Lyapunov stability of flowing magnetohydrodynamic plasmas surrounded by resistive walls

Tasso, H.; Throumoulopoulos, G. N.

doi:10.1063/1.3606470

Cited by 6 publications

(15 citation statements)

References 21 publications

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“…Plasmas surrounded by resistive walls may be unstable within free boundary magnetohydrodynamic theory for fusion relevant β values (See [1,2]). To overcome this difficulty, a boundary control or feedback may be necessary (See [3]- [14]).…”

Section: Introductionmentioning

confidence: 99%

On Lyapunov boundary control of unstable magnetohydrodynamic plasmas

Tasso

Throumoulopoulos

2013

Physics of Plasmas

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Starting from a simple marginally stable model considered for Lyapunov based boundary control of flexible mechanical systems, we add a term driving an instability and prove that for an appropriate control condition the system can become Lyapunov stable. A similar approximate extension is found for the general energy principle of linearized magnetohydrodynamics. The implementation of such external instantaneous actions may, however, impose challenging constraints for fusion plasmas.

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Section: Introductionmentioning

confidence: 99%

On Lyapunov boundary control of unstable magnetohydrodynamic plasmas

Tasso

Throumoulopoulos

2013

Physics of Plasmas

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“…The pertinent instability is known nowadays as resistive wall mode (RWM). Later the prove of the theorem was extended for walls with time dependent electrical conductivity [2] and for stationary ideal MHD equilibria with equilibrium flows [3]. In [4] it is stated that the main relations in [1] have been given there without detailed proves and that there are unknown limitations that restrict the applicability of the Pfisrch-Tasso variational principle, which is claimed to be restored in the framework of a generic plasma model.…”

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confidence: 99%

“…In [4] it is stated that the main relations in [1] have been given there without detailed proves and that there are unknown limitations that restrict the applicability of the Pfisrch-Tasso variational principle, which is claimed to be restored in the framework of a generic plasma model. In view of that criticism we first will give here in detail the proves in [1]- [3].…”

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Comment on "Pfirsch-Tasso versus standard approaches in the plasma stability theory including the resistive wall effects" [Phys. Plasmas 24, 112513 (2017)]

Tasso¹,

Throumoulopoulos²

2021

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In the commended paper it is claimed that the proves of the "Resitive-Wall-Mode theorem" by Pfirsch and Tasso [Nucl. Fusion 11, 259 (1971)] and extensions of that theorem for time dependent wall resistivity and equilibrium plasma flow are not detailed and that there are limitations restricting their applicability. In response, we provide here pertinent detailed derivations showing that the proves of the above mentioned theorems are rigorous and complete, unlike the considerations in the commended paper which ignore the self adjointness of the operator ∇ × ∇× and the fact that the force operator in the linearized ideal MHD momentum equation remains self adjoint in the presence of equilibrium flows. As a matter of fact it is proved here that, because of the self adjointness of the operator ∇ × ∇×, a claimed in the commended paper additional term in Ohm's law vanishes identically.

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Pfirsch-Tasso versus standard approaches in the plasma stability theory including the resistive wall effects

Pustovitov

2017

Physics of Plasmas

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The study is devoted to theoretical description of plasma stability in toroidal fusion systems with a resistive wall. Its aim is elimination of contradictions between the models recently developed for the resistive wall mode analysis and the Pfirsch-Tasso approach originated from the paper published in 1971 [D. Pfirsch and H. Tasso, Nucl. Fusion 11, 259 (1971)]. The main relations have been given there without detailed proofs. Here, a missing chain of derivations is restored and earlier unknown limitations that restrict the applicability of the Pfirsch-Tasso energy principle are established. Its replacement valid in a wider area is proposed. The new result is free from the constraints implicitly imposed in the Pfirsch-Tasso procedure and can be used with any plasma model (not necessarily ideal) and for arbitrary perturbations. The proposed extensions allow applications for analysis of the rotational stabilization and optimization of the ITER scenarios.

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Lyapunov stability of flowing magnetohydrodynamic plasmas surrounded by resistive walls

Cited by 6 publications

References 21 publications

On Lyapunov boundary control of unstable magnetohydrodynamic plasmas

On Lyapunov boundary control of unstable magnetohydrodynamic plasmas

Comment on "Pfirsch-Tasso versus standard approaches in the plasma stability theory including the resistive wall effects" [Phys. Plasmas 24, 112513 (2017)]

Pfirsch-Tasso versus standard approaches in the plasma stability theory including the resistive wall effects

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