### Abstract

In this and the accompanying paper, the problem of the maximally achievable elongation κ in a tokamak is investigated. The work represents an extension of many earlier studies, which were often focused on determining κ limits due to (i) natural elongation in a simple applied pure vertical field or (ii) axisymmetric stability in the presence of a perfectly conducting wall. The extension investigated here includes the effect of the vertical stability feedback system which actually sets the maximum practical elongation limit in a real experiment. A basic resistive wall stability parameter, γτ_{w} is introduced to model the feedback system which although simple in appearance actually captures the essence of the feedback system. Elongation limits in the presence of feedback are then determined by calculating the maximum κ against n = 0 resistive wall modes for fixed γτ_{w}. The results are obtained by means of a general formulation culminating in a variational principle which is particularly amenable to numerical analysis. The principle is valid for arbitrary profiles but simplifies significantly for the Solov'ev profiles, effectively reducing the 2-D stability problem into a 1-D problem. The accompanying paper provides the numerical results and leads to a sharp answer of 'how much elongation is too much'?

Original language | English (US) |
---|---|

Article number | 515810607 |

Journal | Journal of Plasma Physics |

Volume | 81 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2015 |

### Fingerprint

### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Journal of Plasma Physics*,

*81*(6), [515810607]. https://doi.org/10.1017/S0022377815001270

**Tokamak elongation - How much is too much? Part 1. Theory.** / Freidberg, J. P.; Cerfon, Antoine; Lee, J. P.

Research output: Contribution to journal › Article

*Journal of Plasma Physics*, vol. 81, no. 6, 515810607. https://doi.org/10.1017/S0022377815001270

}

TY - JOUR

T1 - Tokamak elongation - How much is too much? Part 1. Theory

AU - Freidberg, J. P.

AU - Cerfon, Antoine

AU - Lee, J. P.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - In this and the accompanying paper, the problem of the maximally achievable elongation κ in a tokamak is investigated. The work represents an extension of many earlier studies, which were often focused on determining κ limits due to (i) natural elongation in a simple applied pure vertical field or (ii) axisymmetric stability in the presence of a perfectly conducting wall. The extension investigated here includes the effect of the vertical stability feedback system which actually sets the maximum practical elongation limit in a real experiment. A basic resistive wall stability parameter, γτw is introduced to model the feedback system which although simple in appearance actually captures the essence of the feedback system. Elongation limits in the presence of feedback are then determined by calculating the maximum κ against n = 0 resistive wall modes for fixed γτw. The results are obtained by means of a general formulation culminating in a variational principle which is particularly amenable to numerical analysis. The principle is valid for arbitrary profiles but simplifies significantly for the Solov'ev profiles, effectively reducing the 2-D stability problem into a 1-D problem. The accompanying paper provides the numerical results and leads to a sharp answer of 'how much elongation is too much'?

AB - In this and the accompanying paper, the problem of the maximally achievable elongation κ in a tokamak is investigated. The work represents an extension of many earlier studies, which were often focused on determining κ limits due to (i) natural elongation in a simple applied pure vertical field or (ii) axisymmetric stability in the presence of a perfectly conducting wall. The extension investigated here includes the effect of the vertical stability feedback system which actually sets the maximum practical elongation limit in a real experiment. A basic resistive wall stability parameter, γτw is introduced to model the feedback system which although simple in appearance actually captures the essence of the feedback system. Elongation limits in the presence of feedback are then determined by calculating the maximum κ against n = 0 resistive wall modes for fixed γτw. The results are obtained by means of a general formulation culminating in a variational principle which is particularly amenable to numerical analysis. The principle is valid for arbitrary profiles but simplifies significantly for the Solov'ev profiles, effectively reducing the 2-D stability problem into a 1-D problem. The accompanying paper provides the numerical results and leads to a sharp answer of 'how much elongation is too much'?

UR - http://www.scopus.com/inward/record.url?scp=85019401715&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019401715&partnerID=8YFLogxK

U2 - 10.1017/S0022377815001270

DO - 10.1017/S0022377815001270

M3 - Article

AN - SCOPUS:85019401715

VL - 81

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

SN - 0022-3778

IS - 6

M1 - 515810607

ER -