Analytic solution for the critical state in superconducting elliptic films

A thin superconductor platelet with elliptic shape in a perpendicular magne tic field is considered. Using a method originally applied to circular disk s, we obtain an approximate analytic solution for the two-dimensional criti cal state of this ellipse. In the limits of the circular disk and the long ship this solution is exact, i.e., the current density is constant in the r egion penetrated by flux. For ellipses with arbitary axis ratio the obtaine d current density is constant to typically 10(-3), and the magnetic moment deviates by less than 10(-3) from the exact value. This analytic solution i s thus very accurate. In increasing applied magnetic field, the penetrating flux fronts are approximately concentric ellipses whose axis ratio b/a les s than or equal to 1 decreases and shrinks to zero when the flux front reac hes the center, the long axis staying finite in the fully penetrated state. Analytic expressions for these axes, the sheet current, the, magnetic mome nt, and the perpendicular magnetic field are presented and discussed. This solution applies also to superconductors with anisotropic critical current if the anisotropy has a particular, rather realistic form. [S0163-1829(99)0 4825-0].