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The realization of compact Angstrom wave length free electron lasers depends critically on the brilliance of their electron sources. Field emitters are attractive given their small emission surface and subsequent high current density. The low emittance gun project (LEG) at PSI focuses on developing suitable field emitter arrays (FEA) with a dual gate structure emitting a total current of 5.5A out of a diameter of 500 microns with an emittance in the order of 50 nm rad. Simulations show for idealized emitters that despite micron scale variations of the charge density a low emittance can be obtained by putting the FEA in a pulsed DC diode at 250 MV/m. The challenge lies in modelling all real world effects in the individual field emitter and assembling these into a global emission model. Field emission is often labeled as a cold emission process, nevertheless quantum physical effects lead to a base line energy spread of an order of 150 meV FWHM for the emitted electrons. Replenishing the conduction band with electrons from deep layers gives a further increase in the momentum spread. For the metallic field emitter used, surface roughness has an important influence on the emission properties. It typically gives an additional field enhancement factor of 2.5 to 3 resulting in lower required gate voltages. Additionally we have a detrimental effect on the transverse momentum spread. Work is in progress on obtaining numerical estimates for these effects using among other things measurements using secondary electron microscopy. Further more, the extraction and focusing gates both both give rise to nonlinear defocusing and focusing forces, which have to be minimized by a careful geometric optimization. Combining all these effects gives a reliable parametrization of the individual emitters, which together with a stochastic spatial distribution of emitter properties is used in the global emission model.
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