in the transverse, in plane (acoustic-) or off-plane (optic-like mode) directions. Either due to the (typically Yukawa type) electrostatic inter-grain interaction forces or to the (intrinsically nonlinear) sheath environment, nonlinearity is expected to play an important role in the dynamics of these lattices. Furthermore, the coupling between the different modes may induce coupled nonlinear modes. Despite this evidence, the elucidation of the nonlinear mechanisms governing dust crystals is in a rather preliminary stage. In this study, we derive a set of (coupled) discrete equations of motion for longitudinal and transverse (out-of-plane) motion in a one dimensional model chain of charged dust grains. In a continuum approximation, i.e. assuming a variation scale which is larger than the lattice constant, one obtains a set of coupled modified Boussinesq-like equations. Different nonlinear solutions of the coupled system are discussed, based on localized travelling wave ansatze and on coupled equations for the envelopes of co-propagating quasi-linear waves.

physics.plasm-ph↗

arXiv2004

Modulated envelope localized wavepackets associated with electrostatic plasma waves

The nonlinear amplitude modulation of known electrostatic plasma modes is examined in a generic manner, by applying a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The moderately nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrodinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright- (pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness, finite temperature and defect (dust) concetration are explicitly considered. The relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.

physics.plasm-ph↗

arXiv2004

Theory of solitary waves in complex plasma lattices

A comprehensive analytical theory for nonlinear excitations related to horizontal (longitudinal, acoustic mode) as well as vertical (transverse, optical mode) motion of charged dust grains in a dust crystal is presented. Different types of localized excitations, similar to those well known in solid state physics, are reviewed and conditions for their occurrence and characteristics in dusty plasma crystals are discussed. By employing a continuum approximation (i.e. assuming a long variation scale, with respect to the inter-particle distance) a dust crystal is shown to support nonlinear kink-shaped supersonic solitary excitations, associated with longitudinal dust grain displacement, as well as modulated envelope localized modes associated with either longitudinal or transverse oscillations. Although a one-dimensional crystal is considered for simplicity, the results in principle apply to a two-dimensional lattice if certain conditions are satisfied. The effect of mode-coupling is also briefly considered. The relation to previous results on atomic chains, and also to experimental results on strongly-coupled dust layers in gas discharge plasmas, is briefly discussed.

physics.plasm-ph↗

arXiv2004

Lagrangean formulation of ion- and dust-ion-acoustic waves

Ion-acoustic modes propagating in unmagnetized dusty plasmas are studied by applying a generic collisionless fluid model. An Eulerian-to-Lagrangean variable transformation leads to a new system of evolution equations, which may be combined into a single (rather complex) equation for the mean ion density. The linear and weakly nonlinear oscillations regimes are studied and their modulational stability is investigated. This study extends known previous results on the Lagrangian description of electron- or ion-acoustic electrostatic plasma modes. The relevance with the description of dust-ion acoustic waves propagating in a dusty plasma is also discussed.

physics.plasm-ph↗

arXiv2004

Intrinsic localized modes in dust lattices

Intrinsic Localized Modes (ILM) (or Discrete Breathers, DB) are localized oscillatory modes known to occur in atomic or molecular chains characterized by coupling and/or on-site potential nonlinearity. Quasi-crystals of charged mesoscopic dust grains (dust lattices), which have been observed since hardly a decade ago, are an exciting paradigm of such a nonlinear chain. In gas-discharge experiments, these crystals are subject to forces due to an externally imposed electric and/or magnetic field(s), which balance(s) gravity at the levitated equilibrium position, as well as to electrostatic inter-grain interaction forces. Despite the profound role of nonlinearity, which may be due to inter-grain coupling, mode- coupling and to the sheath environment, the elucidation of the nonlinear mechanisms governing dust crystals is still in a preliminary stage. This study is devoted to an investigation, from very first principles, of the existence of discrete localized modes in dust layers. Relying on a set of evolution equation for transverse charged grain displacements, we examine the conditions for the existence and sustainance of discrete localized modes and discuss the dependence of their characteristics on intrinsic plasma parameters. In addition, the possibility of DB stabilisation via an external force is discussed.

physics.plasm-ph↗

arXiv2004

Theoretical and numerical investigation of the shock formation of dust ion acoustic waves

We present a theoretical and numerical study of the self-steepening and shock formation of large-amplitude dust ion-acoustic waves (DIAWs) in dusty plasmas. We compare the non-dispersive two fluid model, which predicts the formation of large amplitude compressive and rarefactive dust ion-acoustic (DIA) shocks, with Vlasov/fluid simulations where ions are treated kinetically while a Boltzmann distribution is assumed for the electrons.

physics.plasm-ph↗

arXiv2004

Nonlinear whitlerons

Recently, observations from laboratory experiments have revealed amplitude modulation of whistlers by low-frequency perturbations. We here present theoretical and simulation studies of amplitude modulated whistler solitary waves (whistlerons) and their interaction with background low-frequency density perturbations created by the whistler ponderomotive force. We derive a nonlinear a nonlinear Schrodinger equation which governs the evolution of whistlers in the presence of finite-amplitude density perturbations, and a set of equations for arbitrary large amplitude density perturbations in the presence of the whistler ponderomotive force. The governing equations studied analytically in the small amplitude limit, and are solved numerically to show the existence of large scale density perturbations that are self-consistently created by localized whistlerons. Our numerical results are in good agreement with recent experimental results where the the formation of modulated whistlers and solitary whister waves were formed.

physics.plasm-ph↗

arXiv2004

Weakly nonlinear vertical dust grain oscillations in dusty plasma crystals in the presence of a magnetic field

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 evolution of the modulated wave packet, which is described by a nonlinear Schrödinger--type equation (NLSE), may lead to propagating localized envelope structures whose exact forms are presented and discussed. Explicit suggestions for experimental investigations are put forward.

physics.plasm-ph↗