Abstract
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.
Highlights
Large ensembles of charged particles have tacitly been used as testbed for nonlinear theories
One of many generic nonlinear mechanisms dominating wavepacket propagation in plasmas is amplitude modulation, accounting for a variation of the wavepacket’s amplitude, resulting in a nonlinear frequency shift [15, 16]. This is described by a nonlinear Schrodinger equation (NLSE) [17], which can be obtained from the plasma-fluid dynamical equations via a multiscale technique [15, 16]
The term is earned by their behavior: a sudden appearance from an oscillating ambient background, accompanied by a narrowing of width and growth of amplitude far exceeding the ‘average’ background turbulence, followed by an rapid decay to the background medium [48, 49]. It was earlier suggested [50] that a class of breather-type solutions of the NLSE may be good candidates for modeling of rogue waves, as they capture the essential physics and the qualitative features of freak waves
Summary
Large ensembles of charged particles (plasmas) have tacitly been used as testbed for nonlinear theories. Fusion 56 (2014) 035007 magnetized plasmas, a Zakharov–Kuznetsov model [9] In all of these works, ions were treated as classical particles, while quantum effects were introduced via the electron statistics. This is described by a nonlinear Schrodinger equation (NLSE) [17], which can be obtained from the plasma-fluid dynamical equations via a multiscale technique [15, 16] Such a viewpoint was adopted in [13] for ion-acoustic wavepackets in a dense electron–ion quantum plasma, followed by a similar study on electron-scale wavepackets [14], incorporating diffraction effects from the so-called Bohm potential. Our results are summarized in the concluding section 10
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