A marginal minimum B mirror magnetic field has been proposed as an external plasma confining magnetic field for a single cell open magnetic mirror trap. An analytical expression for the flux tube ellipticity of this magnetic field has in a previous study been derived with a zero plasma β approximation. This mirror field, which consists of straight nonparallel field lines in the confinement region, has a particular interest since it is likely to correspond to the smallest possible ellipticity for a magnetohydrodynamic stable mirror confinement. The plasma current is in this paper taken into account to the first order in β and the influence of the plasma magnetic field on the magnetic flux surface geometry is studied.