  Calculations of tearing mode stability in tokamaks split conveniently into an
external region, where marginally stable ideal MHD is applicable, and a
resonant layer around the rational surface where sophisticated kinetic physics
is needed. These two regions are coupled by the stability parameter. Pressure
and current perturbations localized around the rational surface alter the
stability of tearing modes. Equations governing the changes in the external
solution and - are derived for arbitrary perturbations in axisymmetric toroidal
geometry. The relationship of - with and without pressure flattening is
obtained analytically for four pressure flattening functions. Resistive MHD
codes do not contain the appropriate layer physics and therefore cannot predict
stability directly. They can, however, be used to calculate -. Existing methods
(Ham et al. 2012 Plasma Phys. Control. Fusion 54 025009) for extracting - from
resistive codes are unsatisfactory when there is a finite pressure gradient at
the rational surface and favourable average curvature because of the Glasser
stabilizing effect. To overcome this difficulty we introduce a specific
pressure flattening function that allows the earlier approach to be used. The
technique is first tested numerically in cylindrical geometry with an
artificial favourable curvature. Its application to toroidal geometry is then
demonstrated using the toroidal tokamak tearing mode stability code T7
(Fitzpatrick et al. 1993 Nucl. Fusion 33 1533) which uses an approximate
analytic equilibrium. The prospects for applying this approach to resistive MHD
codes such as MARS-F (Liu et al. 2000 Phys. Plasmas 7 3681) which utilize a
fully toroidal equilibrium are discussed.
