Stability of a diffuse, high β, <i>l</i>=1 system

Berge, Gerhard; Freidberg, Jeffrey P.

doi:10.1063/1.861025

Cited by 15 publications

(8 citation statements)

References 11 publications

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“…Internal m = 1 modes. Ideal magnetohydrodynamic theory applied to diffuse-profile plasmas predicts unstable internal m = 1 modes in addition to the gross mode [18,19]. The growth rate for these modes is given by [ 19] hv A b-ha (5) where n > 1 is the number of radial nodes of the mode.…”

Section: Table I Diffuse-profile Correction Factorsmentioning

confidence: 99%

“…Ideal magnetohydrodynamic theory applied to diffuse-profile plasmas predicts unstable internal m = 1 modes in addition to the gross mode [18,19]. The growth rate for these modes is given by [ 19] hv A b-ha (5) where n > 1 is the number of radial nodes of the mode. This growth rate is a great deal smaller than that for the gross mode and thus the theory has not yet been subjected to experimental test (for the present experiment, \/y n = i = 180 JUS).…”

Section: Table I Diffuse-profile Correction Factorsmentioning

confidence: 99%

“…( 18) are uncertain, but for definiteness the values v A = 18 cm • JUS" 1 , |3 = 0.7, and 7 = 0.3 us' 1 are used. The maximum, or saturation, current of the modules can be expressed as the displacement £ m a x for which the instability force equals the maximum feedback force and is given by max - (19) where b 2 is the maximum feedback field divided by the main field. Also of interest is the calculation of the fraction of the toroidal force represented by the maximum feedback force:…”

Section: Feedback Stabilizationmentioning

confidence: 99%

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Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

et al. 1978

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Feedback stabilization of the Scyllac 120° toroidal sector is reported. The confinement time was increased by 10-20 us using feedback to a maximum time of 35-45 /us, which is over 10 growth times of the long-wavelength m = I instability. These results were obtained after circuits providing flexible waveforms were used to drive auxiliary equilibrium windings. The resultant improved equilibrium agrees well with recent theory. It was observed that normally stable short-wavelength m = I modes could be driven unstable by feedback. This instability, caused by local feedback control, increases the feedback system energy consumption. An instability involving direct coupling of the feedback 1 = 2 field to the plasma 1 = 1 motion was also observed. The plasma parameters were: temperature, T,. a T, a !©0eV; density, n. a 2 X 10" cm" 1 ; radius, a a 1 cm; and P 2 0.7. Beta decreased significantly in 40 ^s, which can be accounted for by classical resistivity and particle loss from the sector ends.

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Section: Table I Diffuse-profile Correction Factorsmentioning

confidence: 99%

Section: Table I Diffuse-profile Correction Factorsmentioning

confidence: 99%

Section: Feedback Stabilizationmentioning

confidence: 99%

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Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

et al. 1978

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“…One important result of the stability theory based on the old Scyllac ordering [4,5] and using a constant-pressure model is that the m = 1, k= 0 mode can be wall-stabilized for a sufficiently small compression ratio b/a by the dipole currents induced in the conducting wall. For a diffuse pressure profile and using the same old ordering, there are, besides the gross m= 1 mode, two additional classes of rather localized m = 1 modes [7]. One set of modes existing for every monotonic pressure profile is localized in the interior of the plasma and cannot be wallstabilized, while the other set of modes is localized rather in the exterior of the dense plasma and can be wall-stabilized.…”

Section: Introductionmentioning

confidence: 99%

Ideal MHD stability of m ≥ 2 modes in diffuse high-β, ℓ = 1 equilibria

Herrnegger

Schneider

1976

Nucl. Fusion

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A time-dependent explicit finite-difference code is developed for computing growth rates of gross magnetohydrodynamic modes in helically symmetric high-6, 8= 1 equilibria. The effect of numerical dispersion on current-and pressure-driven modes and the convergence of the growth rate with the grid size for modes in screw-pinch, O-pinch, and helical equilibria are discussed. In the case of diffuse MHD equilibria with a long helical period length, the eigenvalues computed by this code are in agreement with those of a 6W-analysis and of experiments and are a factor of about two smaller than predicted by the surface current theory. The growth rates o f m i 2 modes are given as functions of the helical periodicity number, the helical amplitude of the magnetic axis, beta, and the longitudinal wave number k. * This work was performed under the terms of the agreement on association between Max-Planck-Institut fflr Plasmaphysik and Euratom.

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“…Much of the early MHD equilibrium and stability theory was based on studies of the sharp-boundary surface-current model [2][3][4][5][6][7][8]. Recently, a great deal of effort has been applied to the investigation of diffuse profile effects [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Stability of a combined ℓ = 0, ℓ = 1 diffuse configuration

Berge¹,

Freidberg

1976

Nucl. Fusion

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The stability of a diffuse high-β, ℓ = 0, ℓ = 1 Scyllac configuration has been investigated. The optimum ratio of ℓ = 0 to ℓ = 1 fields is calculated in order to minimize the m = 1 growth rate. The optimum case scales similarly to sharpboundary predictions but requires a relatively smaller amount of ℓ = 0 field. The growth rate at optimum conditions is about 20 – 30% lower than that predicted by sharp-boundary theory.

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Stability of a diffuse, high β, l=1 system

Cited by 15 publications

References 11 publications

Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

Ideal MHD stability of m ≥ 2 modes in diffuse high-β, ℓ = 1 equilibria

Stability of a combined ℓ = 0, ℓ = 1 diffuse configuration

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