  The formation of beam halos has customarily been described in terms of a
particle-core model in which the space-charge field of the oscillating core
drives particles to large amplitudes. This model involves parametric resonance
and predicts a hard upper bound to the orbital amplitude of the halo particles.
We show that the presence of colored noise due to space-charge fluctuations
and/or machine imperfections can eject particles to much larger amplitudes than
would be inferred from parametric resonance alone.
