Behavior of notional cap-area efficiency (gn) for hemisphere-on-plane and related field emitters

We obtained and compared numerical and analytical results for the hemisphere-on-plane notional cap-area efficiency. For various emitter shapes, the behavior of the notional emission area has been analyzed. The shape contributon to the pre-exponential voltage exponent was obtained by plotting the notional cap-area efficiency against the apex value of dimensionless local surface field.