Anderson-Localized Ballooning Modes in General Toroidal Plasmas

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.