Gyrokinetic global electrostatic ion-temperature-gradient modes in finite β equilibria of Wendelstein 7-X

Kornilov, V.; Kleiber, R.; Hatzky, R.

doi:10.1088/0029-5515/45/4/003

Cited by 21 publications

(27 citation statements)

References 18 publications

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“…As advanced in Section 1, in a stellarator the terms proportional to E r do not cancel out on the right side of (25) in general. It can be checked that (25) reduces to the expression for the radial impurity flux given in [17] when ϕ 1 ≡ 0, and that in that case the right side of (25) does not depend on E r . This can be easily seen by noting that, for ϕ 1 ≡ 0, we have U 1 = u and U 2 ≡ 0, and recalling that the function s appearing in [17] is negligible compared to u when 1.…”

Section: Derivation Of the Expression For The Neoclassical Radial Impmentioning

confidence: 99%

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Stellarator impurity flux driven by electric fields tangent to magnetic surfaces

Calvo¹,

Parra

Velasco³

et al. 2018

Nucl. Fusion

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The control of impurity accumulation is one of the main challenges for future stellarator fusion reactors. The standard argument to explain this accumulation relies on the, in principle, large inward pinch in the neoclassical impurity flux caused by the typically negative radial electric field in stellarators. This simplified interpretation was proven to be flawed by Helander et al. [Phys. Rev. Lett. 118, 155002 (2017)], who showed that in a relevant regime (low-collisionality main ions and collisional impurities) the radial electric field does not drive impurity transport. In that reference, the effect of the component of the electric field that is tangent to the magnetic surface was not included. In this letter, an analytical calculation of the neoclassical radial impurity flux incorporating such effect is given, showing that it can be very strong for highly charged impurities and that, once it is taken into account, the dependence of the impurity flux on the radial electric field reappears. Realistic examples are provided in which the inclusion of the tangential electric field leads to impurity expulsion.

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Section: Derivation Of the Expression For The Neoclassical Radial Impmentioning

confidence: 99%

“…classical transport Figure 1. Neoclassical impurity flux given by (25) as a function of E r for the plasma described in the text and for η = 0. We show pairs of curves, without ϕ 1 (squares) and with ϕ 1 (circles), for three charge states of tungsten, Z z = 24, Z z = 34 and Z z = 44.…”

Section: Derivation Of the Expression For The Neoclassical Radial Impmentioning

confidence: 99%

Stellarator impurity flux driven by electric fields tangent to magnetic surfaces

Calvo¹,

Parra

Velasco³

et al. 2018

Nucl. Fusion

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“…The calculations of the radial fluxes for the impurities and Φ 1 has been carried out using the Monte Carlo f 1 particle in cell (PIC) code EUTERPE [10]. The current version in the gyro-kinetic modality is electro-magnetic, non-linear and considers the full surface and radial domain.…”

Section: The Code Euterpe and The Calculation Of φmentioning

confidence: 99%

Electrostatic potential variation on the flux surface and its impact on impurity transport

et al. 2017

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The particle transport of impurities in magnetically confined plasmas under some conditions does not find, neither quantitatively nor qualitatively, a satisfactory theory-based explanation. This compromise the successful realization of thermo-nuclear fusion for energy production since its accumulation is known to be one of the causes that leads to the plasma breakdown. In standard reactor-relevant conditions this accumulation is in most stellarators intrinsic to the lack of toroidal symmetry, that leads to the neoclassical electric field to point radially inwards. This statement, that the standard theory allows to formulate, has been contradicted by some experiments that showed weaker or no accumulation under such conditions [1,2]. The charge state of the impurities makes its transport more sensitive to the electric fields. Thus, the short length scale turbulent electrostatic potential or its long wavelength variation on the flux surface Φ 1 -that the standard neoclassical approach usually neglects -might possibly shed some light on the experimental findings. In the present work the focus is put on the second of the two, and investigate its influence of the radial transport of C 6+ . We show that in LHD it is strongly modified by Φ 1 , both resulting in mitigated/enhanced accumulation at internal/external radial positions; for Wendelstein 7-X, on the contrary, Φ 1 is expected to be considerably smaller and the transport of C 6+ not affected up to an appreciable extent; and in TJ-II the potential shows a moderate impact despite of the large amplitude of Φ 1 for the parameters considered.

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“…The Fusion Theory unit from CIEMAT collaborates with the IPP and the Barcelona Supercomputing Center (BSC) for the development and exploitation of this code. The code solves the Vlasov equation in connection with the equation of motion for the particles and the quasineutrality equation on a real space grid [1,2,3].The code provided good results both in linear and nonlinear simulations of Ion Temperature Gradient (ITG) instabilities carried out in screw-pinch geometry [4]. In those simulations, especially for the nonlinear ones, it became clear that the amount of computational resources that a global threedimensional PIC code requires for typical simulations is huge, and it is of crucial importance that it can run efficiently on multi-processor architectures.…”

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Improvements of the particle-in-cell code EUTERPE for petascaling machines

Sáez

Soba

Sánchez³

et al. 2011

Computer Physics Communications

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EUTERPE is a Lagrangian or particle-in-cell (PIC) gyrokinetic code for the simulation of fusion plasma instabilities. The aim of this code is to address global linear and nonlinear simulations of fusion plasmas in threedimensional geometries, in particular in stellarators. EUTERPE, like other gyrokinetic codes, is at the forefront of plasma simulations and requires a huge amount of computational resources. It has been developed at CRPP and IPP as a parallel code, using Message Passing Interface (MPI), and has been adapted to different computing platforms. The Fusion Theory unit from CIEMAT collaborates with the IPP and the Barcelona Supercomputing Center (BSC) for the development and exploitation of this code. The code solves the Vlasov equation in connection with the equation of motion for the particles and the quasineutrality equation on a real space grid [1,2,3].The code provided good results both in linear and nonlinear simulations of Ion Temperature Gradient (ITG) instabilities carried out in screw-pinch geometry [4]. In those simulations, especially for the nonlinear ones, it became clear that the amount of computational resources that a global threedimensional PIC code requires for typical simulations is huge, and it is of crucial importance that it can run efficiently on multi-processor architectures. Previously, the code had been heavily optimized and its scaling had 1

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Gyrokinetic global electrostatic ion-temperature-gradient modes in finite β equilibria of Wendelstein 7-X

Cited by 21 publications

References 18 publications

Stellarator impurity flux driven by electric fields tangent to magnetic surfaces

Stellarator impurity flux driven by electric fields tangent to magnetic surfaces

Electrostatic potential variation on the flux surface and its impact on impurity transport

Improvements of the particle-in-cell code EUTERPE for petascaling machines

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