Linear Theory of Ionization Cooling in 6D Phase Space

A linear theory is developed for ionization cooling of muon beams in periodic channels that can provide cooling of the transverse emittances and also of the longitudinal emittance via emittance exchange. The channels incorporate solenoids and quadrupoles for transverse focusing, dipoles to generate dispersion, wedged absorbers for ionization, and rf cavities for acceleration. The beam evolution near equilibrium is described by coupled first-order differential equations for five generalized emittances with two excitation sources. The results should be useful for understanding the cooling process and for designing cooling channels of future muon colliders and neutrino factories.