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Aims. We reinvestigate the parallel pressure-anisotropic MHD shock with an emphasis on the downstream stability of the plasma with respect to the firehose instability. Methods. Aiming to close the underdetermined jump conditions, we take advantage of a kinetic model of the shock transit, based on the Boltzman-Vlasow equation with CGL invariants. In addition, we show that we need to consider plasma waves as an additional component of the system. Results. The system of jump conditions and the kinetic model reduces to a relatively simple form. At first glance, about all parallel magnetosonic shocks must be considerd unstable, at least with respect to plasma-wave generation caused by the firehose instability. In a similar way to this fundamental instability, the system will be also unstable when considering other plasma instabilities.

Modified jump conditions for anisotropic temperature plasmas at parallel shocks