Shaping effects on toroidal magnetohydrodynamic modes in the presence of plasma and wall resistivity

Rhodes, Dov; Cole, Andrew J.; Brennan, D. P.; Finn, John M.; Li, M.; Fitzpatrick, Richard; Mauel, M. E.; Navratil, G.A.

doi:10.1063/1.4991873

Cited by 3 publications

(9 citation statements)

References 64 publications

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“…It is well understood that IPRWMs eliminate the stabilizing influence of the wall on times comparable to the diffusion time, which we have chosen as τ w ω A = 2 × 10 3 and τ w ω A = 2 × 10 4 . The IPRWMs corresponding to static plasmas in figure 4(b) are in qualitative agreement with figure 5 of Betti (1998), which employs τ w ω A = 2 × 10 4 , and with figures 2 and 3 of Rhodes et al (2018), where τ w ω A = 10 3 . It has been pointed out that at zero β the model under consideration is unstable if the wall is at infinity (7.2), accordingly, figure 4(b) shows residual IPRWMs at zero β.…”

Section: The Stability Of N = 1 Modes Surrounded By Ideal and Resistisupporting

confidence: 80%

“…It is observed that D controls the amount of surface current at the plasma-vacuum transition. In many sharp-boundary models (Freidberg & Haas 1973, 1974Freidberg & Grossmann 1975;Betti 1998;Fitzpatrick 2008;Rhodes et al 2018) surface currents originate from the finite jump in the kinetic pressure at the plasma-vacuum interface. In the present model, which possesses a pressure profile that vanishes at the plasma edge, surface currents are not needed, but can be accommodated; however, for simplicity, we consider the D = 0 case only.…”

Section: Equilibrium Model: Vacuummentioning

confidence: 99%

“…Stability boundaries are found for the n = 1 toroidal mode by considering a narrow poloidal spectrum of only five modes, m = 1, 2, 3, 4, 5. In contrast, the stability of highly shaped configurations has been studied in the past by retaining the coupling of up to 45 poloidal modes (Rhodes et al 2018). The condition for instability (7.2) indicates that for n = 1 the plasma is unstable in the entire range 0 ≤ q a ≤ ∞.…”

Section: The Stability Of N = 1 Modes Surrounded By Ideal and Resistimentioning

confidence: 99%

“…It has been pointed out that at zero β the model under consideration is unstable if the wall is at infinity (7.2), accordingly, figure 4(b) shows residual IPRWMs at zero β. On the contrary, the models considered by Betti (1998) and by Rhodes et al (2018) are stable below critical β values, and it is the purpose of those articles to determine the degree to which rigid rotation can increase these β-limits. In the absence of rotation, resistive wall tearing modes constitute the least stable modes, consequently, plasma resistivity should be taken into account (Betti 1998;Rhodes et al 2018).…”

Section: The Stability Of N = 1 Modes Surrounded By Ideal and Resistimentioning

confidence: 99%

“…In contrast, the stability of highly shaped configurations has been studied in the past by retaining the coupling of up to 45 poloidal modes (Rhodes et al. 2018).

Figure 2.Marginal stability boundaries against external kink modes for a static plasma with zero magnetic shear, an ideal wall and varying values of the kink-safety factor.…”

Section: The Stability Of Modes Surrounded By Ideal and Resistive Wallsmentioning

confidence: 99%

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Stability of a tokamak plasma with diffuse toroidal rotation

Lopez

Guazzotto

2020

J. Plasma Phys.

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The present work considers the stability of a high- $\beta$ , large aspect ratio, circular plasma with diffuse profiles for the safety factor and the angular toroidal frequency (López & Guazzotto, Phys. Plasmas, vol. 24, 032501). An application of the Frieman–Rotenberg formalism results in a system of scalar eigenmode equations whose coupling is retained at the plasma–vacuum transition but is disregarded across the plasma column, which is a standard practice. The solution technique consists of a multidimensional shooting method for the poloidal harmonics; robust initial guesses are constructed by solving the dispersion relation in the static scenario with vanishing magnetic shear. Flow shear appears as a high- $\beta$ toroidal contribution, and we illustrate its destabilizing influence on $n=1$ external kink modes in the presence of ideal and resistive walls. Internal resonances are avoided by means of the selection of appropriate equilibrium parameters. The stabilizing influence of a finite positive average magnetic shear is also exemplified.

