A Model of Photoemission Delay Mechanisms and Its Application to Beam Optics Codes

High performance Free Electron Lasers (FEL) and x-ray FELs (xFEL) seek high quantum efficiency (QE) photocathodes (typically semiconductors). An important requirement for the shorter wavelength FELs is the response time of the photocathode as it affects pulse shaping [1]: delayed emission effects, although correlated with enhanced QE [2], contribute to emittance (longitudinal and transverse) and halo formation [3], particularly for short pulses where the tails are not emitted at optimal times. The delayed contribution is a consequence of laser penetration depth effects but also (multiple) scattering mechanisms [4]–[6] that give rise to a diffusive rather than ballistic component to the photocurrent. The incorporation of such effects is mostly absent in beam optics codes that are critical to xFEL simulation and design. In this work, we describe efforts to a delayed emission model developed for the Particle-in-Cell code MICHELLE [7] that includes not only unscattered electrons excited deeper into the bulk photocathode material, but also partially thermalized electron contributions that emerge at later times. The method is based on a string of excitation sites and the monitoring of their contribution to the photocurrent using a Moments-based model (comparable to the Spicer three-step model) as they lose energy to scattering. The significant challenges of doing so shall be discussed regarding the integration of the models into MICHELLE, particularly how the most recent model improves upon the simpler models of Ref. [8]. The methods will be applied to showing the effects of delayed emission on pulse duration and laser jitter as a function of the number of scattering events the electrons typically experience for both metals and semiconductors. The extension to semiconductor photocathodes is critical as their QE is higher given that the scattering events are not nearly as fatal to emission.