The occurrence of rogue waves (freak waves) associated with electromagnetic pulse propagation interacting with a plasma is investigated, from first principles. A multiscale technique is employed to solve the fluid-Maxwell equations describing a weakly nonlinear circularly polarized electromagnetic pulses in magnetized plasmas. A nonlinear Schrodinger (NLS) type equation is shown to govern the amplitude of the vector potential. A set of non-stationary envelope solutions of the NLS equation are considered, as potential candidates for modeling of rogue waves (freak waves) in beam-plasma interactions, namely in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov-Ma breather. The variation of the structural properties of the latter structures with relevant plasma parameters is investigated, in particular focusing on the ratio between the (magnetic field dependent) cyclotron (gyro-) frequency and the plasma frequency.
The occurrence of rogue waves (freak waves) associated with electrostatic wavepacket propagation in a quantum electron-positron-ion plasma is investigated from first principles. Electrons and positrons follow a Fermi-Dirac distribution, while the ions are subject to a quantum (Fermi) pressure. A fluid model is proposed and analyzed via a multiscale technique. The evolution of the wave envelope is shown to be described by a nonlinear Schrödinger equation (NLSE). Criteria for modulational instability are obtained in terms of the intrinsic plasma parameters. Analytical solutions of the NLSE in the form of envelope solitons (of the bright or dark type) and localized breathers are reviewed. The characteristics of exact solutions in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov-Ma breather are proposed as candidate functions for rogue waves (freak waves) within the model. The characteristics of the latter and their dependence on relevant parameters (positron concentration and temperature) are investigated.
Articles you may be interested inA self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schr€ odinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case-in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed. Published by AIP Publishing.
The dispersion properties of electrostatic waves propagating in ultrahigh density plasma are investigated, from first principles, in a one-dimensional geometry. A self-consistent multispecies plasma fluid model is employed as starting point, incorporating electron degeneracy and relativistic effects. The inertia of all plasma components is retained, for rigor. Exact expressions are obtained for the oscillation frequency, and the phase and group velocity of electrostatic waves is computed. Two branches are obtained, namely an acoustic low-frequency dispersion branch and an upper (optic-like) branch: these may be interpreted as ion-acoustic and electron-plasma (Langmuir) waves, respectively, as in classical plasmas, yet bearing an explicit correction in account of relativistic and electron degeneracy effects. The electron-plasma frequency is shown to reduce significantly at high values of the density, due to the relativistic effect. The result is compared with approximate models, wherein either electrons are considered inertialess (low-frequency ionic scale) or ions are considered to be stationary (Langmuir-wave limit).
Motivated by observations of localized electrostatic wavepackets by the Cassini – and (earlier) by Voyager 1 and 2 – mission(s) in Saturn’s magnetosphere, we have investigated the existence conditions and the dynamical evolution of localized multi-dimensional structures in the Saturnian dusty plasma environment. To this effect, we have adopted a plasma-fluid model for dust-ion acoustic (DIA) excitations, taking into account the presence of a highly energetic (suprathermal, kappa-distributed) electron population in combination with massive dust dust particulates in the background. A multiple scales perturbation method was shown to lead to a Davey-Stewartson (DS) system of evolution equations, if one assumes perpendicular carrier wave propagation across the magnetic field (direction). The system is then shown to possess two regimes mainly, known in the literature as DS-I and DS-II. In the former case, if certain conditions are fulfilled, exponentially localized solutions are obtained, known as dromions. The combined effects of various physical parameters such as the electron spectral index, the ambient magnetic field (strength) and the dust concentration have been examined. A numerical investigation reveals that the dromion amplitude increases with higher dust concentration, while it decreases for lower κe (i.e. with an increase in the suprathermal electron population component). A stronger magnetic field results in higher amplitude but narrower dromions. Our results provide a comprehensive framework for modeling modulated electrostatic wavepackets, in direct comparison with experimental data in planetary environments, in Saturn’s magnetosphere and elsewhere.
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