Equilibrium and Stability of a Collisionless Cylinder

Abstract

This chapter deals with cylindrical models, which may simulate stellar systems strongly elongated in one direction. We shall assume that there is no rotation around the x- and y-axes; at the same time, the cylinder as a whole and the particles can rotate about the z-axis. Elongated systems rotating with respect to the transverse axis (x or y) are treated in Chapter IV, which is devoted to ellipsoidal (two- or three-axial) systems. Such cylindrical systems seem to be of interest, first of all, as the simplest self—consistent models of gravitating systems for the investigation of some principal questions of the theory (see, for instance, §1, Chapter VI, where the possibility of the development of a beam instability in gravitating systems is shown).