Collective mechanism of cooling-damping resistance in 2 D pairs and plasmons of crystal absorbers for muon beams

The conception of cooling resistance R_c and damping resistance R_e are introduced. The explicit formulations of energy spread <ΔE²>_rms and emittance œ₀ of muon beam are deduced as a function of elementary excitation in absorbers. Both are the monotone increasing functions in the energy range of optimum cooling and damping (0.5-5 GeV) where pairs and plasmons are the dominate excitations in crystal. The excitation energy of plasmons is above pairs which distribute in 0-><!- FORMULA OMITTED ->. Hence, plasmons are the main resistance of cooling and damping. Thus, decreasing the quantum energy of plasmon can decrease energy spread and emittance of muon beam. A conception of multi-layer crystal of 2D plasmon absorber is suggested to strengthing the effects of cooling and damping.