Integrated physics optimization of a quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength

Субботин, А. А.; Михайлов, М. И.; Shafranov, V. D.; Isaev, M. Yu.; Nührenberg, C.; Nührenberg, J.; Zille, R.; Nemov, V. V.; Kasilov, Sergei; Kalyuzhnyj, V. N.; Cooper, W. A.

doi:10.1088/0029-5515/46/11/006

Cited by 57 publications

(105 citation statements)

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“…The next step should therefore be to simulate microinstabilities in finite-beta plasmas. All the simulations presented here were carried out in vacuum magnetic fields, but it is well known that quasi-isodynamicty and the maximum-J property are much easier to achieve at high beta 3,36 . A finite plasma pressure should act stabilizing on the electrostatic instabilities we have studied, but could also excite electromagnetic modes, particularly as the ideal MHD stability limit is approached.…”

Section: Discussionmentioning

confidence: 99%

“…We therefore devote the present section to introducing the different geometries used -starting with an axisymmetric equilibrium corresponding to the DIII-D tokamak, followed by the quasi-axisymmetric NCSX stellarator and ending with two more quasi-isodynamic configurations, W7-X and QIPC, an almost perfectly quasi-isodynamic stellarator (particularly at high plasma pressure) 3 . The main feature of interest is how well the stability criterion identified in part I of this publication, ω de ω * e < 0, is met in the respective configurations, since we then expect a stabilizing influence on the TEM.…”

Section: The Geometriesmentioning

confidence: 99%

“…Traditionally, stellarators suffered from large neoclassical transport, while in tokamaks the turbulent transport usually dominates. Optimized stellarator configurations, such as the National Compact Stellarator Experiment (NCSX) 1 and Wendelstein 7-X (W7-X) 2 , or more recently proposed geometries, such as the quasi-isodynamic configuration of Subbotin et al 3 , whose contours of constant magnetic field strength are poloidally closed and we therefore refer to as QIPC, are designed to have reduced neoclassical transport 4 . The question then arises whether this improvement will lead to reduced turbulent transport caused by microinstabilities such as the trapped-electron mode (TEM) or ion temperature gradient driven modes (ITGs).…”

Section: Introductionmentioning

confidence: 99%

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Collisionless microinstabilities in stellarators. II. Numerical simulations

2013

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Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-J geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with the National Compact Stellarator Experiment (NCSX) and the DIII-D tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, ion-temperature-gradient modes, trapped-electron modes and mixed-type instabilities are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilizing in the energy budget. These results suggest that imperfectly optimized stellarators can retain most of the stabilizing properties predicted for perfect maximum-J configurations.

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Section: Discussionmentioning

confidence: 99%

Section: The Geometriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Collisionless microinstabilities in stellarators. II. Numerical simulations

2013

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“…1 -3 as obtained by VMEC. Overall, it is close to a quasi-isodynamic configuration with poloidally closed contours of the field strength [5]. In more detail, the poloidal closure of the contours of the field strength is less perfect near the maximum of B on a magnetic surface, which, as in W7-X, occurs on the inner side of the torus.…”

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confidence: 73%

Improvement of collisionless particle confinement in a non-quasi-symmetric stellarator vacuum magnetic field

et al. 2013

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A non-quasisymmetric stellarator vacuum magnetic field with aspect ratio of about 11 is found in which collisionless particles are confined up to about 2/5 of the minor radius.In conventional stellarator vacuum fields collisionless particles are lost through a loss cone. Quasi-symmetric stellarators can confine collisionless particles well [1]. In quasi-isodynamic stellarator vacuum fields a reduced loss cone persisted [2]. Here, by improved computational optimization of collisionless particle confinement, a nonquasisymmetric configuration is found in which the loss cone is eliminated in the core of the confinement region.The optimization procedure used is essentially the same as in earlier efforts [2]. Additional ingredients here are a weighting procedure which strongly emphasizes early lost particles, an iterative increase of the radius where the particles are started, usage of up to 10 5 particles and a parallelized optimization procedure. The initial configuration was an interpolation between a low-β quasi-isodynamic configuration with poloidally closed contours of its field strength with very low bootstrap current [3] and the old case optimized for collisionless particle confinement [2]. Except for this latter property the optimization was unconstrained. It was terminated when about 0.4 of the minor radius was reached to assess its other properties so that modified goals can be formulated. The results are described below.In a device with the physical parameters of W7-X (volume ≈ 25m 3 , magnetic field ≈ 2.5 T) less than 1 per mil of 100keV protons started at about 0.4 of the minor radius are lost up to 0.1 s. Since this result was obtained in a zero -β VMEC equilibrium it is amenable to an independent test in a vacuum magnetic field given by a set of harmonic functions [4] satisfying the Neumann boundary condition at the VMEC boundary. The VMEC result was essentially verified by following α -particles in the 1 Corresponding author vacuum field scaled to fusion dimensions (volume 10 3 m 3 , magnetic field 5 T). From the 1000 particles started and followed up to 0.1 s, four particles were lost between 0.003 and 0.01 s.Views of the geometry of the configuration and its structure of the field strength is seen in Figs. 1 -3 as obtained by VMEC. Overall, it is close to a quasi-isodynamic configuration with poloidally closed contours of the field strength [5]. In more detail, the poloidal closure of the contours of the field strength is less perfect near the maximum of B on a magnetic surface, which, as in W7-X, occurs on the inner side of the torus. A particular feature is seen in the surfaces of the field strength: while these are convex (see Fig. 2) as seen from the minimum of B located in the triangular flux surface crosssection (as is in accordance with the fact that a true-minimum B on the magnetic axis is not found in toroidal vacuum fields) they become concave (see Fig. 3) near the maximum of B. This suggests a minimum-J (with J the second adiabatic invariant) situation near the minimum of B and a ...

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“…The further optimization of stellarators [29] has to include also simplified engineering solutions. In this respect, a first-of-a-kind device such as W7-X is not optimized.…”

Section: Discussionmentioning

confidence: 99%

From Wendelstein 7-X to a Stellarator Reactor

Wolf

Beidler

Burhenn

et al. 2010

Plasma and Fusion Research

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Wendelstein 7-X is a drift-optimized stellarator with improved thermal and fast ion confinement. Additional optimization criteria are a stiff equilibrium configuration and MHD stability up to a volume averaged β of 5 %. The main objectives are to demonstrate reactor-relevant plasma performance under steady-state conditions including power and particle exhaust with an island divertor. To that effect Wendelstein 7-X has superconducting coils with a maximum average magnetic field of 3 T and will be equipped with actively cooled plasma facing components for heat fluxes of up to 10 MW/m 2 . Besides fulfilling this research mission, the extrapolation from Wendelstein 7-X to a stellarator reactor is an important issue. The capability of such an extrapolation will depend also on the results from other stellarators, on the ITER results and here in particular the experience gained with α-particle heating and operating a nuclear device, and the advancement of first-principle theory required for the extrapolation.

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Integrated physics optimization of a quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength

Cited by 57 publications

References 11 publications

Collisionless microinstabilities in stellarators. II. Numerical simulations

Collisionless microinstabilities in stellarators. II. Numerical simulations

Improvement of collisionless particle confinement in a non-quasi-symmetric stellarator vacuum magnetic field

From Wendelstein 7-X to a Stellarator Reactor

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