• R. Pakter, Y. Levin, F. B. Rizzato
  IF-UFRGS, Porto Alegre

We start by analyzing the image effects of a cylindrical conducting pipe on a continuous beam with elliptical symmetry. In particular, we derive an exact expression for the self-field potential of the beam inside the pipe without using any sort of multipole expansion. By means of a variational method, the potential for beams with varying density profiles along an elliptical shape is used to search for equilibrium solutions for intense beams. For that, we assume a uniform focusing in the smooth-focusing approximation. A curious result is that the product of the rms sizes along the ellipsis semi-axis stays constant as the pipe radius is varied. Finally, we prove that despite the nonlinear forces imposed by the image charges of an arbitrary shape conducting pipe, intense beams in uniform focusing fields preserve a uniform density in the equilibrium.

• R. P. Nunes, Y. Levin, R. Pakter, F. B. Rizzato
  IF-UFRGS, Porto Alegre

We analyze the dynamics of inhomogeneous, magnetically focused high-intensity beams of charged particles. While for homogeneous beams the whole system oscillates with a single frequency, any inhomogeneity leads to propagating transverse density waves which eventually result in a singular density build up, causing wave breaking and jet formation. The theory presented in this paper allows to analytically calculate the time at which the wave breaking takes place. It also gives a good estimate of the time necessary for the beam to relax into the final stationary state consisting of a cold core surrounded by a halo of highly energetic particles.