Stability of muon beams to Langmuir waves during ionization cooling

Fast cooling of muon beams will be needed for building either TeV muon coll iders that might explore the electroweak gauge symmetry breaking or muon st orage rings that could become ultrabright neutrino soul ces. Stochastic and electron cooling take longer than the muon lifetime, so attention has been focused on the potentially faster but less explored ionization cooling. Ad dressing recent concerns that excitation of Langmuir waves might be deleter ious for ionization cooling techniques, we show that, while the hydrodynami c instability indeed might be dangerous, the waves are, in fact, stabilized through a combination of resistive and kinetic effects at a very modest em ittance of the beam.