  Recently, it was shown that giant vortices with arbitrarily large quantum
numbers can possibly be created in dilute Bose-Einstein condensates by
cyclically pumping vorticity into the condensate. However, multiply quantized
vortices are typically dynamically unstable in harmonically trapped nonrotated
condensates, which poses a serious challenge to the vortex pump procedure. In
this theoretical study, we investigate how the giant vortices can be stabilized
by the application of a Gaussian potential peak along the vortex core. We find
that achieving dynamical stability is feasible up to high quantum numbers. To
demonstrate the efficiency of the stabilization method, we simulate the
adiabatic creation of an unsplit 20-quantum vortex with the vortex pump.
