[en] This article deals with the magnetohydrodynamic instability of a thin layer which is characterized by a high magnetic shear, a constant curvature radius, and a plasma velocity shear. The magnetic field and the plasma parameters are considered to be piecewise constant inside the layer and in the regions adjacent to the layer. The plasma parameters and the magnetic field are assumed to obey the ideal incompressible magnetohydrodynamics. Fourier analysis is used to calculate small perturbations of the magnetic field and plasma parameters near the layer in linear approximation. The instability growth rate is obtained as a function of different parameters: the magnetic shear angle, the velocity direction angle, the tangential plasma velocity, the layer thickness, the wave number, and the curvature radius. The resulting instability is a mixture of interchange and Kelvin-Helmholtz instabilities on a surface with nonzero curvature. For a fixed velocity shear and curvature radius, the instability growth has a maximum in the case of antiparallel magnetic fields (maximal magnetic shear). This growth rate is an increasing function of the tangential velocity component perpendicular to the magnetic field, and a decreasing function of the velocity component along the magnetic field. The instability is stronger for smaller curvature radius

[en] The reconnection rate is obtained for the simplest case of two-dimensional (2D) symmetric reconnection in an incompressible plasma. In the short note [Erkaev et al., Phys. Rev. Lett. 84, 1455 (2000)], the reconnection rate is found by matching the outer Petschek solution and the inner diffusion region solution. Here the details of the numerical simulation of the diffusion region are presented and the asymptotic procedure which is used for deriving the reconnection rate is described. The reconnection rate is obtained as a decreasing function of the diffusion region length. For a sufficiently large diffusion region scale, the reconnection rate becomes close to that obtained in the Sweet-Parker solution with the inverse square root dependence on the magnetic Reynolds number Re_m, determined for the global size of the current sheet. On the other hand, for a small diffusion region length scale, the reconnection rate turns out to be very similar to that obtained in the Petschek model with a logarithmic dependence on the magnetic Reynolds number Re_m. This means that the Petschek regime seems to be possible only in the case of a strongly localized conductivity corresponding to a small scale of the diffusion region