Bengt Eliasson

Nonlinear aspects of quantum plasma physics

Dense quantum plasmas are ubiquitous in planetary interiors and in compact astrophysical objects (e.g., the interior of white dwarf stars, in magnetars, etc.), in semiconductors and micromechanical systems, as well as in the next-generation intense laser–solid density plasma interaction experiments and in quantum X-ray free-electron lasers. In contrast to classical plasmas, quantum plasmas have extremely high plasma number densities and low temperatures. Quantum plasmas are composed of electrons, positrons and holes, which are degenerate. Positrons (holes) have the same (slightly different) mass as electrons, but opposite charge. The degenerate charged particles (electrons, positrons, and holes) obey the Fermi–Dirac statistics. In quantum plasmas, there are new forces associated with (i) quantum statistical electron and positron pressures, (ii) electron and positron tunneling through the Bohm potential, and (iii) electron and positron angular momentum spin. Inclusion of these quantum forces allows the existence of very high-frequency dispersive electrostatic and electromagnetic waves (e.g., in the hard X-ray and gamma-ray regimes) with extremely short wavelengths. In this review paper, we present theoretical backgrounds for some important nonlinear aspects of wave–wave and wave–electron interactions in dense quantum plasmas. Specifically, we focus on nonlinear electrostatic electron and ion plasma waves, novel aspects of three-dimensional quantum electron fluid turbulence, as well as nonlinearly coupled intense electromagnetic waves and localized plasma wave structures. Also discussed are the phase-space kinetic structures and mechanisms that can generate quasistationary magnetic fields in dense quantum plasmas. The influence of the external magnetic field and the electron angular momentum spin on the electromagnetic wave dynamics is discussed. Finally, future perspectives of the nonlinear quantum plasma physics are highlighted.

Colloquium: nonlinear collective interactions in quantum plasmas with degenerate electron fluids

The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, model equations (e.g., the quantum hydrodynamic and effective nonlinear Schrodinger-Poisson equations) are presented that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg’s uncertainty principle and Pauli’s exclusion principle for overlapping electron wave functions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2 quantum particles), there also appears an electron spin current and a spin force acting on electrons due to the Bohr magnetization. The quantum effects produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a quantum plasma that are summarized in here. Furthermore, nonlinear features of ES ion waves and electron plasma oscillations are discussed, as well as the trapping of intense EM waves in quantum electron-density cavities. Specifically, simulation studies of the coupled nonlinear Schrodinger and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. The effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic equations are also discussed. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects (e.g., the cores of white dwarf stars and giant planets), as well as in plasma-assisted nanotechnology (e.g., quantum diodes, quantum free-electron lasers, nanophotonics and nanoplasmonics, metallic nanostructures, thin metal films, semiconductor quantum wells, and quantum dots, etc.), and in the next generation of intense laser-solid density plasma interaction experiments relevant for fast ignition in inertial confinement fusion schemes.

Surface plasma rogue waves

It is shown that the electrostatic surface plasma rogue waves can be excited and propagate along a plasma-vacuum interface due to the nonlinear coupling between high-frequency surface plasmons and low-frequency ion oscillations. The nonlinear pulse propagation condition and its behavior are discussed. The nonlinear structures may be useful for controlling and maximizing plasmonic energy along the plasma surface.

Novel attractive force between ions in quantum plasmas

We report a 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-type potential. Physically, the new electric potential is attributed to the consideration of the quantum statistical pressure and 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 or molecules, as well as for critical points and phase transitions in quantum plasmas at nanoscales.

Magnetosonic solitons in a fermionic quantum plasma.

Starting from the governing equations for a quantum magnetoplasma including the quantum Bohm potential and electron spin- 12 effects, we show that the system of quantum magnetohydrodynamic (QMHD) equations admits rarefactive solitons due to the balance between nonlinearities and quantum diffraction and tunneling effects. It is found that the electron spin- 12 effect introduces a pressurelike term with negative sign in the QMHD equations, which modifies the shape of the solitary magnetosonic waves and makes them wider and shallower. Numerical simulations of the time-dependent system shows the development of rarefactive QMHD solitary waves that are modified by the spin effects.

