  In the large flux limit vortices become flux tubes with almost constant
magnetic field in the interior region. This occurs in the case of non-Abelian
vortices as well, and the study of such configurations allows us to reveal a
close relationship between vortex zero modes and the gyromagnetic instabilities
of vector bosons in a strong background magnetic field discovered by Nielsen,
Olesen and Ambj{\o}rn. The BPS vortices are exactly at the onset of this
instability, and the dimension of their moduli space is precisely reproduced in
this way. We present a unifying picture in which, through the study of the
linear spectrum of scalars, fermions and W bosons in the magnetic field
background, the expected number of translational, orientational, fermionic as
well as semilocal zero modes is correctly reproduced in all cases.
