Emittance and entropy of electron beams
Creating high-brightness electron beams, which have many practical applications, is done with cathodes in regions with large electric field by field emission. The brightness is high when the current is high and the volume of the beam in phase space is small. An estimate of the phase space volume is the rms emittance. The simulations described in this report show that the beam emitted by a gated diamond field emitter of the type fabricated at Vanderbilt has an exquisitely small emittance, on the order of a few nm. This is probably too small to measure. The rms emittance is generally thought to be constant for a beam or increasing in the presence of aberrations in the beam optics, but simulations show that this is not true. The rms emittance rises and falls according to the geometry that surrounds the beam. The entropy of an electron beam can be calculated, and should be constant if done in six dimensional phase space, and approximately constant in four dimensions. Calculations show that the entropy is not constant in two nor four dimensions. Rather, the entropy changes over time with a shape similar to how the emittance changes, which includes a local maxima at the entrance to an aperture and minima on either side. It is not clear if the fault is with the calculations or theory. To our knowledge, this is the first time that the entropy of a particle beam has been computed and used in a quantitative fashion. Future research should explore the applications and limitations of this concept.
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