Characteristics of the spatial structure of Martian magnetic flux ropes recovered by the Grad-Shafranov reconstruction technique

Mars is a unique planet because it locally possesses strong crustal magnetic fields mainly located in the southern hemisphere [e.g., Acuna et al., 1999]. The Martian electromagnetic environment can thus become highly complicated and variable, since the interplanetary magnetic field embedded in the solar wind interacts with the Martian crustal magnetic fields. Whereas it is known that the Martian upper atmosphere is escaping to interplanetary space due to the interaction with the solar wind [e.g., Lundin et al., 1989; Barabash et al., 2007], the contribution of crustal magnetic fields to atmospheric escape from Mars has not yet been well understood. Flux ropes are characteristic magnetic field structures seen throughout the solar system, e.g., at the Sun, in the interplanetary space, and at the terrestrial magnetosphere. Flux ropes are also observed at planets such as at Venus and Mars [e.g., Russell and Elphic, 1979; Vignes et al., 2004], which do not possess a global intrinsic magnetic field. Brain et al. [2010] found a large-scale isolated magnetic flux rope filled with Martian atmospheric plasma located downstream from the crustal magnetic fields with respect to the solar wind flow based on the Mars Global Surveyor (MGS) measurements. They suggested that the magnetic flux rope could be intermittently detached from Mars, and remove significant amounts of atmosphere away from Mars. They proposed that this process might occur frequently and account for as much as 10% of the total present-day ion escape from Mars. However, this estimation of the ion escape rate is somewhat ambiguous, because it is difficult to infer the spatial structure of them from the single spacecraft data. We here investigated characteristics of the Martian magnetic flux ropes based on the Grad-Shafranov (GS) reconstruction technique using the MGS magnetic field data. This technique is capable of recovering the two-dimensional spatial structure of the magnetic flux ropes from single spacecraft data [e.g., Hu and Sunnerup, 2002]. The resultant structure allows us to provide a reliable observational restriction on the spatial scales of magnetic flux ropes. We applied the GS reconstruction technique to 135 obvious magnetic flux rope events observed by MGS. As a result, their spatial structures were successfully recovered for 70 events. The reconstruction results indicated that magnetic flux rope axes are mostly oriented horizontally with respect to the Martian surface. We demonstrated that the events, which have solar zenith angle larger than 75 deg and duration longer than 240 sec, are mostly in the region where the upstream crustal magnetic field strength is larger than the other events. Using the shape and size of the flux ropes obtained from the GS reconstruction technique, we are able to calculate lower limits on their volume and the potential ion escape rates. The volumes can vary by factors of 2--3 orders of magnitude. Ion escape rates via the flux ropes based on the GS reconstruction technique turn out to attain to the order of 10^22 -- 10^23 ion/sec. This result could be comparable to the global ion escape rate obtained from the ion mass analyzer onboard the Mars Express orbiter at solar minimum [e.g., Barabash et al., 2007].