Stability of an MHD shear flow with a piecewise linear velocity profile

In this paper we present the results of the stability analysis of a simple shear flow of an incompressible fluid with a piecewise linear velocity profile in the presence of a magnetic field. In the flow, a finite transitional magnetic-free layer with a linear velocity profile is sandwiched by two semi-infinite regions. One of these regions is magnetic-free and the flow velocity in the region is constant. The other region is magnetic and the fluid in it is quiescent. The magnetic field is constant and parallel to the flow in the transitional layer. The fluid density is constant both in the magnetic as well as the magnetic-free regions, while it has a jump-type discontinuity at the boundary between the transitional layer and the magnetic region. The effect of gravity is included in the model, and it is assumed that the lighter fluid is overlaying the heavier one, thus no Rayleigh-Taylor instability is present. The dispersion equation governing the normal-mode stability of the flow is derived and its properties are analysed. We study stability of two cases: (i) magnetic-free flow in the presence of gravity, and (ii) magnetic flow without gravity. In the first case, the flow stability is controlled by the Rayleigh number, R. In the second case, the control parameter is the inverse squared Alfvénic Mach number, H . Stability of a particular monochromatic perturbation also depends on its dimensionless wavenumber α. We combine the analytical and numerical approaches to obtain the neutral stability curves in the (α,R)-plane in the case of the magnetic-free flow, and in the (α,H)-plane in the case of the magnetic flow. The dependence of the instability increment on R in the first case, and on H in the second case is treated. We apply the results of the analysis to the stability of a strongly subsonic portion of the heliopause. Our main conclusion is as follows: The inclusion of a transitional layer near the heliopause into the model increases by an order of magnitude the strength of the interstellar magnetic field required to stabilize this portion of the heliopause in comparison with the corresponding stabilizing strength of the magnetic field required when modelling the heliopause as a tangential discontinuity

Nonlinear theory of resonant slow waves in anisotropic and dispersive plasmas

The solar corona is a typical example of a plasma with strongly anisotropic transport processes. The main dissipative mechanisms in the solar corona acting on slow magnetoacoustic waves are the anisotropic thermal conductivity and viscosity [Ballai et al., Phys. Plasmas 5, 252 (1998)] developed the nonlinear theory of driven slow resonant waves in such a regime. In the present paper the nonlinear behavior of driven magnetohydrodynamic waves in the slow dissipative layer in plasmas with strongly anisotropic viscosity and thermal conductivity is expanded by considering dispersive effects due to Hall currents. The nonlinear governing equation describing the dynamics of nonlinear resonant slow waves is supplemented by a term which describes nonlinear dispersion and is of the same order of magnitude as nonlinearity and dissipation. The connection formulas are found to be similar to their nondispersive counterparts

A three-dimensional outer magnetospheric gap model for gamma-ray pulsars: Geometry, pair production, emission morphologies, and phase-resolved spectra

A three-dimensional pulsar magnetosphere model is used to study the geometry of outer magnetospheric gap accelerators, following seminal work of Romani and coworkers. The size of the outer gap is self-consistently limited by pair production from collisions of thermal photons from polar cap heating of backflow outer gap current with curvature photons emitted by gap-accelerated charged particles. In principle, there could be two topologically disconnected outer gaps. Conditions for local pair production such as local field line curvature, soft X-ray density, electric field, etc., support pair production inside an outer gap only between r in(φ) (the radius of the null surface at azimuthal angle φ) and r lim(φ) ≈ 6r in(φ = 0) ≪ R L (the light cylinder radius). Secondary pairs, on the other hand, are produced almost everywhere outside the outer gap by collisions between curvature photons and synchrotron X-rays emitted by these secondary pairs. These processes produce a wide X-ray fan beam in the outgoing direction and a very narrow beam in the incoming direction for each outer gap. For pulsars with a large magnetic dipole inclination angle, part of the incoming y-ray beam will be absorbed by the stellar magnetic field. If the surface magnetic field is dominated by a far off-center dipole moment (e.g., as in a proposed "plate tectonic" model), gravitational bending of photons from polar cap accelerators and their ultimate conversion into outflowing e ± pairs can result in the quenching of one of these two outer gaps. Various emission morphologies for the pulsar (depending on magnetic inclination angle and viewing angle) are presented. Double-peak light curves with strong bridges are most common. From the three-dimensional structure of the outer gap and its local properties, we calculate phase-resolved spectra of gamma-ray pulsars and apply them to observed spectra of the Crab pulsar.published_or_final_versio

