Muon Collider Low-to-Medium Energy Lifetime Enhancement via Topological Impedance Matching

In geometric representation of Clifford algebra, gauge fields are of two varieties - translation and rotation. Translation gauge fields are associated with scale-dependent geometric impedances, rotation with scale-invariant topological impedances. In the baseline muon collider design, translation gauge fields of RF cavities provide high-energy lifetime enhancement via time dilation of special relativity. At 255 GeV/c the enhancement is  gamma = ~2500, providing lifetimes of a few milliseconds. However, our muon sources provide muon energies of only a few GeV, where lifetimes are a few microseconds. This first low-energy step is perhaps the most challenging of the project, to cool and accelerate enough low-emittance muons to provide useful luminosity.

In principle it seems that here, at low-to-medium energy, rotation gauge fields might offer complementary support to the RF cavities. Geometric representation of QED is on the light cone, where the low-energy effect of Terrell rotation far exceeds that of the Lorentz transform, as nicely shown by this tweet from John Baez: 

https://twitter.com/johncarlosbaez/status/1107322770751262721.

There appears to be no reason (in either physics or technology) why rotation gauge fields would not be as effective as translation, if not moreso. Improved lifetime reduces load on the muon source, opening the way to low emittance of LEMMA technique, perhaps in combination with additional ionization cooling. In this poster we propose to explore details of how such a scheme might be implemented.