locked and nearly-locked islands by W. Choi, K.E.J. Olofsson, R. - - PowerPoint PPT Presentation

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Simulated dynamics and feed-back control of locked and nearly-locked islands

Choi/APS-DPP/Nov. 2015

by

• W. Choi, K.E.J. Olofsson, R. Sweeney, F. Volpe, and M.

Okabayashi

Presented at the

APS-DPP Meeting, Savannah, Georgia

• Nov. 15, 2015

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Abstract

• A model has been developed at DIII-D to predict the dynamics of

saturated m/n = 2/1 tearing modes subject to various torques.

• Modes interact with the error fields, magnetic perturbations applied

by internal and external active coils, the conducting wall, and the graphite tiles.

• Model also accepts input auxiliary torques (viscous drag, neutral

beam torque, etc).

• Maximum entrainment frequency is dependent on island width and

current in control coils.

• Applicable in assisting island suppression with electron cyclotron

current drive, as well as to prevent mode locking and possible disruption. *This work was supported in part by the US Department of Energy under DE-SC0008520.

Choi/APS-DPP/Nov. 2015

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Motivation

Choi/APS-DPP/Nov. 2015

• Neoclassical Tearing Modes (NTMs), or magnetic islands,
• ften appear in high performance plasmas and can degrade

confinement

• These NTMs can slow and lock in the lab frame, becoming

Locked Modes (LMs), which can grow in size and may lead to disruptions

• The toroidal phase of LMs can be controlled through Resonant

Magnetic Perturbations (RMPs), which is needed to align the LM with electron cyclotron current drive (ECCD), an effective suppression technique

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Introduction

Choi/APS-DPP/Nov. 2015

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Island and coils being modeled at DIII-D

Choi/APS-DPP/Nov. 2015

• Island is associated with a moment of inertia (I) and current (Js)
• Torque from Currents in the I-coils (Jb) and C-coils (Jc)
• effect of resistive wall is accounted for (Bw)

accepted as auxiliary torque Steady state entrainment General equation of motion

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System of equations modeling 2/1 island dynamics

• (x1, x2) are the magnetic field at

the wall (Bw)

• x3 is angular velocity of the

mode (ω)

• (x4, x5) is the current associated

with the mode (Js)

• (J1

b, J2 b) and (J1 c, J2 c) are the

prescribed currents in the I- and C-coils respectively

• τ is the resistive decay time of

the wall

Choi/APS-DPP/Nov. 2015

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Simulations

Choi/APS-DPP/Nov. 2015

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• Study of tendency of mode locking to EF

– only include wall braking and constant EF – does not have I-coils or C-coils

Study of mode locking to error field (EF)

Choi/APS-DPP/Nov. 2015

No EF Small EF Large EF

Time [ms] Phase [°] Time [ms] Time [ms]

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• For given EF amplitude, varied

initial mode position

Variance decreases as EF amplitude increases

Initial position [°] final position [°]

• Final position variance for

different EF amplitudes variance = Σ(final position)2

variance [°2] Error Field amplitude (a.u.)

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Simulation of “pre-emptive” I-coil entrainment Case 1: Successful entrainment

• Rotating n=1 field applied by I-coil before mode appears
• Simulation confirms expectation that, as mode slows down, it

will lock directly to the applied, rotating resonant magnetic perturbation (RMP)

Choi/APS-DPP/Nov. 2015

Successful entrainment of a 5 cm island at 130 Hz with 3 kA in I-coils

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Case 2: Failed entrainment

• failure to entrain due to smaller I-coil amplitude
• mode continuously tries to align with RMP

Choi/APS-DPP/Nov. 2015

Failed entrainment of a 5 cm island at 130 Hz with 1.5 kA in I-coils

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Contour plot of maximum entrainment frequency

• Result of competition between wall braking and EM torque from

RMP

• large islands experience

strong wall braking

• small islands experience

weaker interaction with RMP

Choi/APS-DPP/Nov. 2015

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Steady-state wall torque experienced by entrained mode

• assuming steady-state entrainment
• braking torque from the wall is balanced by applied torque

from RMP

Choi/APS-DPP/Nov. 2015

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Experimental Result

Choi/APS-DPP/Nov. 2015

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Experimental result at DIII-D: pre-emptive entrainment successful

Rotating phase: signal lost at 2514 ms n1rms = 17G n1freq = 1.04 kHz Locked to rotating RMP phase: signal found at 2516 ms freq = 70 Hz Used 3.6 kA in I-coils, rotating at 70 Hz

Choi/APS-DPP/Nov. 2015

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Example of repeated mode disappearance?

Choi/APS-DPP/Nov. 2015

• Attempted 70 Hz entrainment
• Smooth rotation between 2200 ms to 2300 ms
• Observe mode amplitude disappearance and phase flip
• Causes still under investigation

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Conclusions

• A model has been developed to study the dynamics of

magnetic islands under various torques: wall braking, applied fields, error fields, etc.

• Mode entrainment by pre-emptively rotating RMP was shown

to be a feasible way of preventing mode locking

• An experiment on this technique was recently performed,

data still being analyzed

• Future work will be to apply this model to a feedback

controller

Choi/APS-DPP/Nov. 2015

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Entrainment and Torque contour at NSTX

Choi/APS-DPP/Nov. 2015

• coils: external 1x6 coils at mid-plane
• major radius: 0.86 m
• wall time: 5 ms
• density: 3x1019 m-3
• Bt: 0.18 T