Statistical analysis of m/n  =  2/1 locked and quasi-stationary modes with rotating precursors at DIII-D

<jats:title>Abstract</jats:title> <jats:p>A database has been developed to study the evolution, the nonlinear effects on equilibria, and the disruptivity of locked and quasi-stationary modes with poloidal and toroidal mode numbers <jats:italic>m</jats:italic>  =  2 and <jats:italic>n</jats:italic>  =  1 at DIII-D. The analysis of 22500 discharges shows that more than 18% of disruptions are due to locked or quasi-stationary modes with rotating precursors (not including born locked modes). A parameter formulated by the plasma internal inductance <jats:italic>l</jats:italic> <jats:sub> <jats:italic>i</jats:italic> </jats:sub> divided by the safety factor at 95% of the poloidal flux, <jats:italic>q</jats:italic> <jats:sub>95</jats:sub>, is found to exhibit predictive capability over whether a locked mode will cause a disruption or not, and does so up to hundreds of milliseconds before the disruption. Within 20 ms of the disruption, the shortest distance between the island separatrix and the unperturbed last closed flux surface, referred to as <jats:italic>d</jats:italic> <jats:sub>edge</jats:sub>, performs comparably to <jats:inline-formula> <jats:tex-math/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mstyle displaystyle="false"> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mi>i</mml:mi> </mml:msub> </mml:mstyle> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mstyle displaystyle="false"> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mn>95</mml:mn> </mml:mrow> </mml:msub> </mml:mstyle> </mml:mstyle> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="nfaa4523ieqn001.gif" xlink:type="simple"/> </jats:inline-formula> in its ability to discriminate disruptive locked modes. Out of all parameters considered, <jats:italic>d</jats:italic> <jats:sub>edge</jats:sub> also correlates best with the duration of the locked mode. Disruptivity following a <jats:italic>m</jats:italic>/<jats:italic>n</jats:italic>  =  2/1 locked mode as a function of the normalized beta, <jats:inline-formula> <jats:tex-math/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mstyle displaystyle="false"> <mml:msub> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">N</mml:mi> </mml:mrow> </mml:msub> </mml:mstyle> </mml:mstyle> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="nfaa4523ieqn002.gif" xlink:type="simple"/> </jats:inline-formula>, is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between <jats:inline-formula> <jats:tex-math/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mstyle displaystyle="false"> <mml:msub> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">N</mml:mi> </mml:mrow> </mml:msub> </mml:mstyle> </mml:mstyle> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="nfaa4523ieqn003.gif" xlink:type="simple"/> </jats:in ...