[en] A semi-phenomenological formula is proposed for the change of emittance of a self-pinched beam which is not matched to its equilibrium radius. Near equilibrium this formula, coupled with an envelope equation, yields the damped sausage oscillations observed in simulation and experiments. For a beam which is injected cold (no transverse velocity spread), the formula coincides with the analytically calculated initial growth of emittance. The basic theory is developed here and used to compute the linear damping rate for several current profiles. The resultant non-linear increase in equilibrium quantities is also calculated in lowest order of the degree of mismatch