The energy confinement time in stellarators

Коврижных, Л. М.

doi:10.1088/0029-5515/24/4/004

Cited by 78 publications

(62 citation statements)

References 5 publications

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“…These have been reviewed in great detail elsewhere [25,26,27,28,29], and it has been established that the neoclassical heat flux is very significant in the plasma core of most experiments. At low collisionality, the electrons are usually in the 1/ν-regime, where the diffusivity is inversely proportional to the collision frequency ν,…”

Section: Typical Collisionality Regimesmentioning

confidence: 99%

Stellarator and tokamak plasmas: a comparison

Helander

Beidler

Bird

et al. 2012

Plasma Phys. Control. Fusion

138

181

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An overview is given of physics differences between stellarators and tokamaks, including magnetohydrodynamic equilibrium, stability, fast-ion physics, plasma rotation, neoclassical and turbulent transport, and edge physics. Regarding microinstabilities, it is shown that the ordinary, collisionless trapped-electron mode is stable in large parts of parameter space in stellarators that have been designed so that the parallel adiabatic invariant decreases with radius. Also, the first global, electromagnetic, gyrokinetic stability calculations done for Wendelstein 7-X suggest that kinetic ballooning modes are more stable than in a typical tokamak.

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Section: Typical Collisionality Regimesmentioning

confidence: 99%

Stellarator and tokamak plasmas: a comparison

Helander

Beidler

Bird

et al. 2012

Plasma Phys. Control. Fusion

138

181

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“…This can be related to the importance of offdiagonal terms for the neoclassical particle flux in the toroidal helical plasma; 21,22 e.g., Eq. ͑1͒ is reduced into ⌫ Neo ӍD T…”

Section: Transport At the Connection Layermentioning

confidence: 99%

“…Figure 41͑c͒ indicates two examples of the neoclassical radial current during the transitions as a function of the radial electric field. 21,22,40 In this calculation, plausible parameters of the CHS plasma are chosen to satisfy bifurcation conditions. The profiles of ion temperature and electron density in calculation are assumed to be all parabolic, with the central values being 0.35 keV and 0.5ϫ10 13 cm Ϫ3 .…”

Section: Fig 41 ͑A͒mentioning

confidence: 99%

“…The strongly positive E r should have a better neoclassical transport property than the slightly positive E r . 21,22 Hence, the transition of E r to the strongly positive branch may potentially contribute to the formation of the internal transport barrier in toroidal helical plasmas through the improvement in the neoclassical collisional transport.…”

Section: Bifurcation and Transport Barriermentioning

confidence: 99%

“…18,19 Before these findings, bifurcation of the radial electric field had been expected in toroidal helical plasmas by a neoclassical theory including helical ripple diffusion. [20][21][22] In contrast to tokamaks, the neoclassical theory had predicted that the absolute value of the radial electric field affected the transport in toroidal helical plasmas. The radial electric field, therefore, had been a primary physical quantity in toroidal helical plasmas, even without the discovery of the H-mode.…”

Section: Introductionmentioning

confidence: 99%

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Experimental study of the bifurcation nature of the electrostatic potential of a toroidal helical plasma

et al. 2000

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The bifurcation nature of the electrostatic structure is studied in the toroidal helical plasma of the Compact Helical System ͑CHS͒ ͓K. Matsuoka et al., Proceedings of the 12th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Nice, 1988 ͑International Atomic Energy Agency, Vienna, 1989͒, Vol. 2, p. 411͔. Observation of bifurcation-related phenomena is introduced, such as characteristic patterns of discrete potential profiles, and various patterns of self-sustained oscillations termed electric pulsation. Some patterns of the electrostatic structure are found to be quite important for fusion application owing to their association with transport barrier formation. It is confirmed, as is shown in several tokamak experiments, that the thermal transport barrier is linked with electrostatic structure through the radial electric field shear that can reduce the fluctuation resulting in anomalous transport. This article describes in detail spatio-temporal evolution during self-sustained oscillation, together with correlation between the radial electric field and other plasma parameters. An experimental survey to find dependence of the temporal and spatial patterns on plasma parameters is performed in order to understand systematically the bifurcation property of the toroidal helical plasma. The experimental results are compared with the neoclassical bifurcation property that is believed to explain the observed bifurcation property of the CHS plasmas. The present results show that the electrostatic property plays an essential role in the structural formation of toroidal helical plasmas, and demonstrate that toroidal plasma is an open system with a strong nonlinearity to provide a new attractive problem to be studied.

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Monte carlo calculation of transport for three‐dimensional magnetohydrodynamic equilibria

Bauer

Betancourt

Garabedian

1986

Comm Pure Appl Math

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A Monte Carlo algorithm has been implemented which couples the results of a three-dimensional magnetohydrodynamic equilibrium code with particle transport calculations similar to those of Boozer and Kuo-Petravic. The equilibrium results are in a form which lends itself to easy and accurate computation of the coefficients required to follow particle orbits in flux variables at finite pressure. In particular. the parallel current and the Clebsch potential for the current are obtained from Fourier series solutions of first-order partial differential equations with constant coefficients.Confinement times are estimated from the exponential decay of expected values of appropriately chosen functionals of the particle distribution. The observation that these functionals satisfy boundary conditions helps us to compute confinement times over a wide range of collision frequencies. including cases where losses due to particle trapping are very high. Initial conditions are chosen to optimize the Monte Carlo calculation by using known information about the expected particle distribution.Results for actual and proposed stellarator experiments are given. Electron and ion confinement times are compared, since this is relevant to the issue of the effect of ambipolar electric fields on stellarator confinement. A spectral method is given to determine the elcctric field from charge neutrality. and numerical evidence is presented to suggest that anomalous electron transport may be due to small resonant terms in the electric potential. Also, comparisons are made with a simplified theory of particle transport already incorporated in the equilibrium code. zero net current stellarators are characterized by a quiet plasma, which might be more accurately represented by the neoclassical transport theory than tokamaks, which exhibit turbulence and anomalous transport; see [13].We take full account of the complicated geometry and finite p effects by solving the equilibrium problem numerically with a computer code BETA that has been described in detail elsewhere; see [l]. This results in a solution of the MHD equations where B is the magnetic field, J is the current density and p is the fluid pressure. A basic assumption is that there exists a nested set of flux surfaces s = const., with the pressure restricted to be a function p = p ( s ) of s alone. The magnetic field can be represented in terms of flux functions s and JI and Clebsch potentials 9 and S. We have B = 0 s X vJI = V+ + ~J v s , and as a consequence J = p,VS X VS.We introduce s as an independent variable in the radial direction, together with two angle variables u and u. These variables are normalized so that u has a unit period in the poloidal direction while remaining periodic in the toroidal direction, whereas u is periodic in the poloidal direction with unit period in the toroidal direction. The functions JI, + and 5 are multi-valued on each torus s = const., with periods given by the representations are single-valued. Here the total toroidal flux is equal to s, so that the pe...

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The energy confinement time in stellarators

Cited by 78 publications

References 5 publications

Stellarator and tokamak plasmas: a comparison

Stellarator and tokamak plasmas: a comparison

Experimental study of the bifurcation nature of the electrostatic potential of a toroidal helical plasma

Monte carlo calculation of transport for three‐dimensional magnetohydrodynamic equilibria

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