ELECTRIC-POTENTIAL AND FIELD NEAR POINTED SHAPED SURFACES

The trajectories of charged particles, emitted from within or from the close vicinity of pointed shaped surfaces, requires the knowledge of the electric field resulting from the potential bias between surface a nd detector, or screen. Frequently it is necessary the use of numerica l methods for solving Laplace's equation as a result of difficulties i n obtaining an analytical expression. Recently we have shown that, whe n any two coordinate surfaces of an orthogonal system are kept at two different but constant potentials, it is possible to obtain an analyti cal solution for the potential in a relatively simple manner. Using th is general property of orthogonal coordinate systems, we present the s olution for the electric potential and field in the vicinity of pointe d surfaces for several cases of practical interest in field emission, field ionisation, atom-probe field ion spectroscopy and related phenom ena.