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One-fluid ideal MHD model is applied for description of\udcurrent sheet flapping disturbances appearing due to a gradient\udof the normal magnetic field component. The wave modes are\udstudied which are associated to the flapping waves observed in\udthe Earth's magnetotail current sheet. In a linear\udapproximation, solutions are obtained for model profiles of the\udelectric current and plasma densities across the current sheet,\udwhich are described by hyperbolic functions. The flapping\udeigenfrequency is found as a function of wave number. For the\udEarth's magnetotail conditions, the estimated wave group speed\udis of the order of a few tens kilometers per second. The\udcurrent sheet can be stable or unstable in dependence on the\uddirection of the gradient of the normal magnetic field\udcomponent. The obtained dispersion function is used for\udcalculation of the flapping wave disturbances, which are\udproduced by the given initial Gaussian perturbation at the\udcenter of the current sheet and propagating towards the flanks.\udThe propagating flapping pulse has a smooth leading front, and\uda small scale oscillating trailing front, because the short\udwave oscillations propagate much slower than the long wave\udones

MHD aspect of current sheet oscillations related to magnetic field gradients