Influence of pressure-gradient and shear on ballooning stability in stellarators

Abstract

Abstract. 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 variation in the pressure-gradient and the average magnetic shear from an original equilibrium has recently been introduced [Phys. Plasmas, 11(9):L53, 2004.]. 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 in general it is 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.

Magnetohydrodynamic stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators

“…Thus, an increase in the pressure gradient that improves stability is possible; naively, there would be no limit. This lack of a stability limit at zero magnetic shear in a stellarator is not a new concept (see Hudson, Hegna & Nakajima 2005). It could for instance lead to a configuration that is unstable at small plasma , but becomes stable above some critical value, introducing the concept of a second stability regime.…”

Helically localized ballooning instabilities in three-dimensional tokamak pedestals

“…The ideal MHD ballooning eigensolver used in this work is an extension of the STESA code [29][30][31][32] and its successor developed for studying ballooning in local 3D equilibria [12,22]. These codes are based on and utilize numerical techniques from the well studied ballooning solver COBRA [33], with STESA having been benchmarked directly against the COBRA solver [29].…”

Magnetic confinement theory summary

“…A more 'realistic' treatment of the plasma boundary region by Nakajima, effectively reducing the 'bumpiness', improves stability and also the agreement with experiment in LHD; β ∼ 3% is effectively stable, whereas β ∼ 1% is less so [96]. Based on the work of Greene and Chance [98], a perturbative approach by Hudson [99] was employed for locating second stability regimes in LHD and NCSX. Improved, two-fluid, non-linear modelling with M3D was found by Sugiyama [100] to simulate experimental results better.…”