Quantum Macroscopic Effects in a Degenerate Strongly Magnetized Nucleon Gas

A model of a degenerate gas consisting of neutrons that are in chemical equilibrium with degenerate protons and electrons in a stationary and homogeneous superstrong magnetic field is used to describe the state of the matter in central regions of strongly magnetized neutron stars. Expressions for thermodynamic quantities (such as energy density, particle density, pressure, and magnetization) characterizing a degenerate gas of neutrons, protons, and electrons are obtained. In these expressions, the contributions determined by the interaction between anomalous magnetic moments of fermions and the magnetic field are taken into account. Macroscopic effects that may occur in strongly magnetized neutron stars are discussed. We show that all thermodynamic quantities characterizing electrically charged fermions in a strong magnetic field are subject to nonperiodic oscillations caused by the interaction of the anomalous magnetic moments of protons and electrons with the magnetic field. We also show that if the nucleon density and the electron density exceed threshold values that are relatively small and depend on the magnetic field strength, all fermions are fully polarized with respect to the spin. The full spin polarization effect in neutrons is caused by the interaction between the anomalous magnetic moment and the magnetic field. The obtained results may prove useful in understanding processes that occur in the nucleus of a neutron star with a magnetic field frozen into the star.     

Electroweak Nucleon Decays in a Superstrong Magnetic Field

We study the influence of a magnetic field on the electroweak processes of nucleon decay in a degenerate ideal gas of neutrons, protons, and electrons situated in an external superstrong constant and homogeneous magnetic field with effects due to the interaction of nucleon anomalous magnetic moments with the magnetic field taken into account. For different values of the chemical potentials of degenerate fermions, we obtain expressions for probabilities of electroweak processes, which are assumed to be responsible for the chemical equilibrium in the central domain of a neutron star with a frozen superstrong magnetic field. We show that the difference between the neutron decay probabilities in the presence of a magnetic field B ≪ 10¹⁷ G and without this field is completely determined by changing the phase volume of electron states. We discuss the process of proton decay into a neutron, positron, and neutrino. This process is energetically allowed only when the interaction of nucleon anomalous magnetic moments with a superstrong magnetic field is taken into account. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 108–122, October, 2005.     

Nucleon Instability in a Degenerate Magnetized Nucleon–Electron Gas

In the framework of the model of a degenerate relativistic ideal neutron–proton–electron gas (np ⁺ e ^– gas) in an external superstrong constant and homogeneous magnetic field, we study the effect of the magnetic field on the state of chemical equilibrium of the np ⁺ e ^– gas and on the processes of electronic (^–) and positronic (⁺) nucleon decay taking the effects due to the interaction between the nucleon anomalous magnetic moments and the magnetic field into account. For sufficiently large values of the magnetic induction, the proton density in chemical equilibrium must exceed the neutron density. Including the interaction between the nucleon anomalous magnetic moments M _n,p and the magnetic field results in an insignificant reduction of the proton density, but, as in the case M _n,p=0, the proton density in chemical equilibrium in the presence of the superstrong magnetic field exceeds the neutron density. We show that if the interaction between the nucleon anomalous magnetic moments and the superstrong magnetic field is taken into account, then the positronic decay of a free proton (i.e., a proton not entering the composition of an atomic nucleus) into a neutron, a positron, and a neutrino can become energetically allowed. We discuss the necessary conditions for realizing the phase transition from the nucleon phase to the quark phase of the substance in the central region of a strongly magnetized neutron star.     

On the motion of a solid in a magnetic field

The problem of the motion of a magnetic solid in a constant uniform magnetic field, taking gyromagnetic effects into account, is considered. The equations of motion are derived, the Hamiltonian structure is studied, and the cases of integrability indicated. Certain classes of stationary motions are studied and their stability examined.

The gyromagnetic effects arise because the electrons have magnetic and mechanical spin moments /1/. The rotation of the body causes it to become magnetized (the Barnett effect) and when a freely suspended body is magnetized, it begins to rotate (the Einsteinde Haas effect). It is found that gyromagnetic phenomena must be taken into account when analysing the motion of gyroscopic precision systems.     

Nonlinear Electromagnetic Delay of Electromagnetic Signals Propagating in the Magnetic Meridian Plane of Pulsars and Magnetars

We analyze the propagation of electromagnetic waves in the magnetic meridian planes of neutron stars with a strong magnetic field in the framework of the parameterized post-Maxwellian electrodynamics of the vacuum. The origin of these electromagnetic waves is the curvature emission of X-rays and gamma rays from high-energy electrons in the vicinity of the magnetic poles of neutron stars. We show that in the case of a slowly varying intensity of X-ray and gamma-ray emission, the delay of the slow normal mode of electromagnetic waves relative to the fast mode results in a shift of the time dependence of the intensity of the detected radiation with one polarization relative to that of the radiation with the orthogonal polarization. In the case of single X-ray or gamma-ray pulses, the delay effect results in the polarization of the detected pulse varying during the pulse length, the leading edge of all pulses being polarized normally to the magnetic equator plane of the neutron star. We note that the modern level of the experimental technique, in principle, allows observing the manifestations of the delay effect for signals of different polarizations.     

