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1 0 1 2 3 4 5 6 0 1 2 3 4 5 q95 q0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 q95 q0 GA PCS Design Studies for ITER Include Analytic Ideal MHD Boundary and Real-time Error Field Correction Algorithm • Approximate ideal MHD stability boundary: – Validated with DIII-D data – Enables study of active control to maintain stability, prevent disruption • Real-time Error Field Correction – Extremum-Seeking algorithm – Varies correction field amplitude phase to maximize plasma rotation – Automatically finds optimal correction (if enough rotation…) EXS/P6-37 D.Humphreys/IAEA FEC Kyoto/October 2016 q a ≈ 1 q 0 20 - 0.5 + 2 q 0 + 0.2sin 4π q 0 - 0.5 [ ] ( = q 95 q 0 q 0 Disrupts Remains stable DIII-D Rampup Trajectories #167062 #167134 Stable region Stable region

GA PCS Design Studies for ITER Include Analytic Ideal MHD ... · EXS/P6-37 D.Humphreys/IAEA FEC Kyoto/October 2016 q a » 1 q 0 20 - 0.5+ 2q 0 + 0.2sin(4p[q 0 - 0.5]) q 95 q 0 q 0

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0 1 2 3 4 5 60

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167134 q95 vs q0

q9

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q00 1 2 3 4 5 6 7 8

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167062 q95 vs q0

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GA PCS Design Studies for ITER Include Analytic Ideal MHD

Boundary and Real-time Error Field Correction Algorithm

• Approximate ideal MHD

stability boundary:

– Validated with DIII-D data

– Enables study of active control

to maintain stability, prevent

disruption

• Real-time Error Field Correction

– Extremum-Seeking algorithm

– Varies correction field amplitude

phase to maximize plasma

rotation

– Automatically finds optimal

correction (if enough rotation…)

EXS/P6-37 D.Humphreys/IAEA FEC Kyoto/October 2016

qa »1

q020

-0.5+2q0 + 0.2sin 4p q0 - 0.5[ ]( )

q95

q0 q0

Disrupts

Remains

stable

DIII-D Rampup Trajectories

#167062 #167134

Stable region

Stable

region

1 Coordinate descent methods for composite functionsverify that the point (0.5, 0.5) is minimized along both coordinate axis, while it is not an optimum point. 1 0.5 0-0.5-1-0.5 0

1 Coordinate descent methods for composite functionsverify that the point (0.5, 0.5) is minimized along both coordinate axis, while it is not an optimum point. 1 0.5 0-0.5-1-0.5 0

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