Dependence of total emittance on photon energy, electron emittance, and beta; dependence of coherent fraction on total emittance
The first of these four animations follows the dependence of the total emittance on electron emittance, assuming that the photon- and electron phase-space beta ellipses are perfectly matched, that is, their ratios of the source size to divergence are identical. Three representative photon energies are also selected to show the change in phase space, shown on the right. Note that, for a given photon energy, the total emittance will at some arbitrarily small electron emittance be limited by the photon emittance. This happens first in the three examples for the lowest photon energy of 300 eV, which has the largest phase-space ellipse. Note also that the moving blue dot represents the diffraction-limited energy for a given electron emittance, and occurs when the electron- and photon ellipses overlap.
The following two animations follow the change in emittance as a function of the electron beta function for a third-generation facility with = 5500 pm.rad and for a DLSR with = 150 pm.rad. Both examples use radiation from a 2-m undulator. As a consequence, the optimal electron emittance is when the beta function matches that of the photon emittance, i.e. for m.
The final animation follows the coherent fraction as a function of total emittance, assuming perfectly matched electron- and photon emittances, that is, they have the same beta function.