The thermionic emission current from electron beam guns is often used to weld, melt, or evaporate materials cleanly in a vacuum environment. To efficiently evaporate aluminum to coat potato chip bags,...

The thermionic emission current from electron beam guns is often used to weld, melt, or evaporate materials cleanly in a vacuum environment. To efficiently evaporate aluminum to coat potato chip bags, a power of 2 kW is required to heat the Al charge. The power supply delivers a 10-kV potential between the cathode (emitter) of the electron beam gun filament and ground (Al).

a. For a tantalum emitter what minimum surface area of filament would be required?

b. For a thoriated tungsten emitter what minimum surface area of filament would be required?