Observation of tearing mode deceleration and locking due to eddy currents induced in a conducting shell

Chapman, B. E.; Fitzpatrick, Richard; Craig, D.; Martin, P.; Spizzo, G.

doi:10.1063/1.1689353

Cited by 37 publications

(47 citation statements)

References 37 publications

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“…The torque localized near the rational surface can eventually be transported to the other plasma region through the momentum transport mechanisms, 23 or through the viscous torque balance. 9,24 The detailed radial structures of the torque density near the rational surface are related to the local profiles of the perturbed current density and the magnetic field. Figure 12 shows the radial profiles of the perturbed current components, including both the real and imaginary parts (in the complex representation of the perturbed quantities), for the b N ¼ 1.13 case.…”

Section: Electromagnetic Torque Generated By Tearing Modementioning

confidence: 99%

Resistive wall tearing mode generated finite net electromagnetic torque in a static plasma

et al. 2014

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The MARS-F code [Y. Q. Liu et al., Phys. Plasmas 7, 3681 (2000)] is applied to numerically investigate the effect of the plasma pressure on the tearing mode stability as well as the tearing mode-induced electromagnetic torque, in the presence of a resistive wall. The tearing mode with a complex eigenvalue, resulted from the favorable averaged curvature effect [A. H. Glasser et al., Phys. Fluids 18, 875 (1975)], leads to a re-distribution of the electromagnetic torque with multiple peaking in the immediate vicinity of the resistive layer. The multiple peaking is often caused by the sound wave resonances. In the presence of a resistive wall surrounding the plasma, a rotating tearing mode can generate a finite net electromagnetic torque acting on the static plasma column. Meanwhile, an equal but opposite torque is generated in the resistive wall, thus conserving the total momentum of the whole plasma-wall system. The direction of the net torque on the plasma is always opposite to the real frequency of the mode, agreeing with the analytic result by Pustovitov [Nucl. Fusion 47, 1583(2007]. When the wall time is close to the oscillating time of the tearing mode, the finite net torque reaches its maximum. Without wall or with an ideal wall, no net torque on the static plasma is generated by the tearing mode. However, re-distribution of the torque density in the resistive layer still occurs. V C 2014 AIP Publishing LLC.

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Section: Electromagnetic Torque Generated By Tearing Modementioning

confidence: 99%

Resistive wall tearing mode generated finite net electromagnetic torque in a static plasma

et al. 2014

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“…20 This has been shown to be important during quasisingle helicity (QSH) discharges in MST where the dominant mode grows to large amplitude. 21 The strong mode growth observed in QSH plasmas does not occur in most of the discharges studied here but the eddy current mechanism can still be important, specifically if the intrinsic flow drive that normally operates in standard plasmas has been reduced or eliminated in PPCD. The eddy-current torque acts in the vicinity of the mode resonant surfaces and hence can explain the observed profile evolution including the lack of significant flow damping near the magnetic axis.…”

Section: Momentum Loss Mechanism During Ppcdmentioning

confidence: 85%

“…(36) in Ref. 21. If this torque is applied to an isolated toroidal shell of plasma with a thickness of $ 0.1 m located at the n ¼ 6 resonant surface, we would observe a deceleration time of s em $ 1 ms. Factoring in the interaction of this plasma shell with the If the eddy current explanation is correct, we expect there to be an approximately quadratic dependence of the deceleration rate on the dominant n ¼ 6 mode amplitude.…”

Section: Momentum Loss Mechanism During Ppcdmentioning

confidence: 87%

“…13,19 Interaction of the modes with surrounding conducting walls and with magnetic field errors can also have a strong effect on the plasma rotation in the RFP. 17,[20][21][22] These effects are interesting scientifically but are also important to understand on a practical level. For example, the locking of the modes to the wall and the associated increase in plasma-wall interaction has often been an important limitation on RFP operation.…”

Section: Introductionmentioning

confidence: 99%

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Intrinsic flow and tearing mode rotation in the RFP during improved confinement

et al. 2019

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We use charge exchange recombination spectroscopy to make the first localized measurements of impurity ion flow velocity profiles in the reversed field pinch. Measurements in improved confinement plasmas reveal an intrinsic flow profile that is peaked on the axis and mostly parallel to the equilibrium magnetic field. The toroidal flow decreases in time at off-axis locations where tearing modes are resonant, giving rise to a highly sheared flow profile near the axis. The tearing mode phase velocity correlates strongly with toroidal flow near the resonant surface and weakly with flow in other locations, providing an opportunity to verify the commonly held assumption that the plasma and mode move together at the resonant surface. Mechanisms for the observed momentum loss during the improved confinement period are evaluated, and it is found that eddy currents in the conducting shell caused by the rotation of the dominant tearing mode dominate over other losses.

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“…In addition to the TM interaction with an RMP, TM braking can also be produced by eddy currents induced in the wall. 33,35,36 Because of the finite conductivity of the wall, the eddy currents have a phase that lags the tearing mode's phase. The phase difference leads to an EM torque that brakes the TM, and its magnitude is proportional to the square of the TM amplitude.…”

Section: Introductionmentioning

confidence: 99%

Tearing mode dynamics and locking in the presence of external magnetic perturbations

et al. 2016

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In normal operation, Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch plasmas exhibit several rotating tearing modes (TMs). Application of a resonant magnetic perturbation (RMP) results in braking of mode rotation and, if the perturbation amplitude is sufficiently high, in a wall-locked state. The coils that produce the magnetic perturbation in MST give rise to RMPs with several toroidal harmonics. As a result, simultaneous deceleration of all modes is observed. The measured TM dynamics is shown to be in qualitative agreement with a magnetohydrodynamical model of the RMP interaction with the TM [R. Fitzpatrick, Nucl. Fusion 33, 1049 (1993)] adapted to MST. To correctly model the TM dynamics, the electromagnetic torque acting on several TMs is included. Quantitative agreement of the TM slowing-down time was obtained for a kinematic viscosity in the order of νkin≈10–20 m2/s. Analysis of discharges with different plasma densities shows an increase of the locking threshold with increasing density. Modeling results show good agreement with the experimental trend, assuming a density-independent kinematic viscosity. Comparison of the viscosity estimates in this paper to those made previously with other techniques in MST plasmas suggests the possibility that the RMP technique may allow for estimates of the viscosity over a broad range of plasmas in MST and other devices.

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Observation of tearing mode deceleration and locking due to eddy currents induced in a conducting shell

Cited by 37 publications

References 37 publications

Resistive wall tearing mode generated finite net electromagnetic torque in a static plasma

Resistive wall tearing mode generated finite net electromagnetic torque in a static plasma

Intrinsic flow and tearing mode rotation in the RFP during improved confinement

Tearing mode dynamics and locking in the presence of external magnetic perturbations

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