The mode structure of high-n resistive ballooning modes

The higher-order corrections (in an n^-1/2 expansion) to resistive ballooning theory are analyzed in order to gain information about the radial structure of the Δ′-driven modes. This higher-order theory also predicts that the ballooning phase angle θ₀ (which is undetermined in the leading-order theory) must be chosen so as to maximize the value of Δ′. The importance of applying this maximization is illustrated by an analytical calculation of Δ′ as a function of θ₀ for the s-α model in the limit of small α. It is demonstrated that for this case, one should choose θ₀ = 90° and that the resulting value of Δ′ can be very different from that obtained by setting θ₀ = 0, as is frequently imposed.