Upstream ions converting into downstream pick-up ions: the effect of shock-decelerated frozen-in fields

Context. Observations by Voyager-2 at the crossing of the solar wind termination shock have led to unexpected discoveries, such as the downstream solar wind protons still having Mach numbers higher than 1 and temperatures, though increased by a factor of about 30, nevertheless being much lower than those expected from classical MHD shock theory. Though our earlier semi-kinetic theories of the ion passage over the termination shock, in which the conservation of the magnetic ion moment was required, provided interesting insights into the detailed microphysics occurring at the shock, our predictions for the downstream ion pressure and temperature in view of observations were both too low. Aims. Here we improve on our earlier theoretical approach by introducing a so-called effective magnetic moment by which we not only take into account the increase in the magnetic field magnitude over the shock, but we also respect that the ions comoving with the bulk of the plasma flow gyrate around a decelerated frozen-in field. Methods. We derive a differential equation for the behaviour of the perpendicular pressure across the shock, which accounts for the conservation of the newly derived effective magnetic moment, and generalises the results of earlier studies. The resulting differential equation is then solved analytically. Results. With this new concept of conservation of the newly introduced effective magnetic moment we arrive at interesting new relations between upstream and downstream ion pressures and temperatures which now nicely represent the recent Voyager-2 results.