The Bethe-Heitler Process as a Source of Muons

in high-energy photon interactions with a nucleus A, as recently suggested in [7] (slide 23). Of course, muon-pair production by this process is suppressed relative to electron-positron pair production by the ratio (me/mμ) 2 ≈ 1/40, 000, so there is an issue of the efficiency of muon production via reaction (1). The Bethe-Heitler process (1) is further suppressed near threshold, so it would be appropriate to consider photons of energy ≈ 400 MeV, which would yield muons with average kinetic energy ≈ 100 MeV, high enough that the threshold-suppression factor is only ≈ 3/4, and also the kinetic energy desired for the muon source at Muon Collider/Neutrino Factory. Approximately 10 muons/s of each sign are desired, so the beam power of these muons is roughly 3 kW. But, in addition to the desired muons there are 40,000 times as many electrons/positrons, whose beam power is therefore ≈ 120 MW. Thus, the Bethe-Heitler process (1) for muon production would require a 120-MW beam of 400-MeV photons, essentially all of which power must then be dissipated as “waste” in the muon beam transport. The 400-MeV photon beam would be generated by backscattering of a laser off an electron (or proton or heavy ion) beam, which latter beam would have to provide the 120 MW of power. In sum, the Bethe-Heitler production process for muons is too inefficient to be useful for a Muon Collier/Neutrino Factory.