We show that Aharonov-Bohm (AB) oscillations in the magnetic moment of
an integrable ballistic quantum dot can be destroyed by a time depend
ent magnetic flux. The effect is due to a nonequilibrium population of
perfectly coherent electronic states. For real ballistic system the e
quilibriation process, which involves a special type of inelastic elec
tron backscattering, can be so ineffective that AB oscillations axe su
ppressed when the flux varies with frequency omega approximately 10(7)
-10(8) s-1. The effect can be used to measure relaxation times for ine
lastic backscattering.