Problem of stability of multidimensional solutions of the BK class equations in space plasma

© 2018 COSPAR The problem of stability of the multidimensional solutions of the BK class equations describing the nonlinear waves which are forming on the low-frequency branch of oscillations in plasma for cases when β≡4πnT/B2«1 and β>1 is studied. In first case, for ω<ωB=eB/Mc,kλD«1 the FMS waves are excited, and their dynamics under conditions kx2≫k⊥2, vx«cAnear the cone of θ=arctan(M/m)1/2, is described by the equation of the BK class known as the GKP equation for magnetic field h=B∼/B with due account of the high order dispersive correction defined by values of plasma parameters and angle θ=(B,k). In another case, the dynamics of the finite-amplitude Alfvén waves propagating near-to-parallel to B is described by the equation of the same class known as the 3-DNLS equation for h=(By+iBz)/2B|1-β|. To study the stability of multidimensional solutions in both cases the method of investigation of the Hamiltonian bounding with deformation conserving momentum by solving the variation problem is used. As a result, we have obtained the conditions of existence of the 2D and 3D soliton solutions in the BK system for cases of the GKP and 3-DNLS equation (i.e. for the FMS and Alfvén waves, respectively) in dependence on the equations’ coefficients, i.e. on the parameters of both plasma and wave

Power Spectra of Ionospheric Scintillations

Second order statistical moments of the phase fluctuationsare obtained taking into account the boundary condition,diffraction effects and polarization coefficients of theordinary and extraordinary waves. The variance and thecorrelation function are calculated for arbitrary 3D spectralfunction of electron density fluctuations containing bothanisotropic Gaussian and power-law spectra; anisotropycoefficient and the orientation angle of elongated plasmairregularities. The phase scintillation index and thescintillation level are analyzed numerically. Maximum ofthe scintillation index for small-scale irregularities is in theinterval 0.2-0.3 corresponding to the moderate scintillationintensity, within the weak-scatter regime. Splashes arerevealed for different anisotropy factor of elongated largescaleirregularities varying orientation angle with respect tothe lines of force of geomagnetic field. Scintillation index iscalculated for small-scale irregularities using the “frozenin”assumption and taking into account movement of rigidirregularities. Log-log plots of the power spectrum of theintensity fluctuations have the same minimums satisfyingthe “standard relationship” of scattered ordinary andextraordinary waves. It was shown that the normalizedscintillation level growth in both non-fully-developeddiffraction pattern and in transition zone increasinganisotropy factor. Rising orientation angle scintillation leveldecreases and splashes arises in fully developedscintillation region

Statistical Moments and Scintillation Level of Scattered Electromagnetic Waves in the Magnetized plasma

Statistical characteristics of scattered ordinary and extraordinary electromagnetic waves in the magnetized plasma are considered using the smooth perturbation method. Diffraction effects and polarization coefficients are taken into account. Second order statistical moments of scattered radiation are obtained for arbitrary correlation function of electron density fluctuations. Broadening of the spatial power spectrum and displacement of its maximum, wave phase structure function and the angle-of-arrivals are obtained for three-dimensional spectral function containing anisotropic Gaussian and power-law spectral functions. Scintillation level of scattered radiation is analyzed for different parameters characterizing anisotropic plasma irregularities for the ionospheric F-region. The spectral widths (first and second moments) of the power spectrum and scintillation periods are calculated for “frozen-in” drifting elongated plasma irregularities using the experimental data

Swift Observations of Mrk 421 in Selected Epochs. II. An Extreme Spectral Flux Variability in 2009-2012

We present the results from a detailed spectral and timing study of Mrk 421 based on the rich archival Swift data obtained during 2009-2012. Best fits of the 0.3-10 keV spectra were mostly obtained using the log-parabolic model showing the relatively low spectral curvature that is expected in the case of efficient stochastic acceleration of particles. The position of the synchrotron spectral energy density peak E p of 173 spectra is found at energies higher than 2 keV. The photon index at 1 keV exhibited a very broad range of values a = 1.51-3.02, and very hard spectra with a -1. Moreover, 113 instances of intraday variability were revealed, exhibiting shortest flux-doubling/halving times of about 1.2 hr, as well as brightenings by 7%-24% in 180-720 s and declines by 68%-22% in 180-900 s. The X-ray and very high-energy fluxes generally showed a correlated variability, although one incidence of a more complicated variability was also detected, indicating that the multifrequency emission of Mrk 421 could not be generated in a single zone

