Numerical studies of non-linear evolution of kink and tearing modes in tokamaks

A set of numerical techniques for investigating the full nonlinear unstable behavior of low-$beta$ kink modes of given helical symmetry in tokamaks is presented. Uniform current density plasmas display complicated deformations including the formation of large vacuum bubbles, provided that the safety factor q is sufficiently close to integral. Fairly large m = 1 deformations, but not bubble formation, persist for a plasma with a parabolic current density profile (and hence shear). Deformations for m greater than or equal to 2 are however greatly suppressed. (auth)