Boris E. Meierovich

Electromagnetic collapse. Problems of stability, emission of radiation and evolution of a dense pinch

Abstract Stability, emission of radiation, and some problems of evolution for pinch systems are considered on the basis of the theory of equilibrium of a plasma with a high current. The analysis of small oscillations in the approximation of two-fluid hydrodynamics of ideal charged liquids shows that the most dangerous instability is the one resulting in the filamentation of a diffuse equilibrium state of the current into separate jets. The criterion of stability for a pinch systems is established. According to this criterion the plasma compressed up to the electron degeneration is stable. The theory of emission of radiation by pinch systems shows a very important role of stimulated synchrotron radiation in the process of evolution of a high-current channel. The experimental properties of high-current pinches find a natural explanation in the theory. Aside from evident practical applications, the electromagnetic selfcompression of plasma in high-current devices provides the unique possibility to create and investigate ultradense matter, huge electric and magnetic fields, and ultrahigh pressures in the Earth laboratory experiments.

Global monopole in general relativity

We consider the gravitational properties of a global monopole on the basis of the simplest Higgs scalar triplet model in general relativity. We begin with establishing some common features of hedgehog-type solutions with a regular center, independent of the choice of the symmetry-breaking potential. There are six types of qualitative behaviors of the solutions; we show, in particular, that the metric can contain at most one simple horizon. For the standard Mexican hat potential, the previously known properties of the solutions are confirmed and some new results are obtained. Thus, we show analytically that solutions with the monotonically growing Higgs field and finite energy in the static region exist only in the interval 1 < λ < 3, where λ is the squared energy of spontaneous symmetry breaking in Planck units. The cosmological properties of these globally regular solutions apparently favor the idea that the standard Big Bang might be replaced with a nonsingular static core and a horizon appearing as a result of some symmetry-breaking phase transition at the Planck energy scale. In addition to the monotonic solutions, we present and analyze a sequence of families of new solutions with the oscillating Higgs field. These families are parametrized by n, the number of knots of the Higgs field, and exist for λ < γn=6/[(2n + 1)(n + 2)]; all such solutions possess a horizon and a singularity beyond it.

Towards the theory of the evolution of the Universe

Self-consistent account of the most simple non-gauge vector fields leads to a broad spectrum of regular scenarios of temporal evolution of the Universe completely within the frames of the Einstein’s General relativity. The longitudinal non-gauge vector field is “the missing link in the chain”, displaying the repulsive elasticity and allowing the macroscopic description of the main features of the Universe evolution. The singular Big Bang turns into a regular inflation-like state of maximum compression with the further accelerated expansion at late times. The parametric freedom of the theory allows to forget the troubles of fine tuning. In the most interesting cases the analytical solutions of the Einstein’s equations are found. ∗URL: http://www.kapitza.ras.ru/people/meierovich/Welcome.html

Hydrodynamics of plasma in a dense pinch

Equilibrium configurations and low-frequency radial oscillations (ionic sound) in dense streams of charged particles are considered in the approximation of hydrodynamics of ideal electron and ion liquids, interacting via the electromagnetic field created by the charges. The macroscopic approach used in this paper is valid without assumptions on the equations of state. Properties of the oscillations, due to a special form of the equation of state of the medium, are expressed by means of a single macroscopic parameter, the sound velocity. In the intermediate region of weak currents the ionic sound oscillations with a wavelength higher than a critical value increase exponentially. This instability is related to a trend towards stratification of the beam into separate jets, if the magnetic field of a current in a separate channel is able to prevent the charges from scattering in the radial direction. In a high current beam the instability to excitation of the radial ionic sound oscillations is suppressed by the current magnetic field.

Galaxy rotation curves driven by massive vector fields: Key to the theory of the dark sector

The non-gauge vector field with as simple as possible Lagrangian (1) turned out an adequate tool for macroscopic description of the main properties of dark matter. The dependence of the velocity of a star on the radius of the orbit V (r) – galaxy rotation curve – is derived analytically from the first principles completely within the Einstein’s general relativity. The Milgrom’s empirical modification of Newtonian dynamics in nonrelativistic limit (MOND) gets justified and specified in detail. In particular, the transition to a plateau is accompanied by damping oscillations. In the scale of a galaxy, and in the scale of the whole universe, the dark matter is described by a vector field with the same energy-momentum tensor. It is the evidence of the common physical nature. Now, when we have the general expression (9) for the energy-momentum tensor of dark matter, it is possible to analyze its influence on the structure and evolution of super heavy stars and black holes.

