Effects of magnetic drift tangential to magnetic surfaces on neoclassical transport in non-axisymmetric plasmas

Abstract. In general, the orbit-averaged radial magnetic drift of trapped particles in stellarators is non-zero due to the three-dimensional nature of the magnetic field. Stellarators in which the orbit-averaged radial magnetic drift vanishes are called omnigeneous, and they exhibit neoclassical transport levels comparable to those of axisymmetric tokamaks. However, the effect of deviations from omnigeneity cannot be neglected in practice, and it is more deleterious at small collisionalities. For sufficiently low collision frequencies (below the values that define the 1/ν regime), the components of the drifts tangential to the flux surface become relevant. This article focuses on the study of such collisionality regimes in stellarators close to omnigeneity when the gradient of the non-omnigeneous perturbation is small. First, it is proven that closeness to omnigeneity is required to actually preserve radial locality in the drift-kinetic equation for collisionalities below the 1/ν regime. Then, using the derived radially local equation, it is shown that neoclassical transport is determined by two layers located at different regions of phase space. One of the layers corresponds to the so-called √ ν regime and the other to the so-called superbanana-plateau regime. The importance of the superbanana-plateau layer for the calculation of the tangential electric field is emphasized, as well as the relevance of the latter for neoclassical transport in the collisionality regimes considered in this paper. In particular, the role of the tangential electric field is essential for the emergence of a new subregime of superbanana-plateau transport when the radial electric field is small. A formula for the ion energy flux that includes the √ ν regime and the superbanana-plateau regime is given. The energy flux scales with the square of the size of the deviation from omnigeneity. Finally, it is explained why below a certain collisionality value the formulation presented in this article ceases to be valid.

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“…In the quasineutrality equation defined by (21) and (22) the expansions (17) and (18) have not been employed yet. Using them, we obtain…”

Section: Low-collisionality Drift-kinetic Equation In Stellarators CLmentioning

confidence: 99%

“…the components of the drifts tangential to the flux surface matter [1,15,16,17]. In this paper we study stellarators close to omnigeneity in the collisionality regime (4), relevant for a stellarator reactor [18].…”

Section: Introductionmentioning

confidence: 99%

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity

Calvo¹,

Parra

Velasco³

et al. 2017

Plasma Phys. Control. Fusion

205

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“…1415 The recent studies indicate the contribution of the magnetic tangential drift 161718 in the evaluation of radial neoclassical transport when the E × B drift velocity is slower than the magnetic drift. Matsuoka 16 has devised a way to include the tangential magnetic drift in the local drift-kinetic equation solver. There are also some global neoclassical codes which treat the full 3dimensional guiding-center motion including both the radial and tangential magnetic drift term.…”

Section: Introductionmentioning

confidence: 99%

Benchmark of the local drift-kinetic models for neoclassical transport simulation in helical plasmas

et al. 2017

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The benchmarks of the neoclassical transport codes based on the several local drift-kinetic models are reported here. Here, the drift-kinetic models are ZOW, ZMD, DKES-like, and global, as classified in [Matsuoka et al., Physics of Plasmas 22, 072511 (2015)]. The magnetic geometries of HSX, LHD, and W7-X are employed in the benchmarks. It is found that the assumption of E ×B incompressibility causes discrepancy of neoclassical radial flux and parallel flow among the models when E × B is sufficiently large compared to the magnetic drift velocities. For example, M p ≤ 0.4 where M p is the poloidal Mach number. On the other hand, when E × B and the magnetic drift velocities are comparable, the tangential magnetic drift, which is included in both the global and ZOW models, fills the role of suppressing unphysical peaking of neoclassical radial-fluxes found in the other local models at E r ≃ 0. In low collisionality plasmas, in particular, the tangential drift effect works well to suppress such unphysical behavior of the radial transport caused in the simulations. It is demonstrated that the ZOW model has the advantage of mitigating the unphysical behavior in the several magnetic geometries, and that it also implements evaluation of bootstrap current in LHD with the low computation cost compared to the global model.

