In the source-surface approach to field modeling, the magnetosphere is divided conceptually into inner and outer regions (called S and T) by prescribing a cross-magnetospheric surface that marks the tail entrance. The source surface thus consists of the prescribed magnetopause and the prescribed tail-entrance surface. In the inner region (S) enclosed by the source surface, the magnetic field B is expanded formally in a series of analytical functions (e.g., gradients of spherical harmonics) with coefficients determined by a least-squares fit to the desired boundary conditions (namely that the field be tangential to the magnetopause and normal to the tail-entrance surface). Field lines in the tail region (T) are constructed geometrically so as to intersect the tail-entrance surface normally but not to intersect each other or the magnetopause. Expansion coefficients for region S are determined by minimizing a user-specified linear combination of the mean-square normal component of B on the magnetopause and the mean-square tangential component of B on the tail-entrance surface. This model leads to a neutral line (contour of vanishing normal component of B) on the prescribed cross-tail surface. The neutral line constitutes the inner edge of the neutral sheet and marks the boundary (separatrix) between closed and open magnetic field lines. A mapping of the separatrix along magnetic field lines to the planetary surface defines (in the absence of a penetrating interplanetary magnetic field, which can be added later) the poleward boundary of the auroral oval. This mapping accounts well for quiet-time auroral ovals seen in DMSP images. The source-surface model also yields the position and shape of the neutral sheet in the tail region (T), where the strength of B can be calculated (from the normal component of B at the tail-entrance surface) by invoking flux conservation. The current density J in region T can be computed from ∇¿B there. ¿ American Geophysical Union 1996