The HeH+HeH^+ molecular ion in a magnetic field

A detailed study of the low-lying electronic states {}^1\Si,{}^3\Si,{}^3\Pi,{}^3\De of the $\rm{HeH}^+$ molecular ion in parallel to a magnetic field configuration (when \al-particle and proton are situated on the same magnetic line) is carried out for $B=0-4.414\times 10^{13}$ G in the Born-Oppenheimer approximation. The variational method is employed using a physically adequate trial function. It is shown that the parallel configuration is stable with respect to small deviations for \Si-states. The quantum numbers of the ground state depend on the magnetic field strength. The ground state evolves from the spin-singlet {}^1\Si state for small magnetic fields $B\lesssim 0.5$ a.u. to the spin-triplet {}^3\Si unbound state for intermediate fields and to the spin-triplet strongly bound $^3\Pi$ state for $B \gtrsim 15$ a.u. When the $\rm{HeH}^+$ molecular ion exists, it is stable with respect to a dissociation.Comment: 13 pages, 5 figures, 4 table

Charged Hydrogenic, Helium and Helium-Hydrogenic Molecular Chains in a Strong Magnetic Field

A non-relativistic classification of charged molecular hydrogenic, helium and mixed helium-hydrogenic chains with one or two electrons which can exist in a strong magnetic field $B \lesssim 10^{16}$G is given. It is shown that for both $1e-2e$ cases at the strongest studied magnetic fields the longest hydrogenic chain contains at most five protons indicating to the existence of the $\rm{H}_5^{4+}$ and $\rm{H}_5^{3+}$ ions, respectively. In the case of the helium chains the longest chains can exist at the strongest studied magnetic fields with three and four \al-particles for $1e-2e$ cases, respectively. For mixed helium-hydrogenic chains the number of heavy centers can reach five for highest magnetic fields studied. In general, for a fixed magnetic field two-electron chains are more bound than one-electron ones.Comment: 32 pages, 2 figures, 9 table

Effects of Line-tying on Magnetohydrodynamic Instabilities and Current Sheet Formation

An overview of some recent progress on magnetohydrodynamic stability and current sheet formation in a line-tied system is given. Key results on the linear stability of the ideal internal kink mode and resistive tearing mode are summarized. For nonlinear problems, a counterexample to the recent demonstration of current sheet formation by Low \emph{et al}. [B. C. Low and \AA. M. Janse, Astrophys. J. \textbf{696}, 821 (2009)] is presented, and the governing equations for quasi-static evolution of a boundary driven, line-tied magnetic field are derived. Some open questions and possible strategies to resolve them are discussed.Comment: To appear in Phys. Plasma

Soliton Instabilities and Vortex Streets Formation in a Polariton Quantum Fluid

Exciton-polaritons have been shown to be an optimal system in order to investigate the properties of bosonic quantum fluids. We report here on the observation of dark solitons in the wake of engineered circular obstacles and their decay into streets of quantized vortices. Our experiments provide a time-resolved access to the polariton phase and density, which allows for a quantitative study of instabilities of freely evolving polaritons. The decay of solitons is quantified and identified as an effect of disorder-induced transverse perturbations in the dissipative polariton gas

Extra Dimensions: A View from the Top

In models with compact extra dimensions, where the Standard Model fields are confined to a 3+1 dimensional hyperplane, the $t \bar t$ production cross-section at a hadron collider can receive significant contributions from multiple exchange of KK modes of the graviton. These are carefully computed in the well-known ADD and RS scenarios, taking the energy dependence of the sum over graviton propagators into account. Using data from Run-I of the Tevatron, 95% C.L. bounds on the parameter space of both models are derived. For Run-II of the Tevatron and LHC, discovery limits are estimated.Comment: Typos corrected, references added. 12 pages, LaTeX, 2 ps figure

Nonlinear Dynamics of the Parker Scenario for Coronal Heating

The Parker or field line tangling model of coronal heating is studied comprehensively via long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy. In physical space this corresponds to a magnetic topology where magnetic field lines are barely entangled, nevertheless current sheets (corresponding to the original tangential discontinuities hypothesized by Parker) are continuously formed and dissipated. Current sheets are the result of the nonlinear cascade that transfers energy from the scale of convective motions ($\sim 1,000 km$) down to the dissipative scales, where it is finally converted to heat and/or particle acceleration. Current sheets constitute the dissipative structure of the system, and the associated magnetic reconnection gives rise to impulsive ``bursty'' heating events at the small scales. This picture is consistent with the slender loops observed by state-of-the-art (E)UV and X-ray imagers which, although apparently quiescent, shine bright in these wavelengths with little evidence of entangled features. The different regimes of weak and strong MHD turbulence that develop, and their influence on coronal heating scalings, are shown to depend on the loop parameters, and this dependence is quantitatively characterized: weak turbulence regimes and steeper spectra occur in {\it stronger loop fields} and lead to {\it larger heating rates} than in weak field regions.Comment: 22 pages, 18 figures, uses emulateapj, for mpeg file associated to Figure 17e see (temporarily) http://www.df.unipi.it/~rappazzo/arxiv/jfl.mpg, ApJ, in pres

Energy of eigen-modes in magnetohydrodynamic flows of ideal fluids

Analytical expression for energy of eigen-modes in magnetohydrodynamic flows of ideal fluids is obtained. It is shown that the energy of unstable modes is zero, while the energy of stable oscillatory modes (waves) can assume both positive and negative values. Negative energy waves always correspond to non-symmetric eigen-modes -- modes that have a component of wave-vector along the equilibrium velocity. These results suggest that all non-symmetric instabilities in ideal MHD systems with flows are associated with coupling of positive and negative energy waves. As an example the energy of eigen-modes is calculated for incompressible conducting fluid rotating in axial magnetic field.Comment: 10 pages, 3 figure

X-point collapse and saturation in the nonlinear tearing mode reconnection

We study the nonlinear evolution of the resistive tearing mode in slab geometry in two dimensions. We show that, in the strongly driven regime (large Delta'), a collapse of the X-point occurs once the island width exceeds a certain critical value ~1/Delta'. A current sheet is formed and the reconnection is exponential in time with a growth rate ~eta^1/2, where eta is the resistivity. If the aspect ratio of the current sheet is sufficiently large, the sheet can itself become tearing-mode unstable, giving rise to secondary islands, which then coalesce with the original island. The saturated state depends on the value of Delta'. For small Delta', the saturation amplitude is ~Delta' and quantitatively agrees with the theoretical prediction. If Delta' is large enough for the X-point collapse to have occured, the saturation amplitude increases noticeably and becomes independent of Delta'.Comment: revtex4, 4 pages, 18 figure

Evolution of rarefaction pulses into vortex rings

The two-dimensional solitary waves of the Gross-Pitaevskii equation in the Kadomtsev-Petviashvili limit are unstable with respect to three-dimensional perturbations. We elucidate the stages in the evolution of such solutions subject to perturbations perpendicular to the direction of motion. Depending on the energy (momentum) and the wavelength of the perturbation different types of three-dimensional solutions emerge. In particular, we present new periodic solutions having very small energy and momentum per period. These solutions also become unstable and this secondary instability leads to vortex ring nucleation.Comment: 5 pages, 5 figure