One of the discoveries made by the radar sounder on the Mars Express spacecraft is the existence of magnetically controlled structures in the ionosphere of Mars, which result in bulges in the ionospheric electron density contours. These bulges lead in turn to oblique echoes, which show up as hyperbola-shaped features in the echograms. A hyperbola-shaped feature observed over an isolated region of strong crustal magnetic field is associated with a plasma cavity in the upper ionosphere and a corresponding density enhancement in the lower levels of the ionosphere. We suggest that along open magnetic field lines, the solar wind electrons are accelerated downward and the ionospheric ions are accelerated upward in a manner similar to the field line-driven auroral acceleration at Earth. This heating due to precipitating electrons may cause an increase in the scale height and may drive a loss of ionospheric plasma at high altitudes.