Fast-ion-driven vertical modes in magnetically confined toroidal plasmas

Barberis, T.; Porcelli, Francesco; Adil, Yolbarsop

doi:10.1088/1741-4326/ac5ad0

Cited by 12 publications

(14 citation statements)

References 25 publications

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“…Nevertheless, we would like to bring the attention of the tokamak physics community on the importance of these oscillatory solutions. As we have shown in this article (see also Porcelli et al 2021;Barberis et al 2022), their oscillation frequency is slightly below the poloidal Alfvén frequency, which makes these modes immune to Alfvén continuum damping. Thus, these modes are only weakly damped by wall resistivity.…”

Section: Discussionmentioning

confidence: 52%

“…Under special circumstances, discussed in some detail in Barberis et al. (2022), this resonant interaction may drive the VDOM unstable.…”

Section: Discussionmentioning

confidence: 99%

“…2021; Barberis et al. 2022), their oscillation frequency is slightly below the poloidal Alfvén frequency, which makes these modes immune to Alfvén continuum damping. Thus, these modes are only weakly damped by wall resistivity.…”

Section: Discussionmentioning

confidence: 99%

“…On the other hand, they can interact resonantly with fast ion populations, which are present in a tokamak plasma due to auxiliary heating and/or as fusion reaction products. Under special circumstances, discussed in some detail in Barberis et al (2022), this resonant interaction may drive the VDOM unstable.…”

Section: Discussionmentioning

confidence: 99%

“…Olofsson (2022) and Pfefferlé & Bhattacharjee (2018); however, in those references, the emphasis was on the growth and control of the usual, non-rotating vertical resistive wall mode, while the importance of the oscillatory solutions was played down. In fact, in our view, the VDOM solutions of the relevant dispersion relation are very interesting, as their oscillatory character opens the possibility that they are driven unstable by the resonant interaction with energetic particles, see also Barberis, Porcelli & Yolbarsop (2022). Observations of saturated oscillations were reported in recent JET experiments where energetic fast ion populations were produced by intense auxiliary plasma heating (Oliver et al.…”

Section: Introductionmentioning

confidence: 86%

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Vertical displacement oscillatory modes in tokamak plasmas

Barberis

Adil²,

Porcelli³

2022

J. Plasma Phys.

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Vertical displacement normal modes in shaped tokamak plasmas are studied analytically, based on the reduced ideal-magnetohydrodynamic model. With the help of quadratic forms, and using the appropriate eigenfunction for vertical displacements with toroidal mode number $n=0$ and dominant elliptical-angle mode number $m=1$ , a dispersion relation is derived, including the effects of ideal or resistive walls through a single parameter, $D_w(\gamma )$ , which is, in general, a function of the complex eigenfrequency $\gamma = -{\rm i}\omega$ . For the resistive-wall case, the dispersion relation is cubic in $\gamma$ . One root corresponds to the well-known, non-rotating resistive-wall vertical mode, growing on the resistive-wall time scale. The other two roots are weakly damped by wall resistivity, but oscillate with a frequency below the poloidal Alfvén frequency, which makes them immune to continuum damping, but subject to possible instability due to resonant interaction with fast ions.

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Section: Discussionmentioning

confidence: 52%

“…Under special circumstances, discussed in some detail in Barberis et al. (2022), this resonant interaction may drive the VDOM unstable.…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 86%

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Vertical displacement oscillatory modes in tokamak plasmas

Barberis

Adil²,

Porcelli³

2022

J. Plasma Phys.

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Axisymmetric oscillatory modes in cylindrical magnetized plasma bounded by a conducting wall

et al. 2023

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Toroidal vs cylindrical analytical description of the magnetic field outside the elongated evolving plasma in tokamaks

Pustovitov

Chukashev

2023

Physics of Plasmas

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In the plasma equilibrium theory, Gajewski's analytical expression [Gajewski, Phys. Fluids 15, 70 (1972)] for the poloidal magnetic flux [Formula: see text] outside the plasma is known. It was obtained as a solution of the two-dimensional Laplace equation outside an infinite straight cylinder with an elliptical cross section and a uniform current density [Formula: see text]. An example of its use for analysis of static configurations is given in the study by Porcelli and Yolbarsop [Phys. Plasmas 26, 054501 (2019)]. Here, we consider the question of its applicability in dynamic problems including, for example, the current quench (CQ) or vertical displacement event (VDE), when the electromagnetic response of the vacuum vessel to the plasma magnetic field evolution has to be accounted for. It is shown that the mentioned cylindrical model does not provide enough information for calculation of the current induced in the wall. Mathematically, this manifests itself in the fact that Gajewski's expression contains an indefinite constant of integration [Formula: see text] (hereinafter it is [Formula: see text] at the plasma boundary), which, in analytical applications, is replaced either by zero or by a value that makes [Formula: see text] on the magnetic axis. This does not affect the magnitude of the magnetic field [Formula: see text], but it would incorrectly give the electric field at [Formula: see text]. To eliminate this shortcoming, an additional block of calculations in the toroidal geometry is needed. Here, the problem is solved analytically. The resulting final expression with [Formula: see text] well-defined in the toroidal configuration also includes the effects of the Shafranov's shift and inhomogeneity of [Formula: see text]. The proposed extensions allow generalization of the earlier results to a wider area and cover such events as CQ or VDE.

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Fast-ion-driven vertical modes in magnetically confined toroidal plasmas

Cited by 12 publications

References 25 publications

Vertical displacement oscillatory modes in tokamak plasmas

Vertical displacement oscillatory modes in tokamak plasmas

Axisymmetric oscillatory modes in cylindrical magnetized plasma bounded by a conducting wall

Toroidal vs cylindrical analytical description of the magnetic field outside the elongated evolving plasma in tokamaks

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