Fringing field effects in a cylindrical condenser

The electrode curvature contributes as a first-order effect to the field strength in a cylindrical condenser: its effect decreases as the gap width decreases. This paper is intended to revise an earlier paper, where the field form was carried out as a series expansion involving universal coefficients. In spite of its attractive features, this technique happens to fail whenever a strong field-penetration takes place, which is often the case in the presence of field clamps. A new technique is thus devised, enabling the electrostatic potential to be a carried out as the sum of a zeroth- and a first-order term fulfilling a two-dimension Laplace and Poisson equation, respectively, in cartesian coordinates. The Poisson equation involves a fictitious charge distribution accounting for the electrode curvature. The potential being known in a first-order approximation, second-order terms may be included in the motion equations. Their integration shows that the flight time of a charged particle is affected by first-order potential corrections. The shape of the trajectory is unaffected and formally coincides with the path in a parallel-plate condenser. Values of the virtual-boundary abscissa and of the main fringe-field integral are plotted against the clamp-to-condenser distance for several clamp widths. (orig.)