Analytic evaluation of field emission enhancement factors for ellipsoidal cones and elliptic cross-section wedges

An unambiguous comparison for the magnification factor, M, in field emission is derived by solving rigorously Laplace equations for the cases of individual prolate ellipsoids (cones) of revolution on one side, and for an elliptical wedge on the other side, under the assumption that a uniform electric field exists at some distance away from the emitting surface. Significant superiority of M for individual emitters with rotational symmetry is demonstrated as compared to the wedge. Also discussed is the case of a floating sphere. >