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Hollow Cathodes 251 be discussed in detail after the actual thermionic electron emitter properties are described. 6.3 Thermionic Electron Emitter Characteristics Electrons are introduced into the system by thermionic emission from the insert surface. Thermionic emission by cathodes is described by the Richardson– Dushman equation [7]: J = A T2 e–e /kT , (6.3-1) where A is, ideally, a constant with a value of 120 A/cm2K2, T is the temperature in kelvins, e is the charge, k is Boltzmann’s constant, and is the work function. Experimental investigations of the thermionic emission of different materials reported values of A that vary considerably from the theoretical value. The cause of the deviation of A from a constant has been attributed to several different effects, such as variations in the crystal structure of the surface, variations in the surface coverage (for dispenser cathodes), changes in the density of states at the surface due to thermal expansion, etc. This issue has been handled [8] for many of the thermionic electron emitters used in hollow cathodes by introducing a temperature correction for the work function of the form = o + T , (6.3-2) where o is the classically reported work function and is an experimentally measured constant. This dependence can be inserted into Eq. (6.3-1) to give J=Ae–e /kT2 e–e o/kT =DT2 e–e o/kT , (6.3-3) where D is a material-specific modification to the Richardson–Dushman equation. In the presence of strong electric fields at the surface of the cathode, the potential barrier that must be overcome by the electrons in the material’s conduction band is reduced, which results effectively in a reduced work function. This effect was first analyzed by Schottky [9], and the so-called Schottky effect is included in the emission equation by the addition of a term [10] to describe the effect of the surface electric field on the emission current density: J=DT2 exp e o exp e eE , (6.3-4) k T k T 4 oPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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