Improved evolution equations for magnetic island chains in toroidal pinch plasmas subject to externally applied resonant magnetic perturbations

Fitzpatrick, Richard; Rossi, Enrico; Yu, Edmund

doi:10.1063/1.1404384

Cited by 36 publications

(70 citation statements)

References 31 publications

(66 reference statements)

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“…30 In this paper, we have developed an asymptotic procedure to derive nonlinear equation for saturation of magnetic islands, which generalizes the previous results for the case of the symmetric current profile. 5,7 Our asymptotic matching procedure includes such effects as the asymmetry of the outer region and nonlinear modification of the equilibrium current (m ¼ 0 harmonics).…”

Section: Discussionmentioning

confidence: 90%

Higher order and asymmetry effects on saturation of magnetic islands

et al. 2013

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Higher order asymptotic matching procedure is developed to derive the nonlinear equation for saturated magnetic island with the symmetric profile of the equilibrium current. The theory extends the previous results to include higher order effects such as nonlinear modification of the equilibrium current and asymmetry in the boundary conditions in the outer region. It is shown that due to a finite width of the nonlinear region, the magnitude of the magnetic flux at the rational surface is different from the asymptotic value found from the outer solution, resulting in the suppression of the island growth for higher values of D 0 parameter. V C 2013 AIP Publishing LLC.

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Section: Discussionmentioning

confidence: 90%

Higher order and asymmetry effects on saturation of magnetic islands

et al. 2013

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“…6(a), in the phase range of 0.5π < Φ < 1.5π, the RMP has a stabilizing effect on 2/1 TM as the island width decreases monotonously, while in the phase range -0.5π (or 1.5π) < Φ < 0.5π, RMP is destabilizing for 2/1 TM，which are in good agreement with the analytical theory. 23 (ii) As shown in Fig. 6(c), in the phase range of 0 < Φ <π, F em is negative and contributes a deceleration to the mode rotation, while in the phase range π < Φ < 2π, F em is…”

Section: /18mentioning

confidence: 99%

“…Another important consequence of rotation modulation by F em and F vs is that the island spends more time in the deceleration phase (0 < Φ <π, corresponding time Δt 3 = 6×10 -4 τR) in which it is slowed down by the F em than the acceleration phase (π < Φ < 2π, corresponding time Δt 4 = 4.5×10 -4 τR) in which F em causes it to speed up. 23 This accounts for the net braking effect seen in Figs. 5 and 7, and the net braking effect explains the rotation frequency reduction shown in Figs.…”

Section: Fig 7 Time Evolution Of (A) Normalized Island Width W/a (mentioning

confidence: 99%

“…6 To explain the changed TM dynamics caused by applied RMPs, many theoretical and numerical studies related to RMPs have been carried out. 2,[19][20][21][22][23][24][25][26][27][28][29][30][31][32] Some authors supposed that RMPs changed ∆' so as to stabilize tearing instability. 19 However, only the active RMPs experiment could be explained in which RMPs had a constant phase with respect to the a) Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

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Understanding the effect of resonant magnetic perturbations on tearing mode dynamics

Ren

et al. 2013

Physics of Plasmas

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Abstract. Numerical understandings of the effect of resonant magnetic perturbations (RMPs) on 2/1 tearing mode (TM) dynamics observed on J-TEXT tokamak (Hu Q. et al 2012 Nucl. Fusion 52 083011) are presented in this paper. The non-uniform mode rotation frequency, modulated by electromagnetic force (F em ) and viscous force (F vs ), results in the applied RMPs contributing both net stabilizing and braking effect on TM. Numerical evaluation based on analytical theory shows the applied RMP contributes a dominant stabilizing effect, which are responsible for the suppression of TM. The dynamics of the first discovered small locked island (SLI) are investigated. It is found that the island is locked at the stabilizing phase and the saturated island width is less than the linear layer width. The simulated Mirnov signal indicates the small locked island is likely to be the complete suppression case observed in experiments. Associated with the application of RMP, the shape of Mirnov signal deviates from sinusoidal before mode locking, which is explained by numerical modeling. The comparisons between the numerical and experimental results are in good agreement phenomenally.

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“…Resistive resonant modes are known as tearing modes (TMs). They are usually treated by inserting a thin resistive layer at r s , and they typically seed magnetic islands governed by nonlinear dynamics [12]. Here, only ideal MHD modes are considered, modeled by…”

Section: Magnetohydrodynamic Unstable Modes Modelmentioning

confidence: 99%

Stability analysis and model-based control in EXTRAP-T2R with time-delay compensation

Olofsson¹,

Witrant

Briat

et al. 2008

2008 47th IEEE Conference on Decision and Control

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Abstract-In this paper, we investigate the stability problems and control issues that occur in a reversed-field pinch (RFP) device, EXTRAP-T2R (T2R), used for research in fusion plasma physics and general plasma (ionized gas) dynamics. The plant exhibits, among other things, magnetohydrodynamic instabilities known as resistive-wall modes (RWMs), growing on a time-scale set by a surrounding non-perfectly conducting shell. We propose a novel model that takes into account experimental constraints, such as the actuators dynamics and control latencies, which lead to a multivariable time-delay model of the system. The openloop field-error characteristics are estimated and a stability analysis of the resulting closed-loop delay differential equation (DDE) emphasizes the importance of the delay effects. We then design a structurally constrained optimal PID controller by direct eigenvalue optimization (DEO) of this DDE. The presented results are substantially based on and compared with experimental data.

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Improved evolution equations for magnetic island chains in toroidal pinch plasmas subject to externally applied resonant magnetic perturbations

Cited by 36 publications

References 31 publications

Higher order and asymmetry effects on saturation of magnetic islands

Higher order and asymmetry effects on saturation of magnetic islands

Understanding the effect of resonant magnetic perturbations on tearing mode dynamics

Stability analysis and model-based control in EXTRAP-T2R with time-delay compensation

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