Quantitative study of kinetic ballooning mode theory in simple geometry

The theory of kinetic ballooning modes (KBMs) in a magnetically confined toroidal plasma is studied analytically and numerically by means of gyrokinetic simulations. A physics-based ordering for β (the ratio of kinetic to magnetic plasma pressure) with small asymptotic parameters is found. This allows us to derive several simplified limits of previously known theories. We introduce a variational approach which provides explicit dispersion relations in terms of integrals of quadratic forms constructed from numerical eigenfunctions. It is found that, for large pressure gradients, the growth rate and frequencies computed by gyrokinetic codes show excellent agreement with those evaluated by using a diamagnetic modification of ideal magnetohydrodynamic if geometric drifts are kept consistent with the equilibrium pressure gradient. For moderate pressure gradients, a new finite-β formulation of the KBM theory is proposed. Also in this case, a good agreement between numerical simulations and analytical theory is found.