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Section: The Stability Of N = 1 Modes Surrounded By Ideal and Resistisupporting

confidence: 80%

Section: Equilibrium Model: Vacuummentioning

confidence: 99%

Section: The Stability Of N = 1 Modes Surrounded By Ideal and Resistimentioning

confidence: 99%

Section: The Stability Of N = 1 Modes Surrounded By Ideal and Resistimentioning

confidence: 99%

“…In contrast, the stability of highly shaped configurations has been studied in the past by retaining the coupling of up to 45 poloidal modes (Rhodes et al. 2018).

Figure 2.Marginal stability boundaries against external kink modes for a static plasma with zero magnetic shear, an ideal wall and varying values of the kink-safety factor.…”

Section: The Stability Of Modes Surrounded By Ideal and Resistive Wallsmentioning

confidence: 99%

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Stability of a tokamak plasma with diffuse toroidal rotation

Lopez

Guazzotto

2020

J. Plasma Phys.

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Real frequency tearing layers with parallel dynamics and the effect on error field locking and resistive wall modes

2019

Self Cite

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Tearing modes with real frequencies in the plasma frame (i.e. in addition to the Doppler shift due to E×B rotation) are of potential importance because of their effect on the locking process. In particular, it has recently been shown [9] that the Maxwell torque on the plasma in the presence of an applied error field is modified significantly for tearing modes having real frequencies near marginal stability. In addition, it is known [10] that resistive wall tearing modes can be destabilized below their nowall limits by rotation, if the tearing modes have real frequencies near marginal stability. In this paper we first derive the tearing mode dispersion relation with pressure gradient, field line curvature and parallel dynamics in the resistive-inertial (RI) regime, neglecting the divergence of the E ×B drift and perpendicular resistivity. The results show that the usual Glasser effect, a toroidal effect which involves real frequencies, occurs in this simplified model, which ignores perpendicular resistivity and the divergence of the E × B drift. We also find, using a similar simple model, the surprising result that in the viscoresistive regime with pressure gradient, favorable curvature due to toroidal effects, and parallel dynamics, a similar Glasser-like effect is found. We show that in both regimes the existence of tearing modes with complex frequencies is related to nearby electrostatic resistive interchange modes with complex frequencies. We discuss the effect on locking to an error field and the significant lowering of the threshold for destabilization of resistive wall tearing modes, which can be much more pronounced than the weak effect observed for RI tearing modes without pressure-curvature drive in Ref. [10].

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Reducing transport via extreme flux-surface triangularity

Pueschel,

Coda,

Balestri

et al. 2024

Nucl. Fusion

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Based on a gyrokinetic analysis of and extrapolation from TCV discharges with large negative and positive triangularity $\delta$, the potential of extreme $|\delta|$ in reducing turbulent transport is assessed. Linearly, both positive and negative $\delta$ can exert a stabilizing influence, with substantial sensitivity to the radial wavenumber $k_x$. Nonlinear fluxes are reduced at extreme $\delta$ in a trapped-electron-mode regime, whereas low-amplitude ion-temperature-gradient turbulence is boosted by large negative $\delta$. Focusing on the former case, nonlinear fluxes exceed quasilinear ones at negative $\delta$, a trend that reverses as $\delta > 0$. A change in saturation efficiency is the cause of these features: the zonal-flow residual is boosted at $\delta > 0$, reducing fluxes compared with the linear drive as $\delta$ is increased, and a shift towards larger zonal-flow scales occurs with increasing $\delta$ due to finite-$k_x$ modes weakening with $\delta$.

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Shaping effects on toroidal magnetohydrodynamic modes in the presence of plasma and wall resistivity

Cited by 3 publications

References 64 publications

Stability of a tokamak plasma with diffuse toroidal rotation

Stability of a tokamak plasma with diffuse toroidal rotation

Real frequency tearing layers with parallel dynamics and the effect on error field locking and resistive wall modes

Reducing transport via extreme flux-surface triangularity

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