Explosive instability and erupting flux tubes in a magnetized plasma

Cowley, S. C.; Cowley, B.; Henneberg, S. A.; Wilson, H. R.

doi:10.1098/rspa.2014.0913

Cited by 18 publications

(43 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Specifically it illustrates the metastability of some linearly stable equilibria. Metastability is a phenomena encountered in many physical systems and indeed it is clear from this paper and from Ref [9] that many confined plasmas are also metastable. However, despite its importance, metastability in confined plasmas is largely unexplored.…”

Section: Pacs Numbers: Valid Pacs Appear Herementioning

confidence: 99%

“…Certainly such elliptical erupting tubes are the long time limit of the weakly nonlinear theory developed in [7,8]. The explosive dynamics and meta-stability of such tubes in a one dimensional line tied gravitational equilibria were studied in [9]. Here we calculate the dynamics and final saturated states of erupting flux tubes; first in general (Eqs.…”

Section: Pacs Numbers: Valid Pacs Appear Herementioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks

et al. 2016

View full text Add to dashboard Cite

Section: Pacs Numbers: Valid Pacs Appear Herementioning

confidence: 99%

Section: Pacs Numbers: Valid Pacs Appear Herementioning

confidence: 99%

Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks

et al. 2016

View full text Add to dashboard Cite

“…15,23,24 Nevertheless, the rapid disappearance of eigenmodes in our model may allude to a condition for the rapid unidirectional transition to the non-modal perturbation. In this regard, our model may be considered complementary to the existing trigger theory 25,26 and the nonlinear multi-harmonic simulations where the energy of the linearly dominant mode is redistributed into a broad spectrum as approaching to the ELM crash. 22,27,28 To conclude, it is critical to consider the time-varying A for explanation of dynamic features in ELM phenomena using the given models (1) and (12)- (13) for single and coupled-modes, respectively.…”

Section: Discussionmentioning

confidence: 89%

Effect of time-varying flow-shear on the nonlinear stability of the boundary of magnetized toroidal plasmas

Hwang

Leconte

et al. 2018

AIP Advances

View full text Add to dashboard Cite

We propose a phenomenological yet very general model in a form of generalized complex Ginzburg-Landau equation to understand the dynamics of the quasi-periodic fluid instabilities (called edge-localized modes) in the boundary of toroidal magnetized high-temperature plasmas. The model reproduces key dynamical features of the boundary instabilities observed in the high-confinement state plasmas on the KSTAR tokamak, including quasi-steady states characterized by field-aligned filamentary eigenmodes, transitions between different eigenmodes, and rapid transition to non-modal filamentary structure prior to the relaxation. It is found that the inclusion of time-varying perpendicular sheared flow is crucial for reproducing the observed dynamical features.

show abstract

“…We have also defined

\overset{ξ^{2}}{true}

as the y 0 average of the squared displacement, ξ 2 and

\frac{\partial^{2} u}{\partial y_{0}^{2}} = ξ

. The local linear growth rate Γ is given by

Γ^{2} ((), x_{0}) = prefix- \frac{B_{0}^{2} π^{2}}{ρ_{0} ℒ^{2}} + \frac{ρ_{0} g^{2}}{p_{0}} + \frac{g}{ρ_{0}} \frac{d ρ_{0}}{d x_{0}} .

…”

Section: Non‐linear Interaction Of Filamentary Eruptionsmentioning

confidence: 99%

“…Wilson and Cowley continued these calculations for a more complete tokamak geometry and presented the non‐linear ballooning differential equations for tokamaks. In Cowley et al (or for more details Cowley et al), there is a more detailed description of how filaments behave in plasmas including the non‐linear ballooning model with an additional scalar viscosity term. How filaments with different initial sizes interact with each other has also been investigated .…”

Section: Introductionmentioning

confidence: 99%

Filamentary plasma eruptions: Results using the non‐linear ballooning model

Henneberg

Cowley

Wilson

2018

Contrib. Plasma Phys

Self Cite

View full text Add to dashboard Cite

This paper provides an overview of recent results on two distinct studies exploiting the non-linear model for ideal ballooning modes with potential applications to edge-localized modes (ELMs). The non-linear model for tokamak geometries was developed by Wilson and Cowley in 2004 and consists of two differential equations that characterize the temporal and spatial evolution of the plasma displacement. The variation of the radial displacement along the magnetic field line is described by the first equation, which is identical to the linear ballooning equation. The second differential equation is a two-dimensional non-linear ballooning-like equation, which is often second order in time but can involve a fractional time derivative depending on the geometry. In the first study, the interaction of multiple filamentary eruptions is addressed in a magnetized plasma in a slab geometry. Equally sized filaments evolve independently in both the linear and non-linear regimes. However, if filaments are initiated with slightly different heights from the reference flux surface, they interact with each other in the non-linear regime: lower filaments are slowed down and are eventually completely suppressed, while the higher filaments grow faster because of the non-linear interaction. In the second study, this model of non-linear ballooning modes is examined quantitatively against experimental observations of ELMs in Mega Amp Spherical Tokamak (MAST) geometries. The results suggest that experimentally relevant results can only be obtained using modified equilibria.

show abstract

Explosive instability and erupting flux tubes in a magnetized plasma

Cited by 18 publications

References 47 publications

Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks

Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks

Effect of time-varying flow-shear on the nonlinear stability of the boundary of magnetized toroidal plasmas

Filamentary plasma eruptions: Results using the non‐linear ballooning model

Contact Info

Product

Resources

About