11.3: Emittance, space charge, and sharp electron sources

An analytical formula of the emittance of and space charge effects on a sharply curved emitter surface is given. The 3D formulation makes use of the Point Charge Model (PCM) of a unit cell emitter coupled with a trajectory analysis to follow electrons to an evaluation plane where emittance is determined. The single tip theory extended to an array predicts the emittance of a Field Emitter Array 0.2 cm on a side producing 2000 A/cm² is 23 mm-mrad. Space charge within the unit cell on the beam is estimated from the determination of the apex radius and field enhancement factor for arbitrarily sharp emitter structures Predictions of the impact of space charge on the emitted current are made, and compared to the literature. Methods to extend theory to beam codes are discussed.