On the theory of magnetic diagnostics in stellarators and tokamaks

Pustovitov, V. D.

doi:10.1016/s0920-3796(96)00565-0

Cited by 9 publications

(10 citation statements)

References 6 publications

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“…The saturation of the diamagnetic flux in Fig. 7 results verify the analytic studies by Pustovitov [15], which concluded that higher-order corrections to the diamagnetic flux would be small. We note that the curves in Fig.…”

Section: Introductionsupporting

confidence: 84%

Free-boundary studies for the Large Helical Device

Ichiguchi¹,

Nakajima²,

Gardner³

1996

Nucl. Fusion

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Previous three dimensional magnetohydrodynamic studies of the Large Helical Device are extended to include free-boundary calculations of two realistic equilibrium sequences. The use of an external vertical field to centre the configuration as the plasma pressure increases is shown to give results that are almost identical with the earlier fixed-boundary computations. The expected response of a set of magnetic diagnostic loops is calculated and the sensitivity of the Mercier stability to the treatment of resonances in the parallel current is also considered.

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Section: Introductionsupporting

confidence: 84%

Free-boundary studies for the Large Helical Device

Ichiguchi¹,

Nakajima²,

Gardner³

1996

Nucl. Fusion

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“…Dependence of the diamagnetic signal on the Shafranov shift was demonstrated analytically in [16] and briefly discussed in [34]. This can be illustrated by a simple formula:…”

Section: Diamagnetic Signal and Shafranov Shiftmentioning

confidence: 95%

Diamagnetic measurements and plasma energy in toroidal systems

Pustovitov¹

2010

Plasma Phys. Control. Fusion

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Sensitivity of the diamagnetic signal to several operational and geometrical factors is analysed. Among them are the flux conservation in the plasma, eddy currents induced in the outer structures at fast processes, toroidal shift and deformation of the plasma boundary due to its energy change, and inhomogeneity of the confining magnetic field. It is shown that in each case, under proper experimental circumstances, the contribution, unaccounted in the traditional theory of diamagnetic measurements, can reach a level compared to β (ratio of the volumeaveraged plasma pressure to the magnetic field pressure). The approach is fully analytical with all relevant dependencies shown explicitly, allowing easy estimates and suggesting a resolution of the problem in order to restore the accuracy of finding β from diamagnetic measurements. This essentially extends the analysis [1] of possible measures to improve separation of the useful fraction of the measured diamagnetic signal. The approach is aimed to explanation of the discrepancies between model estimates and experimental results, unification of a knowledge obtained in separate numerical studies, extending a theoretical basis of magnetic diagnostics and uncovering potential dangers in interpretations. This is also an essential step from traditional cylindrical theory to analytical derivations in the toroidal geometry. The results are equally applicable to tokamaks and stellarators.Interpretation of diamagnetic measurements in tokamaks and stellarators is based on a simple formuladerived for a circular plasma cylinder more than 50 years ago, or its modifications. HereΦ is the flux of the magnetic field through the diamagnetic loop and ΔΦ is the difference between the current state and initial state when, B is the magnetic field, v B is the vacuum magnetic field (assumed unchanged in this case),

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“…The number of turns of the conductors in such loops is selected so that the result of the subtraction of the flux produced signals in the vacuum case is equal to zero. It has been found numerically [28] and analytically [8] (through an averaged approach) that for the zero net toroidal current case with a known plasma averaged radius, the cylindrical approximation is adequate. The theory of diamagnetic measurements in conventional stellarators is well developed, therefore it is pertinent to clarify only a few details.…”

Section: Peculiarities Of Conventional Measurementsmentioning

confidence: 99%

“…The direct dependence of the λ p term on the current density value suggests that in the case of stellarators with non-zero net toroidal current the value of δ p is dependent on the direction of the current [1]. The term ∼λ p is usually ignored in some systems of averaged equations [8], but in a limited number of cases, as we can see, it may play a visible role depending on the situation. A final remark, the interpretation of the diamagnetic signal in all cases requires at least the knowledge of the plasma cross-sectional area.…”

Section: Peculiarities Of Conventional Measurementsmentioning

confidence: 99%

“…However, not all of the limitations that are typical for magnetic diagnostics were outlined in [4][5][6][7]. Within the second approach [8,9], it is more likely that some general arguments arise against the possibility of profile determination for both of the 2D and 3D cases, which are strongly different in the mathematical sense. It happens, however, that certain results of [8,9] are not fully correct.…”

Section: Introductionmentioning

confidence: 99%

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Stellarator magnetic analysis: resolvability problems

Shchepetov

Jiménez²,

Кузнецов

2001

Plasma Phys. Control. Fusion

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In all probability the only way to understand the theoretical possibilities and limitations of magnetic analysis is the use of a trial-and-error method. To demonstrate this, a virgin field of rigorous mathematical foundations of a three-dimensional (3D) equilibrium problem is briefly presented. In the first part of the paper we clarify the problem of plasma profile determination. We previously have established the limitations following from a direct 3D plasma equilibrium problem on the possibility of the moderate current density profile identification. Here we demonstrate the limitations on the pressure profile determination under zero net current regime of operation. Realistic experimental conditions that significantly complicate the use of magnetic analysis for equilibrium identification are outlined. The second part of the paper deals with the peculiarities of diamagnetic measurements in stellarators. The influence of the 3D plasma induced magnetic fields is briefly sketched. We will also treat in detail an attractive, although questionable, possibility for the estimation of the electron cyclotron resonance heating absorbed power from the jump in the time derivative of the diamagnetic signal. It is shown that the limitations of such a method are completely determined by the accuracy of the experimental system set-up, but do not depend on the mathematical properties of the equations considered, as was previously expected.

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On the theory of magnetic diagnostics in stellarators and tokamaks

Cited by 9 publications

References 6 publications

Free-boundary studies for the Large Helical Device

Free-boundary studies for the Large Helical Device

Diamagnetic measurements and plasma energy in toroidal systems

Stellarator magnetic analysis: resolvability problems

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