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

Prompt ηc\eta_c meson production at the LHC in the NRQCD with kTk_T-factorization

In the framework of the $k_T$-factorization, the prompt production of $\eta_c$ mesons at the LHC conditions is studied. Our consideration is based on the off-shell amplitudes for hard partonic subprocesses and on the nonrelativistic QCD (NRQCD) formalism for the formation of bound states. We try two latest parametrizations for noncollinear, or transverse momentum dependent (TMD) gluon densities derived from the Catani-Ciafaloni-Fiorani-Marchesini (CCFM) equation. We use the values of the nonperturbative matrix elements obtained from a combined fit of the $\eta_c$ and $J/\psi$ differential cross sections. Finally, we show an universal set of parameters that provides a reasonable simultaneous description for all of the available data on the prompt $J/\psi$ and $\eta_c$ production at the LHC.Comment: 5 pages, 2 figures, 3 table

Prompt charmonia production and polarization at LHC in the NRQCD with kTk_T-factorization. Part III: J/ψJ/\psi meson

In the framework of $k_T$-factorization approach, the production and polarization of prompt $J/\psi$ mesons at the LHC energies is studied. Our consideration is based on the non-relativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. Both the direct production mechanism and feed-down contributions from $\chi_c$ and $\psi(2S)$ decays are taken into account. The transverse momentum dependent (or unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. The non-perturbative color-octet matrix elements were first deduced from the fits to the latest CMS data on $J/\psi$ transverse momentum distributions and then applied to describe the ATLAS and LHCb data on $J/\psi$ production and polarization at $\sqrt s = 7$, $8$ and $13$ TeV. We perform an estimation of polarization parameters $\lambda_\theta$, $\lambda_\phi$ and $\lambda_{\theta \phi}$ which determine $J/\psi$ spin density matrix and demonstrate that treating the soft gluon emission as a series of explicit color-electric dipole transitions within NRQCD leads to unpolarized $J/\psi$ production at high transverse momenta, that is in qualitative agreement with the LHC data.Comment: 23 pages, 14 figures. arXiv admin note: substantial text overlap with arXiv:1508.0548

Heavy quark production in the semihard QCD approach at THERA

In the framework of the semihard ($k_T$ factorization) QCD approach, we consider the photoproduction of D* mesons associated with two hadron jets and the D* production in DIS at THERA conditions with the emphasis on the BFKL and CCFM dynamics of gluon distributions. In the photoproduction of D* mesons the attention is focused on the variable $x_\gamma$, which is the fraction of the photon momentum contributed to a pair of jets with largest $p_T$. We show that our theoretical results are sensitive to the BFKL type dynamics which may be investigated at THERA energies. We also discuss possible effect of \J/\psi meson spin alignement, which is thought to be a vivid manifestation of gluon off-shellness.Comment: 9 pages, 3 figures, in "The THERA Book", DESY-LC-REV-2001-06