Particle-beam approach to collective instabilities—application to space-charge dominated beams

Unified treatment of collective instabilities and nonlinear beam dynamics

“…Here, only the situation of zero angular momentum is discussed [4]. For a weakly mismatched beam, the envelope radius can be written as R = R 0 +∆R cos Q e θ, where Q e is the envelope tune and θ the 'time'.…”

“…Such a procedure may be able to unify our understanding of collective instabilities and nonlinear beam dynamics. Here, the stability issues of a space-charge dominated beam in a uniformly focusing channel are considered as an example [4]. Gluckstern et.…”