Effect of ordering on nonbunched cold beam relaxation in a storage ring

Peculiarities of Coulomb relaxation of energy distribution of a cold non-bunched beam in a storage ring are studied. At particle energy below critical one the equilibrium in the beam is reached due to particle and coherent fluctuation temperatures equalization. The relaxation time and dependences of a longitudinal temperature on the beam current are calculated. The presence of an equilibrium coherent background in the beam leads to ordering in particle motion. Thermodynamical properties of such a beam approach to the properties of a crystal, when the temperature decreases. The conditions, under which the beam transforms into a crystal state, are discussed