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“…The bootstrap current from the ZOW model with finite U ,i agrees with PENTA. In the previous studies [4,7] it is found that neglecting the tangential magnetic drift in DKES and PENTA causes the overestimation of the ion radial particles flux when E r is small. This results in the difference in the ambipolar-E r values as shown in Fig.…”

mentioning

confidence: 99%

“…(3) by analytic formula. In order to carry out a more direct investigation on the impact of the parallel friction on the bootstrap current calculations, this paper performs the benchmark among the ZOW model [4], DKES [5], and PENTA [6], which are all based on local neoclassical models.…”

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confidence: 99%

Benchmark of the Bootstrap Current Simulation in Helical Plasmas

Huang

Satake

Kanno

et al. 2017

Plasma and Fusion Research

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The importance of the parallel momentum balance on the bootstrap current evaluation in non-axisymmetric systems is demonstrated by the benchmarks among the local drift-kinetic equation solvers, i.e., the Zero-Orbitwidth (ZOW) model, DKES, and PENTA. The ZOW model is extended to include the ion parallel mean flow effect on the electron-ion parallel friction. Compared to DKES code in which only the pitch-angle-scattering term is included in the collision operator, PENTA code employs the Sugama-Nishimura method to correct the momentum balance. The ZOW model and PENTA codes, both of which conserve the parallel momentum in like-species collisoins and include the electron-ion parallel frictions, agree each other well on the calculations of the bootstrap current. The DKES results without the parallel momentum conservation deviates significantly from those from the ZOW model and PENTA. This work verifies the reliability of the bootstrap current calculation with the ZOW model and PENTA for the helical plasmas. The study of the bootstrap current is necessary to reproduce accurately the MHD equilibrium for high-beta plasmas. For the axisymmetric magnetic geometry, reliable analytic formulas of bootstrap current is available [1]. For the non-axisymmetric system, one needs to rely on numerical methods to evaluate the bootstrap current, which is complicatedly dependent on the magnetic geometry, the collision frequency, and the radial electric field. The past studies [2] presented the benchmark between the Monte-Carlo global model VENUS+δ f and the local semi-analytical solution SPBSC [3] in LHD. The bootstrap current between the VENUS+δ f and the SPBSC codes shows a systematic difference. Although the difference may be caused in part by the finite-orbit-width effect, a missing discussion in that paper is about the treatment of collision term. The VENUS+δ f code did not treat the friction force between electrons and ions, while SPBSC solved the balance between parallel viscosity and friction force as shown in later in Eq. (3) by analytic formula. In order to carry out a more direct investigation on the impact of the parallel friction on the bootstrap current calculations, this paper performs the benchmark among the ZOW model [4], DKES [5], and PENTA [6], which are all based on local neoclassical models.The ZOW model [7] solves the radially-local driftkinetic equation by the δ f Monte-Carlo method, and the parallel friction F is treated as follows. For the likeauthor's e-mail: huang.botsz@nifs.ac.jp species collisions, the linearized collision operators are employed and this satisfies the parallel momentum balance, i.e., F ,ee = F ,ii = 0. For ion, the ion-electron friction F ,ie is neglected because of the large mass ratio, m e /m i 1. For electron, in the previous work, the electron-ion collision was only approximated as the pitchangle scattering operator with the stationary background Maxwellian ion distribution, i.e., C ei L ei . In the present work, not only the pitch-angle scattering but also the ion parallel mean flow U ...

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Effects of magnetic drift tangential to magnetic surfaces on neoclassical transport in non-axisymmetric plasmas

Cited by 27 publications

References 31 publications

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity

The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity

Benchmark of the local drift-kinetic models for neoclassical transport simulation in helical plasmas

Benchmark of the Bootstrap Current Simulation in Helical Plasmas

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