Beam envelope equations for cooling of muons in solenoid fields

Demonstration of cooling by the Muon Ionization Cooling Experiment

The use of accelerated beams of electrons, protons or ions has furthered the development of nearly every scientific discipline. However, high-energy muon beams of equivalent quality have not yet been delivered. Muon beams can be created through the decay of pions produced by the interaction of a proton beam with a target. Such ‘tertiary’ beams have much lower brightness than those created by accelerating electrons, protons or ions. High-brightness muon beams comparable to those produced by state-of-the-art electron, proton and ion accelerators could facilitate the study of lepton–antilepton collisions at extremely high energies and provide well characterized neutrino beams^1–6. Such muon beams could be realized using ionization cooling, which has been proposed to increase muon-beam brightness^7,8. Here we report the realization of ionization cooling, which was confirmed by the observation of an increased number of low-amplitude muons after passage of the muon beam through an absorber, as well as an increase in the corresponding phase-space density. The simulated performance of the ionization cooling system is consistent with the measured data, validating designs of the ionization cooling channel in which the cooling process is repeated to produce a substantial cooling effect^9–11. The results presented here are an important step towards achieving the muon-beam quality required to search for phenomena at energy scales beyond the reach of the Large Hadron Collider at a facility of equivalent or reduced footprint⁶.

Ionization cooling, a technique that delivers high-brightness muon beams for the study of phenomena at energy scales beyond those of the Large Hadron Collider, is demonstrated by the Muon Ionization Cooling Experiment.

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.

Recursive solution for beam dynamics of periodic focusing channels

We present recursive analysis for beam dynamics of periodic focusing channels based on the Fourier coefficients of the focusing function. Formulas for orbit stability and the envelope function are derived. The results should be useful for numerical calculation and for developing analytical understanding of channels employing extended focusing elements. Applications to muon ionization cooling channels are discussed.

Stability of muon beams to Langmuir waves during ionization cooling

Fast cooling of muon beams will be needed for building either TeV muon colliders that might explore the electroweak gauge symmetry breaking or muon storage rings that could become ultrabright neutrino sources. Stochastic and electron cooling take longer than the muon lifetime, so attention has been focused on the potentially faster but less explored ionization cooling. Addressing recent concerns that excitation of Langmuir waves might be deleterious for ionization cooling techniques, we show that, while the hydrodynamic instability indeed might be dangerous, the waves are, in fact, stabilized through a combination of resistive and kinetic effects at a very modest emittance of the beam.