cases at 5.7 mm to allow a fair comparison). The lower-limit and upper-limit photon energies represent the FEL spectral tuning range possible with a constant 4-GeV electron energy. These plots show that SCU technologies using commercially-available Nb3Sn or NbTi superconductors offer superior FEL performance and can reduce the LCLS-II undulator beamline length by 50-70 m with respect to a PM undulator. Figure 2: LCLS-II undulator beamline length, adding 50% for self-seeding and 20% for a safety margin, as a function of electron energy (a), magnetic full gap (b), electron emittance (c), peak current (d), photon energy (e), and upper-limit photon energy (f). Clearly the SCU technologies of Nb3Sn or NbTi offer superior performance and can reduce the final LCLS-II undulator beamline length by more than 50-70 m with respect to PM undulators. Note that the undulator period, is not fixed in these plots, but is reset at each point (for all but plots u, c and d) in order to maintain the lower-limit of the photon tuning range (1.2 keV nominal here). Electron beam and undulator parameters for the plots in are summarized in The Figure 2 Table 1. undulator periods for each curve, evaluated at the nominal working point (red dots on each curve), are 27.5 mm (blue-solid), 24.8 mm (cyan-dotted), 20.3 mm (green-dashed), and 18.7 mm (red-dash-dot). Table 1: beam and undulator parameters for the plots in Figure 1. Parameter Symbol Value Unit Electron energy E 4.0 GeV Lower-limit photon tuning range u1 1.2 keV Upper-limit photon tuning range u2 4.0 keV Magnetic gap gm 7.5 mm Vacuum chamber aperture 5.7 mm gvc Transverse norm. rms emittance 0.45 mm x,y Peak current Ipk 1.0 kA energy spread (rms) 500 keV E Average beta function in undulator 15 m  Additional undulator length to allow 50 %  self-seeding Additional undulator length to allow 20 %  design safety margin
cases at 5.7 mm to allow a fair comparison). The lower-limit and upper-limit photon energies represent the FEL spectral tuning range possible with a constant 4-GeV electron energy. These plots show that SCU technologies using commercially-available Nb3Sn or NbTi superconductors offer superior FEL performance and can reduce the LCLS-II undulator beamline length by 50-70 m with respect to a PM undulator. Figure 2: LCLS-II undulator beamline length, adding 50% for self-seeding and 20% for a safety margin, as a function of electron energy (a), magnetic full gap (b), electron emittance (c), peak current (d), photon energy (e), and upper-limit photon energy (f). Clearly the SCU technologies of Nb3Sn or NbTi offer superior performance and can reduce the final LCLS-II undulator beamline length by more than 50-70 m with respect to PM undulators. Note that the undulator period, u, is not fixed in these plots, but is reset at each point (for all but plots c and d) in order to maintain the lower-limit of the photon tuning range (1.2 keV nominal here). Electron beam and undulator parameters for the plots in Figure 2 are summarized in Table 1. The undulator periods for each curve, evaluated at the nominal working point (red dots on each curve), are 27.5 mm (blue-solid), 24.8 mm (cyan-dotted), 20.3 mm (green-dashed), and 18.7 mm (red-dash-dot). Table 1: beam and undulator parameters for the plots in Figure 1. Parameter Symbol Value Unit Electron energy E 4.0 GeV Lower-limit photon tuning range u1 1.2 keV Upper-limit photon tuning range u2 4.0 keV Magnetic gap gm 7.5 mm Vacuum chamber aperture gvc 5.7 mm Transverse norm. rms emittance x,y 0.45 mm Peak current Ipk 1.0 kA energy spread (rms) E 500 keV Average beta function in undulator  15 m Additional undulator length to allow self-seeding  50 % Additional undulator length to allow design safety margin  20 %