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In the limit of extremely intense electromagnetic fields the Maxwell equations are modified due to the photon-photon scattering that makes the vacuum refraction index depend on the field amplitude. In presence of electromagnetic waves with small but finite wavenumbers the vacuum behaves as a dispersive medium. We show that the interplay between the vacuum polarization and the nonlinear effects in the interaction of counter-propagating electromagnetic waves can result in the formation of Kadomtsev-Petviashvily solitons and, in one-dimension configuration, of Korteveg-de-Vries type solitons that can propagate over a large distance without changing their shape.
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Three dimensional (3D) relativistic electromagnetic sub-cycle solitons were observed in 3D Particle-in-Cell simulations of an intense short laser pulse propagation in an underdense plasma. Their structure resembles that of an oscillating electric dipole with a poloidal electric field and a toroidal magnetic field that oscillate in-phase with the electron density with frequency below the Langmuir frequency. On the ion time scale the soliton undergoes a Coulomb explosion of its core, resulting in ion acceleration, and then evolves into a slowly expanding quasi-neutral cavity.
The dynamical behaviors of electromagnetic (EM) solitons formed due to nonlinear interaction of linearly polarized intense laser light and relativistic degenerate plasmas are studied. In the slow motion approximation of relativistic dynamics, the evolution of weakly nonlinear EM envelope is described by the generalized nonlinear Schr{o}dinger (GNLS) equation with local and nonlocal nonlinearities. Using the Vakhitov-Kolokolov criteria, the stability of an EM soliton solution of the GNLS equation is studied. Different stable and unstable regions are demonstrated with the effects of soliton velocity, soliton eigenfrequency, as well as the degeneracy parameter $R=p_{Fe}/m_ec$, where $p_{Fe}$ is the Fermi momentum and $m_e$ the electron mass, and $c$ is the speed of light in vacuum. It is found that the stability region shifts to an unstable one and is significantly reduced as one enters from the regimes of weakly relativistic $(Rll1)$ to ultrarelativistic $(Rgg1)$ degeneracy of electrons. The analytically predicted results are in good agreement with the simulation results of the GNLS equation. It is shown that the standing EM soliton solutions are stable. However, the moving solitons can be stable or unstable depending on the values of soliton velocity, the eigenfrequency or the degeneracy parameter. The latter with strong degeneracy $(R>1)$ can eventually lead to soliton collapse.
Starting from the governing equations for a quantum magnetoplasma including the quantum Bohm potential and electron spin-1/2 effects, we show that the system of quantum magnetohydrodynamic (QMHD) equations admit rarefactive solitons due to the balance between nonlinearities and quantum diffraction/tunneling effects. It is found that the electron spin-1/2 effect introduces a pressure-like 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.
We consider vacuum polarization effects in the one-photon annihilation channel within a kinetic description of the e+ e- plasma produced from the vacuum in the focal spot of counter-propagating laser beams. This entails essential changes in the structure of the photon kinetic equation. We investigate the domain of large adiabaticity parameters gamma >> 1 where the photon radiation turns out to be very small. A more thorough examination of the domain gamma < 1 needs separate investigation. However, an exploratory study has shown that the one-photon annihilation channel can lead for some domains of laser field parameters (e.g., for the XFEL) to contributions accessible for observation.
The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical approximations which are tested against a numerical shooting method. The results are particularly simple when the elastic constants are equal, but we discuss the general case of elastic anisotropy. The director field is continuous everywhere apart from a straight line segment whose length depends on the value of the magnetic field. This indicates the possibility of an elongated defect core for disclination lines in nematics due to an external magnetic field.
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