Freak waves and electrostatic wavepacket modulation in a quantum electron–positron–ion plasma

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.

Ion-acoustic envelope modes in a degenerate relativistic electron-ion plasma

“…8,39 Various relevant theoretical investigations have been proposed, predicting excitations that are yet to be detected. 17,[42][43][44] Considering the possibility for experimental confirmation (realization) of our predictions in the laboratory, we note that the present model becomes relevant for ultra-high densities, when both degeneracy and relativistic effects come into play. For instance, an one-dimensional density n 0 % 10 11 m À1 , corresponding to n 0 % 0:1 (and a 3D equivalent of n 3D % 10 33 m À3 ), is not at all inconceivable in view of the already available laser-plasma compression technology.…”

“…The value of Q/P is proportional to the (square) wavenumber j; in other words, a perturbation may become unstable in the window ½0; j. Furthermore, the ratio Q/P is related to the inverse width of a bright pulse of given amplitude w 0 : to see this, recall that a bright soliton solution of the NLSE (17) in the form w 0 sech nÀu e s L satisfies the relation w 0 L $ ðP=QÞ 1=2 . Therefore, for given w 0 (prescribed, i.e., by the lump of energy launched in the system), an envelope soliton will be wider (i.e., larger L) if Q/P acquires smaller values, and vice versa.…”

Relativistic theory for localized electrostatic excitations in degenerate electron-ion plasmas

“…In particular, there is no a priori methodological reason to quickly discard the time derivative of the pressure, manifesting in the ∝ ∂n e /∂t contribution in the electrons force equation in Eq. (9). Note also that we do not discard the electrons' convective derivative, because after restoring physical coordinates it can be shown that the Fermi pressure vanishes in the inertialess limit (formally m e /m i → 0).…”

“…For instance, 1D dense plasmas are of relevance to the target normal sheath acceleration mechanism [2] produced during the irradiation of solid targets with a high-intensity laser available with coherent brilliant x-ray radiation sources [3]. Furthermore, the nonlinear dynamics of 1D degenerate plasmas shows a rich variety of behavior; applications include the dense quantum diode [4], the electron-hole plasma injected into quantum wires [5], the 1D fermionic Luttinger liquid [6], breather-mode oscillations in 1D semiconductor quantum wells [7], Lagrangian structures in dense 1D plasmas [8], and 1D nonlinear envelope modes in dense electron-positronion plasmas [9], among others. Sagdeev's pseudopotential method was used to study the propagation of wave structures of arbitrary amplitude in a relativistically degenerate electron-positron-ion plasmas in Ref.…”

Stark Broadening from Impact Theory to Simulations

“…As W increases, nonlinear phenomena start showing up, enabling, for instance, wave-wave couplings. Although only recently investigated in plasmas, the occurrence of rogue waves has been raised in various plasma conditions [29][30][31]. Rogue waves have been studied in many dynamical systems, and are known to the general public by the observation and study of rogue or freak waves that suddenly appear in the ocean as large isolated waves.…”