The stabilizing effect of sheared axial flows on the Rayleigh-Taylor i
nstability in Z-pinch implosions is investigated. Dispersion relations
are derived that include the effects of a density discontinuity and a
sheared how which produce the Rayleigh-Taylor and Kelvin-Helmholtz in
stabilities. The dispersion relations are examined in two limiting cas
es of practical interest, a uniform plasma implosion and an annular pl
asma implosion. The analytical results show a region of parameter spac
e which provides complete stability. The analytical model is verified
with nonlinear calculations using experimental implosion parameters an
d geometries. The results indicate that mitigation of the Rayleigh-Tay
lor instability is possible with a sufficient sheared axial flow. [S10
70-664X(98)03406-5]