End losses of an inviscid magnetohydrodynamic channel having tensor conductivity and segmented electrodes have been calculated for a magnetohydrodynamic power generator of this geometry. It was found that the constant‐current configuration is more efficient than the constant potential difference case. The efficiencies increase with increasing Hall effect, but constant magnitude extensions to the magnetic field have very little effect. The theoretical efficiency for an aspect ratio of 10 and &ohgr;&tgr;=2 is only 74%.