Abstract
We consider the flux jump instability of the Bean's critical state arising in the flux creep regime in type-II superconductors. We find the flux jump field,
B
j
, that determines the superconducting state stability criterion. We calculate the dependence of
B
j
on the external magnetic field ramp rate,
B
˙
e
. We demonstrate that under the conditions typical for most of the magnetization experiments the slope of the current-voltage curve in the flux creep regime determines the stability of the Bean's critical state, {\it i.e.}, the value of
B
j
. We show that a flux jump can be preceded by the magneto-thermal oscillations and find the frequency of these oscillations as a function of
B
˙
e
.