Advanced method to derive the IMF direction near Mars from cycloidal proton distributions

In a previous paper, we showed a method for deriving the interplanetary magnetic field (IMF) orientation from the velocity distribution of ring-like distributed ions as measured by the Ion Mass Analyser (IMA) on board Mars Express (MEX). This method has been improved so that one can derive the IMF orientation from a very limited portion of the ring distributions, i.e., only the highest energy portion of the ring distribution. This method uses the maximum variance direction L instead of the minimum variance direction N, which are derived from manually selected ring data. Because IMA's count rate for a semi-persistent ring distribution is nearly proportional to energy squire, L is most likely aligned to the tangential direction of the ring distribution at its highest energy, and this tangential direction is parallel or anti-parallel to the electric field. A vector product of L and the solar wind direction (X) gives the IMF orientation projected to the Y-Z plane. The tilt angle of IMF toward the X direction from the Y-Z plane is the same as the angle between the X direction and the ring plane, and is obtained from two methods when the initial speed of the ring ions is estimated to be much smaller than the solar wind speed: (1) angle between the velocity of ring's maximum energy portion and the solar wind vector, and (2) energy ratio between the solar wind and the maximum energy of the ring. The present method is applied to the IMA data from 3 June 2005 (0605-0640 UT) when the Mars Global Surveyor (MGS) magnetometer data are available. Using these data, we also tried to determine the sign of the IMF direction by estimating the evolution direction of the ring ions.