Diamagnetism and beta in beam heated currentless plasmas of heliotron E

Besshou, S.; Thomas, C. E.; Ohba, T.; Iiyoshi, A.; Uo, K.

doi:10.1088/0029-5515/26/10/007

Cited by 14 publications

(10 citation statements)

References 30 publications

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“…The temporal variation of the toroidal flux through the plasma can be measured using the standard technique [3][4][5][8][9][10] or the double loop method [31].…”

Section: Resultsmentioning

confidence: 99%

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Theory of Diamagnetic Signal in Current-Free Stellarators

Pustovitov

2010

Plasma and Fusion Research

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The toroidal magnetic flux through the plasma column is calculated analytically for current-free stellarators of arbitrary geometry without assumptions on the plasma shape, aspect ratio, etc. This is done with accuracy sufficient for extracting the contribution due to the finite plasma pressure from this flux. The final result is a formula relating the measured diamagnetic signal with β, the ratio of the plasma pressure to the magnetic pressure. This formula is obtained assuming small β and the relative depth of the magnetic well. These are natural conditions for stellarators, therefore the final result can be recommended for magnetic diagnostics without practical limitations. Keywords: stellarator, magnetic diagnostics, diamagnetic signal, plasma equilibrium, current-free plasma DOI: 10.1585/pfr.5.S2054 InroductionDiamagnetic measurements are a traditional diagnostics used for determining the plasma energy content in tokamaks and stellarators [1][2][3][4][5]. Interpretation of the measurements are based on a simple formula originally derived for a circular plasma cylinder [6] 2 δΦwhere the measured diamagnetic signal is defined asB is the magnetic field, B v is the vacuum magnetic field, Φ 0 = B 0 S ⊥ with S ⊥ = πb 2 being the transverse crosssection of the plasma column, b is its minor radius, B 0 is the toroidal field, B J is the poloidal field at the plasma boundary due to the net toroidal current,β ≡ 2p/B 2 0 is the ratio of the volume-averaged plasma pressure p to the magnetic field pressure B 2 0 /2. It is known that Eq. (1) can be applied to large-aspectratio tokamaks with a circular plasma [7]. The same or slightly modified formula has been used for conventional stellarators [8][9][10], though the validity of Eq. (1) has been proved for straight stellarators only [11,12]. Strictly speaking, for stellarators with current-carrying plasma (B J 0) Eq. (1) should contain an additional term [11,12]. Here we consider the case when this contribution can be disregarded.The diamagnetic signal for arbitrary shape and aspect ratio current-free plasma in a toroidal conventional stellarator was calculated analytically in [13]. In analytical author's e-mail: pustovit@nfi.kiae.ru * permanent address: Russian Research Centre 'Kurchatov Institute', Pl. Kurchatova, Moscow, 123182, Russia theory, when a cylindrical result is generalized for account of the toroidal effects, this is usually done by large-aspectratio expansion. It was unexpected that the problem considered in [13] turned out to be solvable without this 'natural' simplification and even without any assumption on the plasma shape. The obtained result [13] was ready for practical use. Similar to (1), it directly relates the measured diamagnetic signal δΦ to the value of interest, the integral on the right hand side over the plasma volume. Here the constant F b = 2πrB t describes the vacuum toroidal field B t , r is the radius from the main vertical axis, and δ SH is a small correction related to the Shafranov shift and helical field. Later, numerical calculation...

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“…The temporal variation of the toroidal flux through the plasma can be measured using the standard technique [3][4][5][8][9][10] or the double loop method [31].…”

Section: Resultsmentioning

confidence: 99%

“…(1) can be applied to large-aspectratio tokamaks with a circular plasma [7]. The same or slightly modified formula has been used for conventional stellarators [8][9][10], though the validity of Eq. (1) has been proved for straight stellarators only [11,12].…”

Section: Inroductionmentioning

confidence: 99%

Theory of Diamagnetic Signal in Current-Free Stellarators

Pustovitov

2010

Plasma and Fusion Research

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“…11 Possible origins of this drift can be found in the drift in the rectified coil current, the eddy currents in the vacuum chamber ͑a typical decay time of 15-20 ms for Heliotron J͒, the vibrations, and deformation of the chamber. Although low frequency drift still exists in the rectified current of Heliotron J coils, a good elimination and zero base calibration during the discharge time as shown in Figs.…”

Section: Discussionmentioning

confidence: 99%

“…[5][6][7] In stellarators, compensation for coil currents with eccentric loops and Rogowski coils have previously been reported. [8][9][10][11] Up until now, however, there has been no experimental description of a diamagnetic double-loop system to measure the stored energy in stellarator plasmas.…”

Section: Introductionmentioning

confidence: 99%

Diamagnetic double-loop method for a highly sensitive measurement of energy stored in a Stellarator plasma

Besshou

Aizawa

Tomiyama

et al. 2001

Review of Scientific Instruments

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In this article we describe a diamagnetic double-loop method for measurement of the energy stored in a magnetized plasma. Two concentric diamagnetic loops enclose a plasma column. The advantage of this method is the capability to eliminate to a high extent the background magnetic field and the effect of eddy currents in the measurement of relatively small diamagnetic signals. This method was applied to initial plasmas produced in the helical axis stellarator Heliotron J. A stored energy of 0.7 kJ was measured with a resolution of ±0.02 kJ at rippling magnetic field of 1 T in a plasma heated by rf discharges up to 400 kW. This diamagnetic double-loop method improved the signal to noise ratio of the conventional single loop method sixfold. The magnetic diagnostics hardware, experimental results, and an error estimate are presented.

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“…The higher poloidal flux moments considered are also practically independent of the current distribution. The dependence of $h2) on the pressure profile for a given ( 6 ) is well defined and can, in principle, be used for a rough determination of the pressure profile.…”

Section: Versus (P) Determined From Calculations For the L 2 Stellara...mentioning

confidence: 99%

Is it possible to extract information on the plasma pressure profile from magnetic measurements in stellarators?

Кузнецов¹,

Shchepetov²,

Sychugov³

1994

Nucl. Fusion

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The free boundary stellarator equilibria are studied in the framework of averaged equations. The structure of external magnetic fields created by currents flowing inside the plasma column is analysed. In all cases considered the dipole component of the magnetic field (in agreement with previous investigations) can only be used to determine the volume averaged value of the parameter @ if the net toroidal current is known. For zero net current operation it is shown that the quadrupole component of the external magnetic field can be used for an estimate of the plasma pressure distribution, for example, in the framework of a one parametric set of profiles. The dependence of the external magnetic field on the current distribution for the given pressure profile is also investigated, and it is shown that there is a possibility of distinguishing at least strongly different current distributions (such as the peaked and offcentred current profiles considered here) either for a large shear system at high @ or for a device with averaged vertical elongation of the vacuum magnetic surfaces.

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Diamagnetism and beta in beam heated currentless plasmas of heliotron E

Cited by 14 publications

References 30 publications

Theory of Diamagnetic Signal in Current-Free Stellarators

Theory of Diamagnetic Signal in Current-Free Stellarators

Diamagnetic double-loop method for a highly sensitive measurement of energy stored in a Stellarator plasma

Is it possible to extract information on the plasma pressure profile from magnetic measurements in stellarators?

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