| Summary: | The production of a low emittance muon beam is interesting for muon collider projects. In such context we study the production of positive and negative muon beams at 22 GeV, from e^{+} beam-vs-fixed target collisions, with a very small transverse and longitudinal emittance of 25 π nm rad and 3×1 π mm GeV, respectively. In order to cope with the small conversion efficiency of positrons into muon pairs and the divergence of the beams, we connect thin targets by a quadrupole-only transport line common to three beams (μ^{+}, μ^{-}, and e^{+}) at two different energies (μ at 22 GeV and e^{+} at 44 GeV), where the line is specially designed to match the muon beam phase space over ±5% energy spread and to mitigate the effect of multiple scattering with the targets on all beams. The transport line allows us to use a larger fraction of target material, increasing the muon population by a factor of 10 per positron bunch and splitting the power deposition over 20 to 40 targets, while keeping the muon beam emittance equal or similar to one from a single thin target of 1% of a radiation length. It might be possible to integrate this line into an accumulator ring in order to increase the muon bunch population over hundreds of positron bunches.
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