Optimum Electron Distributions for Space Charge Dominated Beams in Photoinjectors Page: 3 of 39
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INTRODUCTION
The lower limit of the emittance of an electron bunch emitted from the photocathode of an
RF gun is the "cathode emittance". The "cathode emittance" is the product of the rms beam
size and the rms transverse momenta of the photo-electron distribution as it is born at the
cathode. According to the Liouville's theorem, the emittance is preserved during transport.
However, during transport along a beamline, the different temporal slices of the bunch are
subject to forces of different amplitude. The total emittance grows because of this evolving
mismatch between slices. The mismatch coefficient i relates the Twiss parameters of
temporal slice i with those of the total bunch (labeled tot) as follows:
J =1/2(i yr,,, -2ap,,, + fi,,y) (1)
If the forces are linear, (i.e. with respect to the position of the particle in the beam), the
emittance growth is reversible because one can compensate for it. Two examples of linear
forces are linear components of the space charge force and transverse wakefields The former
can be corrected by emittance compensation and the latter by using other transverse
wakefields by steering the beam adequately at the entrance of some linac sections
downstream. For non-linear forces, the emittance growth is usually irreversible. Examples of
non-linear forces responsible for irreversible emittance growth are space charge forces,
incoherent synchrotron radiation emission and RF forces which typically have a sinusoidal
time dependence.
For bunch charges at the nC level, appropriate to X-Ray-FELs, the "cathode emittance"
accounts for half of the total emittance. Of the two other contributions, which combine with
the "cathode emittance" in quadrature, the space charge induced emittance and the RF
emittance, the RF term is negligible. This statement is valid for cylindrical shape laser
pulse.
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Limborg-Deprey, C. & Bolton, P. R. Optimum Electron Distributions for Space Charge Dominated Beams in Photoinjectors, article, June 15, 2006; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc878270/m1/3/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.