Effects of toroidicity on resistive tearing modes

A reduced set of resistive magnetohydrodynamic (MHD) equations is solved numerically in three dimensions to study the stability of tokamak plasmas. Toroidal effects are included self‐consistently to leading and next order in inverse aspect ratio e. The equations satisfy an energy integral. In addition, the momentum equation yields the Grad–Shafranov equation correct to all orders in e. Low‐beta plasmas are studied using several different q profiles. In all cases, the linear growth rates are reduced by finite toroidicity. Excellent agreement with calculations using the resistive PEST code is obtained. In some cases, toroidal effects lead to complete stabilization of the mode. Nonlinear results show smaller saturated island widths for finite aspect ratio compared to the cylindrical limit. If the current channel is wide enough so as to produce steep gradients towards the outside of the plasma, both the finite‐aspect‐ratio cases and cylindrical cases disrupt.