Local, ideal and resistive stability in tokamaks with non-circular cross-section

Green, B. J.; Zehrfeld, H. P.

doi:10.1088/0029-5515/17/6/003

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…The B r signal, measured across the integer q surface near the plasma edge, was single signed, implying that the field perturbation was due to a resistive mode [24]. Estimates for resistive interchange modes showed them to be stable [25], suggesting that the perturbations were due to tearing modes. Such oscillations are caused by magnetic structures (islands) rotating in the direction of the electron diamagnetic drift [26].…”

Section: Kink-mode Stabilitymentioning

confidence: 99%

An experimental study of tokamak plasmas with vertically elongated cross-sections

Robinson

Wootton

1978

Nucl. Fusion

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The production and equilibrium of tokamak plasmas with vertically elongated cross-sections are described. Axisymmetric instabilities, which are controlled by a passive feedback system, restrict the semiaxis ratio to less than 1.5. Both the appearance and growth times of these instabilities are theoretically predicted. Poloidal magnetic field oscillations are shown to confirm the plasma shape deduced from equilibrium calculations. The poloidal beta, central electron temperature and overall energy confinement time increase with increasing semi-axis ratio.

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Section: Kink-mode Stabilitymentioning

confidence: 99%

An experimental study of tokamak plasmas with vertically elongated cross-sections

Robinson

Wootton

1978

Nucl. Fusion

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“…Let ψ s (r, z) denote the Solov'ev solution, (7), and let ψ(r, z) represent our solution. We find that the value of |ψ − ψ s |/ψ X , averaged over the plasma volume, is 6.6 × 10 −4 , whereas the maximum value is 5.6 × 10 −3 .…”

Section: Our Methods For Double-null Equilibriamentioning

confidence: 99%

“…In 1968, Solov'ev [4] obtained a family of exact analytic solutions of the Grad-Shafranov equation. Solov'ev's solutions are useful for benchmarking plasma equilibrium codes [5,6], as well as for magnetohydrodynamical stability analysis of tokamak plasmas [7]. Solov'ev's solutions have been employed to construct model up-down-symmetric tokamak equilibria [8], as well as equilibria with magnetic divertors.…”

Section: Introductionmentioning

confidence: 99%

“…In 1968, Solov'ev [4] proposed simple linear stream functions, and got analytic solution for the Grad-Shafranov equation. Solov'ev's equilibrium configurations are useful for the benchmarking magnetohydrodynamics equilibrium codes [5,6], as well as stability analysis [7] of toroidal axisymmetric tokamaks. They have been used to construct up-down symmetric tokamak equilibria [8], as well as a divertor configuration.…”

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confidence: 99%

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Vacuum solution for Solov’ev’s equilibrium configuration in tokamaks

Fitzpatrick

2019

Nucl. Fusion

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In this work, we construct a simple tokamak plasma equilibrium generated by currents flowing within the plasma and currents flowing in distant external coils. The plasma current density takes the form j ϕ (r, z) = −ar − bR 2 /r inside the plasma, and is zero in the surrounding vacuum. We use Green's function method to compute the plasma current contribution, together with a homogeneous solution to the Grad-Shafranov equation, to construct the full solution. Matching with the constant boundary condition on the last closed flux surface is performed to determine the homogeneous solution. The total solution is then extended into the vacuum region to get a realistic vacuum solution. We find that the actual solution is different from the Solov'ev solution, especially the X-point structure. The X-point obtained at the last closed flux surface is not like the letter "X", and the expanded angle in the vacuum is larger than corresponding angle in the plasma at the null point. The results are important for understanding the X-point and separatrix structure. At the end of the paper, we have extended the classic Solovev's configuration to an ITER-like configuration, and obtained the vacuum solution. PACS number(s): 52.55.-s, 47.65.-d.

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“…The analytical solution of the GS equation obtained with linear stream functions is known as a Solovev solution [3] and this is the earliest analytical study of two-dimensional tokamak equilibria. Even though the choice of profile is limited, these solutions are useful for the validation of numerical equilibrium calculations [4,5] as well as stability analysis [6]. This convenient form of analytical solution has been used to construct up-down symmetric tokamak equilibria [7] as well as a divertor configuration [3,8].…”

Section: Introductionmentioning

confidence: 99%

Analytical description of poloidally diverted tokamak equilibrium with linear stream functions

Srinivasan¹,

Lao

Chu

2010

Plasma Phys. Control. Fusion

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The tokamak plasmas in most of the present experiments and those considered for the future reactors are up-down asymmetric in nature. This asymmetry arises due to external coils and conducting structures which surround the plasma. The analytical description of these equilibria using mathematically simpler methods is useful for the theoretical study of stability and transport. Such a tokamak equilibrium has been constructed analytically for arbitrary aspect ratios. The asymmetric nature arises through the homogeneous part of the exact solution of the Grad-Shafranov equation with a choice of pressure and toroidal function as linear in poloidal flux. These solutions can describe both single-and double-null divertor plasmas with an appropriate choice of plasma boundary. This has been used to construct DIII-D and ITER-like equilibrium and compared with those computed numerically.

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Local, ideal and resistive stability in tokamaks with non-circular cross-section

Cited by 8 publications

References 16 publications

An experimental study of tokamak plasmas with vertically elongated cross-sections

An experimental study of tokamak plasmas with vertically elongated cross-sections

Vacuum solution for Solov’ev’s equilibrium configuration in tokamaks

Analytical description of poloidally diverted tokamak equilibrium with linear stream functions

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