Swift Observations of Mrk 421 in Selected Epochs. I. The Spectral and Flux Variability in 2005-2008

We present detailed results of Swift observations of the nearby TeV-detected blazar Mrk 421, based on the rich archival data obtained during 2005 March-2008 June. The best fits of the 0.3-10 keV spectra were mainly obtained using the log-parabolic model, yielding low spectral curvatures expected in the case of the efficient stochastic acceleration of particles. During strong X-ray flares, the position of the synchrotron spectral energy distribution peak {E}{{p}} was beyond 8 keV for 41 spectra, while it sometimes was situated at the UV frequencies in quiescent states. The photon index at 1 keV exhibited a broad range, and the values a< 1.70 were observed during the strong flares, hinting at the possible presence of a jet hadronic component. The spectral parameters were correlated in some periods, expected in the framework of the first- and second-order Fermi accelerations of X-ray emitting particles, as well as in the case of turbulence spectrum. The 0.3-10 keV flux and spectral parameters sometimes showed very fast variability down to the fluctuations by 6-20% in 180-960 s, possibly related to the small-scale turbulent areas containing strongest magnetic fields. X-ray and very high-energy fluxes often showed correlated variability, although several occurrences of more complicated variability patterns are also revealed, indicating that the multifrequency emission of Mrk 421 could not be generated in a single zone

The modified method of contour dynamics and modeling of vortical structures

© 2019, Kazan Federal University. All rights reserved. This paper considers one of the most effective methods for modeling vortical structures, which are described by the 2-dimensional equation of carry of a vortex and by the Poisson equation for a flow function, namely, the contour dynamics method based on representation of a vortical stream by finite-area vortical regions. A modification of the contour dynamics method minimizing the errors arising at its direct application to description of vortical structures has been elaborated. The examples of the results of numerical experiments on the study of the dynamics of interaction of vortical structures for various configurations of their relative positioning, signs of vorticity, and distances between borders of the finite-area vortical regions have been presented

The modified method of contour dynamics and modeling of vortical structures

© 2019, Kazan Federal University. All rights reserved. This paper considers one of the most effective methods for modeling vortical structures, which are described by the 2-dimensional equation of carry of a vortex and by the Poisson equation for a flow function, namely, the contour dynamics method based on representation of a vortical stream by finite-area vortical regions. A modification of the contour dynamics method minimizing the errors arising at its direct application to description of vortical structures has been elaborated. The examples of the results of numerical experiments on the study of the dynamics of interaction of vortical structures for various configurations of their relative positioning, signs of vorticity, and distances between borders of the finite-area vortical regions have been presented

Investigation of the strong turbulence in the geospace environment

Plasma vortices are often detected by spacecraft in the geospace (atmosphere, ionosphere, magnetosphere) environment, for instance in the magnetosheath and in the magnetotail region. Large scale vortices may correspond to the injection scale of turbulence, so that understanding their origin is important for understanding the energy transfer processes in the geospace environment. In a recent work, turbulent state of plasma medium (especially, ionosphere) is overviewed. Experimental observation data from THEMIS mission (Keiling et al., 2009) is investigated and numerical simulations are carried out. By analyzing the THEMIS data for that event, we find that several vortices in the magnetotail are detected together with the main one and these vortices constitute a vortex chain. Such vortices can cause the strong turbulent state in the different media. The strong magnetic turbulence is investigated in the ionsophere as an ensemble of such strongly localized (weakly interacting) vortices. Characteristics of power spectral densities are estimated for the observed and analytical stationary dipole structures. These characteristics give good description of the vortex structures