  We argue that the radiative zone above the iron core in pre-collapse cores of
massive stars can store strong magnetic fields. To reach this conclusion we use
the stellar evolutionary code MESA to simulate the evolution of two stellar
models with initial masses of 15Mo and 25Mo, and reveal the entropy profile
above the iron core just before core collapse. Just above the iron core there
is a thin zone with convective shells. We assume that a dynamo in these
convective shells amplifies magnetic fields and forms magnetic flux loops. By
considering the buoyancy of magnetic flux loops we show that the steep entropy
rise in the radiative zone above the dynamo can prevent buoyancy of flux loops
with magnetic fields below about 10^{13}G. When this radiative zone collapses
on to the newly born neutron star the converging inflow further amplifies the
magnetic fields by a factor of about a hundred. After passing through the
stalled shock at about a hundred kilometres from the center, these strong
magnetic fields together with instabilities can facilitate the launching of
jets that explode the star in the frame of the jittering jets explosion
mechanism. Our study further supports the claim for the necessity to include
magnetic fields in simulating the explosion of CCSNe.
