The saw-tooth instability in storage rings is studied by means of a time-do
main simulation code which takes into account the self-induced wake fields.
The results are compared with those from a dynamical heuristic model explo
iting two coupled non-linear differential equations, accounting for the tim
e behavior of the instability growth rate and for the anomalous growth of t
he energy spread. This model is shown to reproduce the characteristic featu
res of the instability in a fairly satisfactory way. (C) 1999 Elsevier Scie
nce B.V. All rights reserved.