We consider strong-field effects in laboratory and astrophysical plasmas and high intensity laser and cavity systems, related to quantum electrodynamical (QED) photon-photon scattering. Current state-of-the-art laser facilities are close to reaching energy scales at which laboratory astrophysics will become possible. In such high energy density laboratory astrophysical systems, quantum electrodynamics will play a crucial role in the dynamics of plasmas and indeed the vacuum itself. Developments such as the free electron laser may also give a means for exploring remote violent events such as supernovae in a laboratory environment. At the same time, superconducting cavities have steadily increased their quality factors, and quantum non-demolition measurements are capable of retrieving information from systems consisting of a few photons. Thus, not only will QED effects such as elastic photon-photon scattering be important in laboratory experiments, it may also be directly measurable in cavity experiments. Here we describe the implications of collective interactions between photons and photonplasma systems. We give an overview of strong field vacuum effects, as formulated through the Heisenberg-Euler Lagrangian. Based on the dispersion relation for a single test photon travelling in a slowly varying background electromagnetic field, a set of equations describing the nonlinear propagation of an electromagnetic pulse on a radiation-plasma is derived. The stability of the governing equations is discussed, and it is shown using numerical methods that electromagnetic pulses may collapse and split into pulse trains, as well as be trapped in a relativistic electron hole. Effects, such as the generation of novel electromagnetic modes, introduced by QED in pair plasmas is described. Applications to laser-plasma systems and astrophysical environments are discussed.

Solitary electrostatic structures involving density depletions have been observed in the upper ionosphere by the Freja satellite [Dovner et al., 1994]. If these are interpreted as ion sound solitons, the difficulty arises that the standard Korteweg‐de Vries description predicts structures with enhanced rather than depleted density. Here we show that the presence of non‐thermal electrons may change the nature of ion sound solitary structures and allow the existence of structures very like those observed.

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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, we present model equations (e.g. the quantum hydrodynamic and effective nonlinear Schrödinger-Poisson equations) 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 wavefunctions 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, we discuss nonlinear features of ES ion waves and electron plasma oscillations (ESOs), as well as the trapping of intense EM waves in quantum electron density cavities. Specifically, simulation studies of the coupled nonlinear Schrödinger (NLS) and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. We also discuss the effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic (Q-MHD) equations. 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.

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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

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The ion-acoustic solitons are investigated in three-component plasmas, whose constituents are electrons, positrons, and singly charged ions. It is found that the presence of the positron component in such a multispecies plasma can result in reduction of the ion-acoustic soliton amplitudes.