Emittance and entropy of electron beams
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Date
2014-04
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Vanderbilt University. Department of Physics and Astronomy
Abstract
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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Keywords
electron beams, high-brightness electron beams, emittance, rms emittance, field emission cathode, entropy, beam entropy