Hybrid Simulation of Space Plasmas: Models with Massless Fluid Representation of Electrons. IV. Kelvin–Helmholtz Instability

This is a survey of the literature on hybrid simulation of the Kelvin–Helmholtz instability. We start with a brief review of the theory: the simplest model of the instability—a transition layer in the form of a tangential discontinuity; compressibility of the medium; finite size of the velocity shear region; pressure anisotropy. We then describe the electromagnetic hybrid model (ions as particles and electrons as a massless fluid) and the main numerical schemes. We review the studies on two-dimensional and three-dimensional hybrid simulation of the process of particle mixing across the magnetopause shear layer driven by the onset of a Kelvin–Helmholtz instability. The article concludes with a survey of literature on hybrid simulation of the Kelvin–Helmholtz instability in finite-size objects: jets moving across the magnetic field in the middle of the field reversal layer; interaction between a magnetized plasma flow and a cylindrical plasma source with zero own magnetic field.     

Investigation of the Effective Space–Time of the Vacuum Nonlinear Electrodynamics in a Magnetic Dipole Field

The metric tensor of the effective pseudo-Riemannian space–time for an electromagnetic wave propagating in the magnetic dipole field and the gravitational field of a neutron star is obtained within a parameterized post-Maxwellian vacuum electrodynamics. The angles of the nonlinear electrodynamic and gravitational ray bending for electromagnetic waves propagating in the magnetic equatorial plane of the star are calculated based on an analysis of isotropic geodesics of this space. We show that for all nonlinear theories whose post-Maxwellian parameters do not coincide, the velocity of the electromagnetic signal propagation in external fields and the rays along which these signals propagate depend on the polarization of the electromagnetic waves. The difference of the source-to-detector propagation time of these signals for two principal polarization states is calculated.     

在重力场和磁场影响下自旋刚性航天器的周期运动

考虑重力场和磁场对轴对称航天器本体的影响，研究其质心在圆形轨道上的运动,通过降低系统的运动方程数，并将它变成为一个带电粒子在电磁场作用下的平面运动．确认系统运动是稳定的，并通过Liapunov全纯积分定理，构建其近似的周期运动.     

Electron in the Aharonov-Bohm potential and in the Coulomb field in 2+1 dimensions

We obtain exact solutions of the Dirac equation in 2+1 dimensions and the electron energy spectrum in the superposition of the Aharonov-Bohm and Coulomb potentials, which are used to study the Aharonov-Bohm effect for states with continuous and discrete energy spectra. We represent the total scattering amplitude as the sum of amplitudes of scattering by the Aharonov-Bohm and Coulomb potentials. We show that the gauge-invariant phase of the wave function or the energy of the electron bound state can be observed. We obtain a formula for the scattering cross section of spin-polarized electrons scattered by the Aharonov-Bohm potential. We discuss the problem of the appearance of a bound state if the interaction between the electron spin and the magnetic field is taken into account in the form of the two-dimensional Dirac delta function. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 502–517, December, 2006. An erratum to this article is available at .     

Semiclassical Spectral Series of a Helium-like Atom in a Magnetic Field

We apply the complex WKB method (the Maslov complex germ theory) to the model of two electrons in a field with a fixed center. We construct semiclassical spectral series of the Pauli operator eigenvalues in the external magnetic field with the spin–orbital and spin–spin interactions and the quadrupole moment of the nucleus taken into account. These series correspond to a new type of closed phase trajectories, the relative equilibrium positions of the corresponding classical nonintegrable system. Explicit effective formulas are derived for the fine (Zeeman effect) and the hyperfine splitting of semiclassical energy levels of a helium-like ion with an arbitrary nucleus charge Z in the entire range of the magnetic field magnitude, including the extreme cases of weak and ultrastrong fields.     

Simulation of particle dynamics in a rapidly varying viscous flow

A method for the numerical simulation of the dynamics of particles in a rapidly varying viscous flow has been developed and implemented as a software package. The frequency of variations in the fluid velocity is assumed to be such that the nonlinear terms in the equations of motion can be neglected in comparison with the nonstationary terms. The hydrodynamic interaction of the particles is taken into account. The velocities of the particles and their trajectories are computed. It is found that the trajectories of the particles depend substantially on the ratio of their radii. In the case of dipole particles in a rapidly varying external magnetic field, the hydrodynamic interaction is shown to prevent the particles from approaching each other under the influence of dipole-dipole interaction forces.     

