Pressure driven, ideal ballooning stability calculations are often used to predict the achievable plasma β in stellarator configurations. In this paper, the sensitivity of ballooning stability to plasmas profile variations is addressed. A simple, semi-analytic method for expressing the ballooning growth rate, for each field line, as a polynomial function of the variations in the pressure-gradient and the average magnetic shear from an original equilibrium has recently been introduced (Hudson and Hegna 2004 Phys. Plasmas11 L53). This paper will apply the expression to various stellarator configurations and comment on the validity of various truncated forms of the polynomial expression. In particular, it is shown that it is generally insufficient to consider only the second order terms as previously assumed, and that higher order terms must be included to obtain accurate predictions of stability.
Developing a physics understanding of the quasi-continuous exhaust regime: pedestal profile and ballooning stability analysis