FOCUSING AND ACCELERATION OF BUNCHED BEAMS

A new approach to solving the kinetic equation for the beam distribution function, (very useful from the practical point of view), is discussed, in which the authors also obtain a complement to the Skrinsky's condition for the self-focused bunched beam. This problem belongs to the theory of nonlinear systems in which both regular and chaotic motion is possible. The kinetic approach, based on Vlasov-Poisson equations, are used to investigate the focusing and acceleration of bunched beam. Special attention is given to the studies of stability in a bunched beam by means of the two norm, which may be used to describe t!he motion of high-energy particles