Twin-peak quasiperiodic oscillations as an internal resonance
Two peaks occur in high-frequency power spectra of X-ray lightcurves of several black-hole candidates. We further explore the idea that a non-linear resonance mechanism operating in strong-gravity regime is responsible for these inter-related quasi-periodic oscillations (twin QPOs). By extending the multiple-scales analysis of Rebusco, we construct two-dimensional phase-space sections, which enable us to identify different topologies governing the system and to follow the evolutionary tracks of the twin peaks. This approach suggests that the original (Abramowicz & Kluzniak) parametric-resonance scheme can be viewed as a naive account of the QPOs model with an internal resonance.We show an example of internal resonance in a system with up to two critical points, and describe a general technique that permits other cases to be treated in a systematical manner. A separatrix divides the phase-space sections into regions of different topology. Inside the libration region, the evolutionary tracks bring the observed twin-peak frequencies to an exact rational ratio, whereas the observed frequencies remain off resonance in the circulation region. Our scheme predicts the power should be cyclically exchanged between the two oscillations. Like the high-frequency QPOs in neutron-star binaries, one also expects, as a general property of the non-linear model, that in black-hole sources slight detuning pushes the twin-peak frequencies out of sharp resonance.

title: Magnetic layers and neutral points near a rotating black hole
abstract: Magnetic layers are narrow regions where the field direction changes sharply. They often occur in the association with neutral points of the magnetic field. We show that an organized field can produce these structures near a rotating black hole (BH), and we identify them as potential sites of magnetic reconnection. To that end, we study the field lines affected by the frame-dragging effect, twisting the magnetic structure and changing the position of neutral points. We consider oblique fields in vacuum. We also include the possibility of translational motion of the black hole which may be relevant when the black hole is ejected from the system. The model settings apply to the innermost regions around black holes with the ergosphere dominated by a super-equipartition magnetic field and loaded with a negligible gas content.

title: Stellar capture by an accretion disc
abstract: The long-term evolution of a stellar orbit captured by a massive galactic centre via successive interactions with an accretion disc has been examined. An analytical solution describing the evolution of the stellar orbital parameters during the initial stage of the capture has been found. Our results are applicable to thin Keplerian discs with an arbitrary radial distribution of density and a rather general prescription for the star–disc interaction. Temporal evolution is given in the form of quadrature which can be carried out numerically.

title: Off-equatorial orbits in strong gravitational fields near compact objects
abstract: Near a black hole or an ultracompact star, the motion of particles is governed by a strong gravitational field. Electrically charged particles also feel the electromagnetic force arising due to currents inside the star or plasma circling around. We study the possibility that the interplay between gravitational and electromagnetic actions may allow for the stable, energetically bound off-equatorial motion of charged particles. This would represent the well-known generalized Stormer's 'halo orbits', which have been discussed in connection with the motion of dust grains in planetary magnetospheres. We demonstrate that such orbits exist and can be astrophysically relevant when a compact star or a black hole is endowed with a dipole-type magnetic field. In the case of the Kerr–Newman solution, numerical analysis shows that the mutually connected gravitational and electromagnetic fields do not allow the existence of stable halo orbits above the outer horizon of black holes. Such orbits are either hidden under the inner black-hole horizon, or they require the presence of a naked singularity.

title: Prospects of 3D mapping of the Galactic Centre clouds with X-ray polarimetry
abstract: Despite past panchromatic observations of the innermost part of the Milky Way, the overall structure of the Galactic Centre (GC) remains enigmatic in terms of geometry. In this paper, we aim to show how polarimetry can probe the three-dimensional position of the molecular material in the central ~100 pc of the GC. We investigate a model where the central supermassive black hole Sgr A* is radiatively coupled to a fragmented circumnuclear disc (CND), an elliptical twisted ring representative of the central molecular zone (CMZ), and the two main, bright molecular clouds Sgr B2 and Sgr C. 8 -- 35 keV integrated polarization mapping reveals that Sgr B2 and Sgr C, situated at the two sides of the CMZ, present the highest polarization degrees (66.5 and 47.8 per cent respectively), both associated with a polarization position angle psi = 90deg (normal to the scattering plane). The CND shows a lower polarization degree, 1.0 per cent with psi = -20.5deg, tracing the inclination of the CND with respect to the Galactic plane. The CMZ polarization is spatially variable. We also consider a range of spatial locations for Sgr A* and the reprocessing media, and investigate how the modeled three-dimensional geometry influences the resulting GC polarization. The two reflection nebulae are found to always produce high polarization degrees (>> 10 per cent). We show that a 500 ks observation with a broadband polarimeter could constrain the location and the morphology of the scattering material with respect to the emitting source, revealing the past activity of Sgr A*.

title: 2.5-Dimension Numerical Simulation Of Selfmodulation of Relativistic Electron Bunches in a Plasma.

title: 2,5-dimensional numerical simulation of propagation of the finite sequence of relativistic electron bunches (REB) in tenuous and dense plasmas
abstract: Particle simulation results on the wake-field excitation with the programmed finite sequence of REB in tenuous and dense plasmas are presented. The REB/background plasma configuration is described by full set of 2D3V relativistic Vlasov equations for each plasma species and nonlinear Maxwell equations for self-consistent electromagnetic field. The physical parameters in runs carried out are close to those used in laboratory experiment at Kharkov IPT (Ya. Fainberg et al., 1994). The simulation points to the fact that the reached value of electric field depends on charge distribution and choice of intervals between bunches in programmed sequence.

title: Numerical investigation of high-current ion beam acceleration and charge compensation in two accelerating gaps of induction linac
abstract: The numerical investigation of the hollow high-current ion beam (HHCIB) dynamics in two magnet-isolated accelerating gaps of induction linac are presented. It has been shown that the applied electric field destroys partially the charge and current compensations, and impairs the brightness of the ion beam when the electron beam energy is not sufficient to overcome the potential difference. The acceleration, the charge and current compensations, and the stability of the high-brightness ion beam can be achieved under the optimum parameters choice.<<ETX>>

title: Optimization of high-current ion beam acceleration and charge compensation in two cusps of induction linac
abstract: Results of the numerical simulation of the hollow high-current ion beam (HHCIB) dynamics in two magnet-isolated accelerating gaps separated by the drift gap are presented. The previous study has shown that the good charge and current compensations of the ion beam by the specially injected electron beam occur in the accelerating gaps of the induction linac. However in the drift gap the high positive electric potential due to the positive space charge of HHCIB was obtained because the essential difference between the electron and ion drift velocities exists under this compensation method. This disadvantage impairing the brightness of the ion beam can be considerably reduced by the additional injection of the thermal electrons into the drift region. In present report the some cases of the cold electron injection into drift gap are considered. The more optimal regime for the effective charge and current compensations of HHCIB without loss in the stability of ion beam was found.