  A perturbative hybrid ideal-MHD/drift-kinetic approach to assess the
stability of alpha-particle-driven Alfven eigenmodes in burning plasmas is used
to show that certain foreseen ITER scenarios, namely the Ip = 15 MA baseline
scenario with very low and broad core magnetic shear, are sensitive to small
changes in the background magnetic equilibrium. Slight variations (of the order
of 1%) of the safety-factor value on axis are seen to cause large changes in
the growth rate, toroidal mode number, and radial location of the most unstable
eigenmodes found. The observed sensitivity is shown to proceed from the very
low magnetic shear values attained throughout the plasma core, raising issues
about reliable predictions of alpha-particle transport in burning plasmas.
