Methods of the theory of cross instabilities of relativistic electron beams

The results of analysis of physical pripciples being the basis of methods for theoretical simulation of collective transversal instabilities of relativistic bears in mUlti-section resonance linacs and transversal electron-ion instabilities of relativistic rings are systematized and generalized in the review. The models providing the fullest comparison with the experimental data are singled out. The main directions of further theory development of considered phenomena are pointed out