A three-dimensional outer-magnetospheric gap model for gamma-ray pulsars: I. The crab pulsar

We use a three-dimensional pulsar magnetosphere model to study the geometry of outer-magnetospheric gaps. The vertical size of the 'outer gap' is first determined by a self-consistent model in which the outer gap size is limited by pair production from collisions between (1) thermal photons produced from polar cap heating by backflow 'outer gap' current, and (2) the curvature photons emitted by gap-accelerated charged particles. The transverse size of the outer gap is also determined by local pair production limits. In principle, there are two topologically disconnected outer gaps in the magnetosphere of a pulsar. Both incoming and outgoing particle flows are allowed. However, the emission morphologies produced by incoming particle flow is severely restricted by local pair production in the gap and the absorption of magnetic pair production near the star. Double-peaked light curves with strong bridges are most common. From the three-dimensional structure of the outer gap and its local properties, we calculate the emission morphologies and phase-resolved spectra of gamma-ray pulsars. Applications to the Crab pulsar illustrate the model.published_or_final_versio

Optimal current quality of a single-phase multilevel inverter with a staircase modulation

The authors address the problem of optimal current quality for a single-phase multilevel inverter with a staircase modulation (Fig.1). The current quality is characterized by current ripple Normalized Mean Square (NMSc). The goal is to find theoretically optimal switching angles and respective minimal NMSc values. The previous research didn't provide comprehensive solutions for arbitrary modulation indices and level counts

Indirect coupling between spins in semiconductor quantum dots

The optically induced indirect exchange interaction between spins in two quantum dots is investigated theoretically. We present a microscopic formulation of the interaction between the localized spin and the itinerant carriers including the effects of correlation, using a set of canonical transformations. Correlation effects are found to be of comparable magnitude as the direct exchange. We give quantitative results for realistic quantum dot geometries and find the largest couplings for one dimensional systems.Comment: 4 pages, 3 figure

Linking the X-ray timing and spectral properties of the glitching AXP 1RXS J170849-400910

Previous studies of the X-ray flux and spectral properties of 1RXS J170849-400910 showed hints of a possible correlation with the spin glitches that occurred in 1999 and 2001. However, due to the sparseness of spectral measurements and the paucity of detected glitches no firm conclusion could be drawn. We retrieved and analysed archival XTE pointings of 1RXS J170849-400910 covering the time interval between January 2003 and June 2006 and carried out a detailed timing analysis by means of phase fitting techniques. We detected two relatively large glitches Delta nu / nu of 1.2 and 2.1 10^-6 occurred in January and June 2005. Interestingly, the occurrence times of these glitches are in agreement with the predictions made in our previous studies. This finding strongly suggests a connection between the flux, spectral and timing properties of 1RXS J170849-400910.Comment: Submitted to A&A, 4 pages; results presented at the INT meeting "The Neutron Star Crust and Surface: Observations and Models" on June 27; referee comments adde

Electronic screening and damping in magnetars

We calculate the screening of the ion-ion potential due to electrons in the presence of a large background magnetic field, at densities of relevance to neutron star crusts. Using the standard approach to incorporate electron screening through the one-loop polarization function, we show that the magnetic field produces important corrections both at short and long distances. In extreme fields, realized in highly magnetized neutron stars called magnetars, electrons occupy only the lowest Landau levels in the relatively low density region of the crust. Here our results show that the screening length for Coulomb interactions between ions can be smaller than the inter-ion spacing. More interestingly, we find that the screening is anisotropic and the screened potential between two static charges exhibits long range Friedel oscillations parallel to the magnetic field. This long-range oscillatory behavior is likely to affect the lattice structure of ions, and can possibly create rod-like structures in the magnetar crusts. We also calculate the imaginary part of the electron polarization function which determines the spectrum of electron-hole excitations and plays a role in damping lattice phonon excitations. We demonstrate that even for modest magnetic fields this damping is highly anisotropic and will likely lead to anisotropic phonon heat transport in the outer neutron star crust.Comment: 14 pages, 5 Figure