EEHG Performance and Scaling Laws

This note will calculate the idealized performance of echo-enabled harmonic generation performance (EEHG), explore the parameter settings, and look at constraints determined by incoherent synchrotron radiation (ISR) and intrabeam scattering (IBS). Another important effect, time-of-flight variations related to transverse emittance, is included here but without detailed explanation because it has been described previously. The importance of ISR and IBS is that they lead to random energy shifts that lead to temporal shifts after the various beam manipulations required by the EEHG scheme. These effects give competing constraints on the beamline. For chicane magnets which are too compact for a given R56, the magnetic fields will be sufficiently strong that ISR will blur out the complex phase space structure of the echo scheme to the point where the bunching is strongly suppressed. The effect of IBS is more omnipresent, and requires an overall compact beamline. It is particularly challenging for the second pulse in a two-color attosecond beamline, due to the long delay between the first energy modulation and the modulator for the second pulse.