A comparison of the full and reduced sets of magnetohydrodynamic equations for resistive tearing modes in cylindrical geometry

The results of numerical calculations using a full set of resistive magnetohydrodynamic equations are compared with the results of similar calculations using a reduced set of equations derived for tokamaks in the limits of low beta and large aspect ratio ( β∼ε2≪1). The calculations, which are carried out in three‐dimensional cylindrical geometry using initial value techniques, allow the comparison of linear stability properties as well as detailed nonlinear studies. The results of these calculations (including linear growth rates and eigenfunctions, the nonlinear evolution of single‐helicity magnetic islands, and the nonlinear evolution of multihelicity cases) confirm the validity of the reduced set of equations at low beta in cylindrical geometry.