  Ballooning instabilities are investigated in three-dimensional magnetic
toroidal plasma confinement systems with low global magnetic shear. The lack of
any continuous symmetry in the plasma equilibrium can lead to these modes being
localized along the field lines by a process similar to Anderson localization.
This produces a multibranched local eigenvalue dependence, where each branch
corresponds to a different unit cell of the extended covering space in which
the eigenfunction peak resides. These phenomena are illustrated numerically for
the three-field-period heliac H-1, and contrasted with an axisymmetric
$s$-$\alpha$ tokamak model. The localization allows a perturbative expansion
about zero shear, enabling the effects of shear to be investigated.
