Plasma Phys. Control. Fusion 42 (2000) 641–653. Printed in the UK PII: S0741-3335(00)08751-0 Ballooning stability optimization of low-aspect-ratio stellarators * R Sanchez†, S P Hirshman‡, A S Ware§, L A Berry‡ and D A Spong‡ † Departamento de F´ ısica, Universidad Carlos III, Avda. de la Universidad 30, Legan´ es, 28911 Madrid, Spain ‡ Oak Ridge National Laboratory, PO Box 2009, Oak Ridge, Tennessee 37831-8070, USA § Department of Physics and Astronomy, University of Montana, Missoula, Montana 59801, USA E-mail: rsanchez@fis.uc3m.es Received 15 October 1999, in final form 12 January 2000 Abstract. The implementation of ideal ballooning stability within an optimization code is used to determine stable, moderate-β compact stellarator configurations. Due to the large computational requirements of existing ballooning codes, such calculations within the optimization process were previously impractical. The recently developed COBRA code can efficiently compute ideal ballooning growth rates on various magnetic surfaces, using the VMEC code to supply equilibrium data. The optimization code has been used to minimize these growth rates, giving rise to new stellarator configurations at low aspect ratios with good ballooning stability properties, which also maintain previously determined desirable physics properties. This particular implementation is robust due to the enhanced convergence features included in COBRA, while incurring only a small overhead on the total computational time. 1. Introduction The intrinsic three-dimensional (3D) character of stellarators plays a two-fold role in the design of plasma magnetic confinement devices. First, three dimensionality opens up a wide parameter space allowing a larger degree of freedom in the design. But, on the other side, the exploration of this space is a complex process that requires the integration of sophisticated and efficient equilibrium and stability algorithms together with multi-dimensional nonlinear optimization techniques. In order to limit neoclassical transport in these 3D devices down to present-day tokamak levels, several routes have been followed to improve both the particle and energy confinement properties [1]. These routes differ primarily in the physical concept underlying the optimization but are carried out within the same numerical framework. In all cases, following a method introduced by N¨ uhrenberg and Zille [2], an optimization loop is used to minimize a positive target function that approaches zero when the physical properties of the equilibrium tend to their desired values. The equilibrium space is parametrized using as independent variables the shape of the outermost magnetic flux surface and the rotational transform (or the toroidal current density) profile. The Levenberg–Marquardt algorithm is the core of the optimization method chosen for the calculations described here. It computes a local minimum in that space (one * This paper is an extended version of a contribution to the 12th International Stellarator Workshop, Madison, Wisconsin, 27 September–1 October 1999. 0741-3335/00/060641+13$30.00 © 2000 IOP Publishing Ltd 641