Identification of two-phase free boundary arising in plasma physics

We try to estimate the shape and the location of two-phase free boundary wh ich has been studied in [A. Friedman and Y. Liu, Ann. Scuola Norm. Sup. Pis a Cl. Sci. (4), 22 (1995), pp. 375-448] to model a stationary magnetohydrod ynamics system. A sufficient condition is obtained to check whether a test disk is included in the plasma region D surrounded by a two-phase free boun dary. In the test disk technique, only two simply veri able conditions are used and indispensableness of the conditions is demonstrated using an examp le. The technique is applicable to select some of test disks placed in the domain, which gives a rough guess on the shape of plasma region. Next we dr aw some geometrical properties of plasma region D when the domain possesses a kind of convexity. It is proved that if itself contains the mirror image of the right portion {x is an element of Omega : x . xi > t} of the domain with respect to a line {x : x . xi = t} for all t > t(0), then so does the plasma region.