# The sensitivity of tokamak magnetohydrodynamics stability on the edge equilibrium

## Abstract

Due to the X-point singularity, the safety factor tends to infinity as approaching to the last closed flux surface. The numerical treatments of the near X-point behavior become challenging both for equilibrium and stability. The usual solution is to cut off a small fraction of edge region for system stability evaluation or simply use an up-down symmetric equilibrium without X-point as an approximation. In this work, we assess the sensitivity of this type of equilibrium treatments on the stability calculation. It is found that the system stability can depend strongly on the safety factor value (qa) at the edge after the cutting-off. When the edge safety factor value falls in the vicinity of a rational mode number (referred to as the resonant gap), the system becomes quite unstable due to the excitation of the peeling type modes. Instead, when the edge safety factor is outside the resonant gaps, the system is much more stable and the predominant modes become the usual external kink (or ballooning and infernal) type. It is also found that the resonant gaps become smaller and smaller as qa increases. The ideal magnetohydrodynamic peeling ballooning stability diagram is widely used to explain the experimental observations, and themore »

- Authors:

- Univ. of Texas, Austin, TX (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

- OSTI Identifier:
- 1497845

- Grant/Contract Number:
- [FG02-04ER54742]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- [ Journal Volume: 24; Journal Issue: 10]; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Zheng, L. J., Kotschenreuther, M. T., and Valanju, P. The sensitivity of tokamak magnetohydrodynamics stability on the edge equilibrium. United States: N. p., 2017.
Web. doi:10.1063/1.4986036.
```

```
Zheng, L. J., Kotschenreuther, M. T., & Valanju, P. The sensitivity of tokamak magnetohydrodynamics stability on the edge equilibrium. United States. doi:10.1063/1.4986036.
```

```
Zheng, L. J., Kotschenreuther, M. T., and Valanju, P. Wed .
"The sensitivity of tokamak magnetohydrodynamics stability on the edge equilibrium". United States. doi:10.1063/1.4986036. https://www.osti.gov/servlets/purl/1497845.
```

```
@article{osti_1497845,
```

title = {The sensitivity of tokamak magnetohydrodynamics stability on the edge equilibrium},

author = {Zheng, L. J. and Kotschenreuther, M. T. and Valanju, P.},

abstractNote = {Due to the X-point singularity, the safety factor tends to infinity as approaching to the last closed flux surface. The numerical treatments of the near X-point behavior become challenging both for equilibrium and stability. The usual solution is to cut off a small fraction of edge region for system stability evaluation or simply use an up-down symmetric equilibrium without X-point as an approximation. In this work, we assess the sensitivity of this type of equilibrium treatments on the stability calculation. It is found that the system stability can depend strongly on the safety factor value (qa) at the edge after the cutting-off. When the edge safety factor value falls in the vicinity of a rational mode number (referred to as the resonant gap), the system becomes quite unstable due to the excitation of the peeling type modes. Instead, when the edge safety factor is outside the resonant gaps, the system is much more stable and the predominant modes become the usual external kink (or ballooning and infernal) type. It is also found that the resonant gaps become smaller and smaller as qa increases. The ideal magnetohydrodynamic peeling ballooning stability diagram is widely used to explain the experimental observations, and the current results indicate that the conventional peeling ballooning stability diagram based on the simplified equilibrium needs to be reexamined.},

doi = {10.1063/1.4986036},

journal = {Physics of Plasmas},

number = [10],

volume = [24],

place = {United States},

year = {2017},

month = {10}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

Works referenced in this record:

##
Comparison of bootstrap current and plasma conductivity models applied in a self-consistent equilibrium calculation for tokamak plasmas

journal, December 2004

- Andrade, M. C. R.; Ludwig, G. O.
- Nuclear Fusion, Vol. 45, Issue 1

##
Currents in the scrape-off layer of diverted tokamaks

journal, October 1989

- Staebler, G. M.; Hinton, F. L.
- Nuclear Fusion, Vol. 29, Issue 10

##
ELMs and constraints on the H-mode pedestal: peeling–ballooning stability calculation and comparison with experiment

journal, January 2004

- Snyder, P. B.; Wilson, H. R.; Ferron, J. R.
- Nuclear Fusion, Vol. 44, Issue 2

##
Investigation of the *n* = 1 resistive wall modes in the ITER high-mode confinement

journal, April 2017

- Zheng, L. J.; Kotschenreuther, M. T.; Valanju, P.
- Nuclear Fusion, Vol. 57, Issue 6

##
Numerical studies of edge localized instabilities in tokamaks

journal, April 2002

- Wilson, H. R.; Snyder, P. B.; Huysmans, G. T. A.
- Physics of Plasmas, Vol. 9, Issue 4

##
Low- *n* magnetohydrodynamic edge instabilities in quiescent H-mode plasmas with a safety-factor plateau

journal, May 2013

- Zheng, L. J.; Kotschenreuther, M. T.; Valanju, P.
- Nuclear Fusion, Vol. 53, Issue 6

##
Stability criteria for edge flute modes in the two‐fluid regime

journal, May 1993

- Zheng, L. ‐J.
- Physics of Fluids B: Plasma Physics, Vol. 5, Issue 5

##
Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime

journal, July 1999

- Sauter, O.; Angioni, C.; Lin-Liu, Y. R.
- Physics of Plasmas, Vol. 6, Issue 7

##
Stability Criterion for Arbitrary Hydromagnetic Equilibria

journal, January 1962

- Greene, John M.; Johnson, John L.
- Physics of Fluids, Vol. 5, Issue 5

##
Hydromagnetic stability of tokamaks

journal, January 1978

- Wesson, J. A.
- Nuclear Fusion, Vol. 18, Issue 1

##
Theory-based model for the pedestal, edge stability and ELMs in tokamaks

journal, February 2006

- Pankin, A. Y.; Bateman, G.; Brennan, D. P.
- Nuclear Fusion, Vol. 46, Issue 4

##
Development and validation of a predictive model for the pedestal height

journal, May 2009

- Snyder, P. B.; Groebner, R. J.; Leonard, A. W.
- Physics of Plasmas, Vol. 16, Issue 5

##
AEGIS: An adaptive ideal-magnetohydrodynamics shooting code for axisymmetric plasma stability

journal, January 2006

- Zheng, L. -J.; Kotschenreuther, M.
- Journal of Computational Physics, Vol. 211, Issue 2

##
Simulation of the hybrid and steady state advanced operating modes in ITER

journal, August 2007

- Kessel, C. E.; Giruzzi, G.; Sips, A. C. C.
- Nuclear Fusion, Vol. 47, Issue 9

##
Edge stability of the ELM-free quiescent H-mode on DIII-D

journal, November 2005

- West, W. P.; Burrell, K. H.; Casper, T. A.
- Nuclear Fusion, Vol. 45, Issue 12

##
Regime of Improved Confinement and High Beta in Neutral-Beam-Heated Divertor Discharges of the ASDEX Tokamak

journal, November 1982

- Wagner, F.; Becker, G.; Behringer, K.
- Physical Review Letters, Vol. 49, Issue 19

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*