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In this paper we demonstrate that solar wind ions, passing over the quasiperpendicular portion of the solar wind MHD termination shock, unavoidably develop strongly pronounced pitchangle anisotropies. In order to prove that, we solve the Boltzmann-Vlasov equation for the ions, kinetically describing the ion passage over the MHD structure of the shock. With the solution of the anisotropic downstream ion distribution function we may also calculate higher order velocity moments of this distribution enabling us to calculate anisotropic downstream ion pressures. From these latter results we derive the conclusion that in most likely cases the downstream ion distribution will be mirror-mode unstable and with its free thermal energy will effectively drive magnetosonic turbulences. We estimate the energy that is pumped into this turbulence until marginal stability is achieved. In this newly established intermediate quasi-equilibrium state, as we can show, one can find 35 to 50 percent of the original energy sitting in the thermal mode perpendicular to the magnetic field in the form of magnetosonic turbulences, perhaps already identified by Voyager-1 as downstream trains of magnetic holes and humps. We discuss several consequences of this new quasi-equilibrium MHD plasma state downsstream of the shock.