The choice of boundary conditions in Monte Carlo calculations of noise

Probability density functions and the corresponding cumulative distribution functions for density and Velocity fluctuations at the surface of a thermionic emitter are discussed. In particular, it is shown that as far as velocity fluctuations are concerned, the appropriate probability density function is given by
f(w | r_{c}) = (2 / \pi^{3/2}) \exp (-w^{2})
, where w is the reduced velocity. Some of the misunderstandings encountered in the technical literature are also discussed. It is shown that the mean energy of the emitted electrons is 3/2kT and not 2kT, as is claimed sometimes, the quantity 2kTJ
s
, where J
s
, is the saturation current, representing the magnitude of energy flow.