Electrostatic field enhancement on end-caps of cylindrical field-emitters

The apex field enhancement factor (AFEF) γ a of a cylindrical emitter depends sensitively on its end-cap geometry. The hemispherical end-cap is well studied due to its simplicity, but, in general, a cylindrical emitter may terminate in a variety of end-cap shapes. It is well known that the AFEF depends on the ratio h / R a, where h is the total height of the emitter and R a is the apex radius of curvature. The authors show here that there can be a large variation in γ a as the end-cap geometry is altered while keeping h / R a fixed. They carry out a systematic numerical study and determine an approximate formula for γ a in terms of measurable end-cap geometry parameters such as its height H, the radius of the cylinder R, and the apex radius of curvature R a. They show that the formula is robust and can predict the net field emission current with errors generally less than 40 %.The apex field enhancement factor (AFEF) γ a of a cylindrical emitter depends sensitively on its end-cap geometry. The hemispherical end-cap is well studied due to its simplicity, but, in general, a cylindrical emitter may terminate in a variety of end-cap shapes. It is well known that the AFEF depends on the ratio h / R a, where h is the total height of the emitter and R a is the apex radius of curvature. The authors show here that there can be a large variation in γ a as the end-cap geometry is altered while keeping h / R a fixed. They carry out a systematic numerical study and determine an approximate formula for γ a in terms of measurable end-cap geometry parameters such as its height H, the radius of the cylinder R, and the apex radius of curvature R a. They show that the formula is robust and can predict the net field emission current with errors generally less than 40 %.