Application of a general electron emission equation to surface nonuniformity and current density variation

Abstract

Electron emission nonuniformity is a cause of intrinsic emittance from the electron source, and is a consequence of work function variation due to crystal faces and coatings such as cesium, field enhancement effects due to surface structure, and temperature. Its investigation using particle-in-cell (PIC) codes such as MICHELLE is hampered due to the lack of an emission model that can treat thermal, field, and photoemission effects particularly in crossover regions where the canonical equations, e.g., the Fowler-Nordheim, Richardson-Laue-Dushman, and Fowler-Dubridge equations are compromised. A recently developed thermal-photo-field emission equation is used here to simulate the consequences of nonuniformity due to work function variation induced by coating variation. The analysis is performed both theoretically using simple models as well as using particle-in-cell codes (MICHELLE) to assess changes in current density and emittance. PIC simulations considering an idealized model of geometric effects and crystal face variation indicate that a flat, grainy surface causes the emittance to increase by a factor of 5 while the addition of hemispherical bumps causes the emittance to increase by an additional factor of 6 even though the current is but 10% larger.