Theory of Transverse Ionization Cooling in a Linear Channel

Ionization cooling is the most hopeful method to reduce the emittance of muon beams, which plays an important role in neutrino factory and muon collider. Within the moment-equation approach, we present a way to derive the formulae of emittance in transverse under linear channel. All heating and coupling terms are reserved in the deriving process. From our formulae, it is a way to achieve a small emittance by designing the cooling channel compact to make the beta function changing sharply.