Gravitating global monopoles in extra dimensions and the braneworld concept

Multidimensional configurations with a Minkowski external spacetime and a spherically symmetric global monopole in extra dimensions are discussed in the context of the braneworld concept. The monopole is formed with a hedgehoglike set of scalar fields φi with a symmetry-breaking potential V depending on the magnitude φ2 = φiφi. All possible kinds of globally regular configurations are singled out without specifying the shape of V(φ). These variants are governed by the maximum value φm of the scalar field, characterizing the energy scale of symmetry breaking. If φm < φcr (where φcr is a critical value of φ related to the multidimensional Planck scale), the monopole reaches infinite radii, whereas in the “strong field regime,” when φm ≥ φcr, the monopole may end with a finite-radius cylinder or have two regular centers. The warp factors of monopoles with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the center. All such configurations are shown to be able to trap test scalar matter, in striking contrast to RS2 type five-dimensional models. The monopole structures obtained analytically are also found numerically for the Mexican hat potential with an additional parameter acting as a cosmological constant.

Equilibrium of intergalactic currents

The plasma Universe approach to the structure of the Universe considers space to be filled with a network of currents which can undergo pinch compression. The equilibrium structures of such currents are treated in the same way as the structure in laboratory pinches. The difference, for the galactic case, is that gravitational interaction forces between the particles must be included in the analysis. A simple and straightforward way of achieving this is illustrated. >

Macroscopic Stability of Charged Particle Streams

We compare the analysis of macroscopic instabilities of pinch systems based on classical hydromagnetic theory with an analysis based on two-fluid electromagnetic hydrodynamics. In contrast to the predictions of the hydromagnetic theory, where the sausage-type instability is thought to predominate, the two-fluid electromagnetic hydrodynamics approach indicates that filamentation of the current channel is the most important mechanism at work. We conclude that macroscopic instabilities are not insurmountable obstacles for the laboratory realization of the electromagnetic collapse; that is, the contraction of plasma by the magnetic field of its own current to the condense state.

Macroscopic Theory of Dark Sector

A simple Lagrangian with squared covariant divergence of a vector field as a kinetic term turned out to be an adequate tool for macroscopic description of the dark sector. The zero-mass field acts as the dark energy. Its energy-momentum tensor is a simple additive to the cosmological constant. Massive fields describe two different forms of dark matter. The space-like massive vector field is attractive. It is responsible for the observed plateau in galaxy rotation curves. The time-like massive field displays repulsive elasticity. In balance with dark energy and ordinary matter it provides a four-parametric diversity of regular solutions of the Einstein equations describing different possible cosmological and oscillating nonsingular scenarios of evolution of the Universe. In particular, the singular big bang turns into a regular inflation-like transition from contraction to expansion with the accelerated expansion at late times. The fine-tuned Friedman-Robertson-Walker singular solution is a particular limiting case at the lower boundary of existence of regular oscillating solutions in the absence of vector fields. The simplicity of the general covariant expression for the energy-momentum tensor allows displaying the main properties of the dark sector analytically. Although the physical nature of dark sector is still unknown, the macroscopic theory can help analyze the role of dark matter in astrophysical phenomena without resorting to artificial model assumptions.

Vector fields in multidimensional cosmology

Vector fields in the expanding Universe are considered within the multidimensional theory of General Relativity. Vector fields in general relativity form a three-parametric variety. Our consideration includes the fields with a nonzero covariant divergence. Depending on the relations between the particular parameters and the symmetry of a problem, the vector fields can be longitudinal and/or transverse, ultrarelativistic (i.e. massless) or nonrelativistic (massive), and so on. The longitudinal and transverse vector fields are considered separately in detail in the background of the de Sitter cosmological metric. In most cases the field equations reduce to Bessel equations, and their temporal evolution is analyzed analytically. The energy-momentum tensor of the most simple zero-mass longitudinal vector fields enters the Einstein equations as an additive to the cosmological constant. In this case the de Sitter metric is the exact solution of the Einstein equations. Hence, the most simple zero-mass longitudinal vector field pretends to be an adequate tool for macroscopic description of dark energy as a source of the expansion of the Universe at a constant rate. The zero-mass vector field does not vanish in the process of expansion. On the contrary, massive fields vanish with time. Though their amplitude is falling down, the massive fields make the expansion accelerated. The macroscopic analysis of vector fields in cosmology gives up the hope that the major puzzle -- attraction between individual objects and expansion of the Universe as a whole -- can be solved within the Einsteins theory of general relativity.