  This work analyzes 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.
