Extension of Shafranov’s Equilibrium Theory to the Description of Current Quenches Affected by Resistive Wall Dissipation in Tokamaks

Pustovitov, V. D.

doi:10.1134/s1063780x19120079

Cited by 10 publications

(7 citation statements)

References 73 publications

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“…Calculation of i and/or B w is a separate electromagnetic task [35][36][37][38][39], the main difficulty of which comes from the plasmawall coupling through (3) at S pl because the shape and position of the latter must also react to the plasma changes. Incorporation of this coupling [39,40] is mandatory in the task [19,21,24,34], it leads to an essential difference in the disruption forces from those calculated for the plasma replaced by one [41][42][43] or several [11,[44][45][46][47][48][49] solid current rings. The analysis below is based on the results presented in [39,40] for the large-aspect-ratio model with a circular plasma and almost coaxial wall.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Incorporation of this coupling [39,40] is mandatory in the task [19,21,24,34], it leads to an essential difference in the disruption forces from those calculated for the plasma replaced by one [41][42][43] or several [11,[44][45][46][47][48][49] solid current rings. The analysis below is based on the results presented in [39,40] for the large-aspect-ratio model with a circular plasma and almost coaxial wall. The system is assumed to be axisymmetric and the standard representation 2πB = ∇ψ × ∇ζ + µ 0 I∇ζ (18) for the magnetic field B is used.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Such a field has been calculated in a number of papers starting from [31]. However, the available expressions for B p are sometimes contradicting and/or incomplete, as reviewed in [40]. Here we use those explained and presented along with all necessary definitions there.…”

Section: Magnetic Field In the Plasma-wall Vacuum Gapmentioning

confidence: 99%

“…Here we use those explained and presented along with all necessary definitions there. It is important that both the plasma shift ∆ b and the resistive wall reaction are taken into account in [40].…”

Section: Magnetic Field In the Plasma-wall Vacuum Gapmentioning

confidence: 99%

“…In such a case, for the large-aspect-ratio model [31,32,[53][54][55][56][57][58][59][60] with a circular plasma and almost coaxial wall, we have in the plasma-wall vacuum gap [40] ψ gap = ψ 0 (ρ) + ψ 1 (ρ) cos u + . .…”

Section: Magnetic Field In the Plasma-wall Vacuum Gapmentioning

confidence: 99%

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Dependence of disruption forces on the plasma position inside the vacuum vessel in tokamaks

Pustovitov¹

2020

Plasma Phys. Control. Fusion

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The earlier analytical model (Pustovitov and Kiramov 2018 Plasma Phys. Controlled Fusion 60, 045011) for plasma-wall electromagnetic interaction in tokamaks is revised and extended. In that model, the magnetic field B was treated as tangential to the vacuum vessel (VV) wall, which implied some pre-selected plasma position inside the VV. Here, in contrast, the plasma shift ∆ b with respect to VV is a free parameter, and the wall is not a magnetic surface. The derived expressions explicitly show the effect of ∆ b , or the normal component of B on the poloidal distribution of the disruption force on the wall, while the integral radial force is found to be insensitive to ∆ b . Similar results have been obtained recently in CarMa0NL simulations (Isernia et al 2019 Plasma Phys. Control. Fusion 61 115003), which are now explained and confirmed analytically, including the role and interplay of the normal and tangential forces as functions of ∆ b . The standard large-aspect-ratio model of an axisymmetric tokamak with circular plasma and an almost coaxial wall is used. Additionally, to facilitate comparison with previous studies, the ideal-wall reaction is assumed.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Magnetic Field In the Plasma-wall Vacuum Gapmentioning

confidence: 99%

Section: Magnetic Field In the Plasma-wall Vacuum Gapmentioning

confidence: 99%

Section: Magnetic Field In the Plasma-wall Vacuum Gapmentioning

confidence: 99%

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Dependence of disruption forces on the plasma position inside the vacuum vessel in tokamaks

Pustovitov¹

2020

Plasma Phys. Control. Fusion

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Resolution of the paradox discovered by Freidberg in the Shafranov's theory on plasma equilibrium

Pustovitov

2020

Physics of Plasmas

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Predictions of the Shafranov's analytical theory are so highly respected that some of them are reprinted without any check for consistency. One example of such a kind is considered here: the equation for the plasma shift in a tokamak first introduced in Shafranov, J. Nucl. Energy C 5, 521 (1963). Since then, it has entered a number of review papers and textbooks, though, when tested by Freidberg [Freidberg, Rev. Mod. Phys. 54, 801 (1982)], it revealed some peculiar features. The main (long unnoticed) discovery was that the external vertical magnetic field required by that equation at zero shift was significantly different from the value given by the other famous Shafranov's formula for the same field in the same configuration. It is the tremendous scale of disagreement in the very core of the otherwise perfect theory that attracts attention. Here, a wrong element in the construction is found and repaired. It is established that it must be the incorrectly imposed boundary conditions for the magnetic field at the vacuum vessel wall treated as an ideal conductor. The proposed replacement eliminates the contradiction and extends the model by incorporating the resistive-wall effects.

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Virial relations for elongated plasmas in a tokamak and their potential use in magnetic diagnostics

Pustovitov

2022

Physics of Plasmas

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Virial relations are traditionally considered as providing the diamagnetic parameter, poloidal beta [Formula: see text], and internal inductance [Formula: see text] through the integrals determined by the plasma shape and poloidal magnetic field at the plasma–vacuum interface. This gives rise to discussions of their potential applications for diagnostic purposes. Recently, this concept was analyzed in the numerical study of Bongard et al. [Phys. Plasmas 23, 072508 (2016)]. Here, we analytically calculate three main virial integrals (traditionally denoted as [Formula: see text], [Formula: see text], and [Formula: see text]) for the plasma with elliptical cross section. The results are expressed through the plasma elongation, its radial derivative, and a similar derivative [Formula: see text] of the Shafranov shift, all taken at the plasma boundary. The geometry of magnetic surfaces inside is not constrained, which guaranties the applicability of the results in a wide area. It is shown that [Formula: see text] must be a constant, [Formula: see text] weakly depends on [Formula: see text], and only [Formula: see text] is a sensitive function of the plasma state through [Formula: see text]. This makes [Formula: see text] the quantity most suitable for diagnostics, while independence of [Formula: see text] on the plasma shape, [Formula: see text], and [Formula: see text] can be good for calibrations. The difficulties of inferring [Formula: see text] from the measured [Formula: see text] are now shown explicitly.

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Extension of Shafranov’s Equilibrium Theory to the Description of Current Quenches Affected by Resistive Wall Dissipation in Tokamaks

Cited by 10 publications

References 73 publications

Dependence of disruption forces on the plasma position inside the vacuum vessel in tokamaks

Dependence of disruption forces on the plasma position inside the vacuum vessel in tokamaks

Resolution of the paradox discovered by Freidberg in the Shafranov's theory on plasma equilibrium

Virial relations for elongated plasmas in a tokamak and their potential use in magnetic diagnostics

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