COBRA: An Optimized Code for Fast Analysis of Ideal Ballooning Stability of Three-Dimensional Magnetic Equilibria

“…Following this, in sec. 4 information is given about the verification of PB3D, making use of comparisons with numerical codes MISHKA [2] and COBRA [3], as well as checks on physical consistency. Finally, in sec.…”

Section: Introductionmentioning

confidence: 99%

PB3D: A new code for edge 3-D ideal linear peeling-ballooning stability

Weyens

Sánchez

Huijsmans

et al. 2017

Journal of Computational Physics

View full text Add to dashboard Cite

“…This is a matrix equation, Mξ = γξ, where M is tri-diagonal. The largest eigenvalue and its eigenfunction are then solved using standard numerical routines [21]. The same finite difference approximation is suitable for calculating what amounts to be inner products appearing in the expressions for the derivatives.…”

mentioning

confidence: 99%

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

2005

View full text Add to dashboard Cite

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.

show abstract

“…To solve the ballooning equation, we adopt a finite difference method, as described by Sanchez et al [14]. The eigenfunction is represented by a discrete set of (2N + 1) points ξ i equally spaced along a selected field line on the 'full-grid' according to …”

mentioning

confidence: 99%

“…This is a matrix equation, Mξ = γξ, where M is tri-diagonal. The largest eigenvalue and its eigenfunction are then solved using standard numerical routines [14]. The same finite difference approximation is suitable for calculating what amounts to be inner products appearing in Eqns.…”

mentioning

confidence: 99%

Criteria for second stability for ballooning modes in stellarators

Hudson

Hegna

2004

Physics of Plasmas

View full text Add to dashboard Cite

An expression determining how variations in the pressure gradient and average magnetic shear affect ballooning stability for a stellarator equilibrium is presented. The procedure for determining the marginal stability boundaries, for each field line, depends only on the equilibrium and a single ballooning eigenfunction calculation. This information is sufficient to determine if increasing pressure gradient is stabilizing or destabilizing and to predict whether the configuration possesses a second stable region.

show abstract

COBRA: An Optimized Code for Fast Analysis of Ideal Ballooning Stability of Three-Dimensional Magnetic Equilibria

Cited by 62 publications

References 12 publications

PB3D: A new code for edge 3-D ideal linear peeling-ballooning stability

PB3D: A new code for edge 3-D ideal linear peeling-ballooning stability

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

Criteria for second stability for ballooning modes in stellarators

Contact Info

Product

Resources

About