# Electrons and X-rays to Muon Pairs (EXMP)
## 3 \(e^{-}-\gamma\) Collider Scenarios  
We conceived a novel \(e^{-}-\gamma\) collider scenario achieving ultra-high luminosity. An overarching goal is the quest of very high sustainability: such luminosity levels typically require beam power levels that are hardly compatible with reasonable impacts on society and governmental approvals when power consumption of the whole scenario exceeds the so-called GW scale, which should be considered an unsurpassable borderline. The resulting criterion for the choice of the electron accelerators is the following: since the generation of muon pairs in the collision between the primary electrons and the FEL photons is perturbative on the primary beams, with negligible losses of beam particles and very small energy loss in the beams, a strategy for beam power recovery is mandatory. The scenario we have conceived, named EXMP, is based on PERLE-like ERLs [9; 10]) and ILC schematics [11; 12]. A representation is sketched in Figure 2 and two working points (WP200, WP500), corresponding to the dynamic limits of the parameters, are reported in Table 1.  
The final goal of generating a suitable beam of muons to be used in a TeV-scale muon collider is accomplished by the EXMP scenario based on a twin 200-500-GeV ERL system coupled to a twin 50-GeV FEL ERL system, with residual beam power loss (after recovery, and taking into account all losses of the electron beam and FEL photon beam) of about \(\sim\)300 MW, together with an outstanding few nm rad-normalised emittance of the muon beam at \(\sim\)10\({}^{11}\) muon pairs per second. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **EXMP WP200** & **EXMP WP500** \\ \hline Energy \(e^{-}\) beam (GeV) & 200 & 500 \\ Bunch charge (pC) & 250 & 250 \\ Electrons per bunch (10\({}^{9}\)) & 1.6 & 1.6 \\ Repetition rate (MHz) & 800 & 800 \\ Average current (mA) & \(2\times 200\) & \(2\times 200\) \\ Nominal beam power (GW) & \(2\times 40\) & \(2\times 100\) \\ Beam power recovery fraction (\%) & 99.9 & 99.95 \\ Beam power loss (MW) & \(2\times 40\) & \(2\times 50\) \\ Bunch length (psec) & 0.3 & 0.2 \\ \(\varepsilon_{x,y}^{\mathrm{st}}\) (\(\pi\) um rad) & 0.4 & 0.4 \\ \(\beta_{x,y}\) (mm) & 0.2 & 0.23 \\ \(\sigma_{x,y}\) (mm) & 14 & 10 \\ \hline FEL photon energy (keV) & 150 & 60 \\ Photons per pulse (10\({}^{12}\)) & 5 & 12.5 \\ \(\varepsilon_{x,y}\) (\(\pi\) pm rad) & 0.6 & 1.5 \\ Focal spot size (nm) & 14 & 10 \\ Repetition rate (MHz) & 800 & 800 \\ FEL beam power (MW) & 2 \(\times\) 100 & \(2\times 100\) \\ FEL \(\rho\) (10\({}^{-4}\)) & 5 & 8 \\ FEL efficiency (tapering) (\%) & 1 & 1 \\ FEL \(e^{-}\) beam average current (mA) & 200 & 200 \\ FEL \(e^{-}\) beam bunch charge (pC) & 250 & 250 \\ FEL \(e^{-}\) beam energy (GeV) & 50 & 50 \\ FEL \(e^{-}\) beam power (GW) & \(2\times 10\) & \(2\times 10\) \\ Beam power recovery fraction (\%) & 99.9 & 99.9 \\ Beam power loss (MW) & \(2\times 10\) & \(2\times 10\) \\ \hline Total beam power loss (MW) & 300 & 320 \\ Peak luminosity (10\({}^{41}\) cm\({}^{-2}\)s\({}^{-1}\)) & 2 \(\times\) 2.5 & \(2\times 12.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters table of the EXMP scenario at two working points (WP200, WP500). Primary beam features and peak luminosities are reported. Figure 2: EXMP scheme. Primary \(e^{-}\), accelerated up to 200–500 GeV, collide with the counterpropagating FEL, producing \(\mu^{\pm}\). Both \(e^{-}\) (primary and FEL) are decelerated in the opposite LINACs and the energy recovered. A selected fraction of \(\mu^{\pm}\) is injected in the opposite LINAC and accelerated before storage and collision in a ring. An important consideration concerns the peak properties of the primary electron beams: the parameters listed in the table represent the state-of-the-art for electron beams, with a RMS normalised transverse emittance (0.4 \(\pi\)\(\upmu\)m rad, round beam) quite consistent with the accelerated bunch charge (250 pC). Moreover, the value chosen for the beta function at the collision point (0.2 mm) is very close to state-of-the-art performances.