ABSTRACT
This chapter focuses on the characteristics and applications of low energy muons obtained by the moderation of a surface muon beam. The transport efficiency from moderator to sample position depends on the initial divergency and hence on the angular distribution. At least at the moment, moderation is the method of choice to produce polarized very slow muon (µ+). The muon as a microscopic magnetic probe and muonium as a light hydrogen probe are predestined to be used in these new fields. Phase space compression by stochastic or electron cooling has been successfully applied to stored beams of protons and heavy ions to improve the beam quality and is routinely used at various accelerators. The materials are grouped in four classes: rare gas solids, molecular cryocrystals, solid insulators, and metals. One of the most important properties of the epithermal muons is their polarization. Ultraslow muons are subelectronvolt muons produced for instance by laser ionisation of hot muonium.