Laser acceleration of monoenergetic protons in a self-organized double layer from thin foil

We present a theory for the acceleration of monoenergetic protons, trapped in a self-organized double layer, by short pulse laser irradiation on a thin foil with the specific thickness suggested by the simulation study of Yan et al (2008 Phys. Rev. Lett. 100 135003). The laser ponderomotive force pushes the electrons forward, leaving the ions behind until the space charge electric field balances the ponderomotive force at a distance Δ. For the optimal target thickness D = Δ > c/ωp, the electron sheath is piled up at the rear surface and the sheath electric field accelerates the protons until they are reflected by the inertial force in the accelerated frame. These protons are therefore trapped by the combined forces of the electrostatic field of the electron sheath and the inertial force of the accelerating target. Together with the electron layer, they form a double layer and are collectively accelerated by the laser ponderomotive force, leading to monoenergetic ion production.

Electrostatic solitary waves in a quantum plasma with relativistically degenerate electrons

A model for nonlinear ion waves in an unmagnetized plasma with relativistically degenerate electrons and cold fluid ions is presented here. The inertia is given here by the ion mass while the restoring force is provided by the relativistic electron degeneracy pressure, and the dispersion is due to the deviation from charge neutrality. A nonlinear Korteweg–de Vries equation is derived for small but finite amplitude waves and is used to study the properties of localized ion acoustic solitons for parameters relevant for dense astrophysical objects such as white dwarf stars. Different degrees of relativistic electron degeneracy are discussed and compared.

Dispersion properties of electrostatic oscillations in quantum plasmas

We present a derivation of the dispersion relation for electrostatic oscillations in a zero-temperature quantum plasma, in which degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations. The Poisson equation determines the electrostatic wave potential. We consider parameters ranging from semiconductor plasmas to metallic plasmas and electron densities of compressed matter such as in laser compression schemes and dense astrophysical objects. Owing to the wave diffraction caused by overlapping electron wave function because of the Heisenberg uncertainty principle in dense plasmas, we have the possibility of Landau damping of the high-frequency electron plasma oscillations at large enough wavenumbers. The exact dispersion relations for the electron plasma oscillations are solved numerically and compared with the ones obtained by using approximate formulas for the electron susceptibility in the high- and low-frequency cases.

Arbitrary amplitude dust ion-acoustic shock waves in a dusty plasma with positive and negative ions

Arbitrary amplitude dust ion-acoustic shock waves in a multi-ion dusty plasma (composed of electrons, light positive ions, heavy negative ions, and stationary massive dust grains) has been studied. For this purpose, the coupled Poisson and dust-charging equations, which accounts for the fluctuation of charges on static dust, have been numerically solved. The large amplitude shocks are associated with a sudden decrease in the electrostatic potential and of the dust grain charge. It is found that in the lower speed limit small amplitude shocks are formed, while in the larger speed limit large amplitude shocks are formed. It is anticipated that the profiles and amplitudes of the DIA shocks predicted here will be observed in forthcoming laboratory and space experiments.

Dust ion-acoustic solitary waves in a dusty plasma with positive and negative ions

Properties of small but finite amplitude dust ion-acoustic (DIA) solitary waves in a dusty plasma composed of inertialess electrons, positive and negative inertial ions, and immobile negative/positive charged dust grains are investigated. By using the multifluid dusty plasma model, the Kortweg–de Vries equation and energy integral for small and large amplitude solitary pulses, are derived. It is found that the presence of the negative ions modifies the properties of the solitary DIA waves, and provides the possibility of positive and negative solitary potential structures to coexist. The present results may be useful for understanding the salient features of localized DIA excitations that may appear in data from forthcoming laboratory experiments and space observations.