The Photoelectron Sheath Around a Spherical Body

Abstract

An approximate method based on a variational principle is used to calculate the surface electric field on a spherical body which is photo-emitting electrons. The treatment also allows an estimate of the sheath dimensions to be made. It is shown that, unlike the planar surface, the sheath parameters are strongly dependent on the velocity distributions of the emitted electrons. As the sphere radius is reduced the sheath shrinks for a monoenergetic, isotropic, velocity distribution of electrons at the surface. However for monoenergetic electrons directed radially it expands. The technique is developed because of the possibility of employing it for more complex systems where other methods would prove intractable.

The same problems will be treated by solving the differential equations using a series expansion; this will indicate the accuracy of the method for small spheres.