On the stability of uniformly rotating liquid in a weak magnetic field

We analyze the simplest free boundary problem of magnetohydrodynamics governing the evolution of an isolated mass of a viscous incompressible liquid in the presence of the magnetic field. The motion of the liquid is governed by the Navier–Stokes equations, and for the magnetic field we have the Maxwell equations with an excluded displacement current. The magnetic field should be determined not only in the domain filled with the liquid, but also in the surrounding vacuum region. On the free boundary of the liquid standard jump conditions for the magnetic field are prescribed, as well as kinematic and dynamic boundary conditions, where the magnetic stress tensor is taken into account. We prove that the solution corresponding to a rigid rotation of the fluid and to zero magnetic field is stable if the functional of potential energy has a positive second variation. Bibliography: 11 titles.     

Backlund transformations and Painleve analysis: Exact solutions for a Grad--Shafranov-type magnetohydrodynamic equilibrium

The problem of plasma equilibrium in a gravitational field isinvestigated analytically. For the two-dimensional problem,the system of ideal magnetohydrodynamic equations is reducedto a single nonlinear elliptic equation of the magnetic potentialas a Grad-Shafranov-type equation. By specifying the arbitraryfunctions in this equation, the sinh-Poisson equation can beobtained. Using the Bäcklund-transformation technique andPainlevé analysis, a set of exact solutions are obtainedwhich adequately describe force-free models for solar flaresand plane-parallel filaments of a diffuse magnetized plasmasuspended horizontally in equilibrium in a uniform gravitationalfield.     

Resonance effects in the field of a stationary electromagnetic wave and a constant magnetic field

We analyze the interaction of a charged relativistic particle with the electromagnetic field given by a superposition of a stationary wave and a constant magnetic field. The refraction coefficient of the medium is taken different from one. We investigate the problem in the low-signal approximation. To test the results, we used computer simulation of the original system with two scales of the variation rate of the variables taken into account.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 64–71, January, 2005.     

Submodels of gas motion with a linear velocity field in the degenerate case

We look for solutions in the form of a linear velocity field for the gas dynamics equations with an arbitrary state equation. We find all possible state equations and the corresponding differential equations of submodels when the auxiliary matrix is degenerate.     

Asymptotic behaviour for a non‐monotone fluid in one dimension: the positive temperature case

We consider a one‐dimensional continuous model of neutron star, described by a compressible Navier–Stokes system with a non‐monotone equation of state, due to the effective Skyrme nuclear interaction between particles. We study the asymptotic behaviour of globally defined solutions of a mixed free boundary problem for our model, for large time, assuming that a sufficient thermal dissipation is present. Copyright © 2001 John Wiley & Sons, Ltd.     

On some integral-consistent methods for calculating magnetohydrodynamic phenomena in problems of computational astrophysics

When constructing difference schemes for calculating complex problems of computational astrophysics considering magnetohydrodynamic and gravitational phenomena, the processes of matter overcompression (with a change in density by several orders of magnitude) should be taken into account, and it is important at a discrete level to take into account the corresponding energy transformations of magnetohydrodynamic, gravitational, kinetic, and internal energy during the evolution of a star. This problem is solved by constructing completely conservative difference schemes in a view of these magnetohydrodynamic processes and self-gravitating phenomena. In this work, to study and apply the difference methods for solving problems of magnetic gas dynamics, a discrete representation of symmetrized spatial deformations of the medium was obtained. The representation is consistent with changes in the magnetic, kinetic, and internal energies and does not lead to their distortions when the matter is overcompressed.     

Expansion of a wedge of non-ideal gas into vacuum

We study the problem of expansion of a wedge of non-ideal gas into vacuum in a two-dimensional bounded domain. The non-ideal gas is characterized by a van der Waals type equation of state. The problem is modeled by standard Euler equations of compressible flow, which are simplified by a transformation to similarity variables and then to hodograph transformation to arrive at a second order quasilinear partial differential equation in phase space; this, using Riemann variants, can be expressed as a non-homogeneous linearly degenerate system provided that the flow is supersonic. For the solution of the governing system, we study the interaction of two-dimensional planar rarefaction waves, which is a two-dimensional Riemann problem with piecewise constant data in the self-similar plane. The real gas effects, which significantly influence the flow regions and boundaries and which do not show-up in the ideal gas model, are elucidated; this aspect of the problem has not been considered until now.