arXiv subjects

Bengt Eliasson

Publications and source records attributed to Bengt Eliasson.

27 records · Page 2Linked to original sources

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↗

arXiv2008

Full-scale simulation study of a generalized Zakharov model for the generation of topside ionospheric turbulence

We present a full-scale simulation study of a generalized Zakharov model for the generation of the topside electrostatic turbulence due to the parametric instability during ionospheric heating experiments near the F region peak. The nonlinear tunneling of electromagnetic waves through the ionospheric layer is attributed to multiple-stage parametric decay and mode-conversion processes. At the bottomside of the F region, electrostatic turbulence excited by the parametric instability results in the conversion of the ordinary (O mode) wave into a large amplitude extraordinary (Z mode) wave tunneling through the F peak. At the topside interaction region, the Z mode undergoes parametric decay cascade process that results in the generation of the topside electrostatic turbulence and then conversion process yielding O waves that escape the plasma. This study may explain the observed topside ionospheric turbulence during ground based ionospheric heating experiments.

physics.space-ph↗

arXiv2007

Zakharov simulation study of spectral features of on-demand Langmuir turbulence in an inhomogeneous plasma

We have performed a simulation study of Langmuir turbulence in the Earth's ionosphere by means of a Zakharov model with parameters relevant for the F layer. The model includes dissipative terms to model collisions and Landau damping of the electrons and ions, and a linear density profile, which models the ionospheric plasma inhomogeneity whose length scale is of the order 10--100 km. The injection of energy into the system is modeled by a constant source term in the Zakharov equation. Langmuir turbulence is excited ``on-demand'' in controlled ionospheric modification experiments where the energy is provided by an HF radio beam injected into the overhead ionospheric plasma. The ensuing turbulence can be studied with radars and in the form of secondary radiation recorded by ground-based receivers. We have analyzed spectral signatures of the turbulence for different sets of parameters and different altitudes relative to the turning point of the linear Langmuir mode where the Langmuir frequency equals the local plasma frequency. By a parametric analysis, we have derived a simple scaling law, which links the spectral width of the turbulent frequency spectrum to the physical parameters in the ionosphere. The scaling law provides a quantitative relation between the physical parameters (temperatures, electron number density, ionospheric length scale, etc.) and the observed frequency spectrum. This law may be useful for interpreting experimental results.

physics.space-ph↗

arXiv2007

Simulation study of the interaction between large-amplitude HF radio waves and the ionosphere

The time evolution of a large-amplitude electromagnetic (EM) wave injected vertically into the overhead ionosphere is studied numerically. The EM wave has a carrier frequency of 5 MHz and is modulated as a Gaussian pulse with a width of approximately 0.1 milliseconds and a vacuum amplitude of 1.5 V/m at 50 km. This is a fair representation of a modulated radio wave transmitted from a typical high-power HF broadcast station on the ground. The pulse is propagated through the neutral atmosphere to the critical points of the ionosphere, where the L-O and R-X modes are reflected, and back to the neutral atmosphere. We observe mode conversion of the L-O mode to electrostatic waves, as well as harmonic generation at the turning points of both the R-X and L-O modes, where their amplitudes rise to several times the original ones. The study has relevance for ionospheric interaction experiments in combination with ground-based and satellite or rocket observations.

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

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↗