On-surface potential and radial electric field variations in electron root stellarator plasmas

García-Regaña, J. M.; Estrada, T.; Calvo, I.; Velasco, J. L.; Alonso, Javier; Carralero, D.; Kleiber, R.; Landreman, Matt; Mollén, A.; Sánchez, E.; Slaby, C.; Team, Tj‐Ii; Team, W X

doi:10.1088/1361-6587/aad795

Cited by 22 publications

(33 citation statements)

References 49 publications

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“…Thus, while the effect of Φ 1 is usually small for the main ion or electron, it can be essential for highly charged impurities. While measuring such a small variation in electrostatic potential is still challenging in LHD, it is already technically feasible in the smaller device TJ-II and the potential variation has actually been detected in such experiments (Pedrosa et al 2015;García-Regaña et al 2018;Estrada et al 2019). Also, by several simulation studies, it has already been shown that Φ 1 can have substantial impact on neoclassical impurity transport (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Global calculation of neoclassical impurity transport including the variation of electrostatic potential

et al. 2020

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Recently, the validity range of the approximations commonly used in neoclassical calculation has been reconsidered. One of the primary motivations behind this trend is observation of an impurity hole in LHD (Large Helical Device), i.e. the formation of an extremely hollow density profile of an impurity ion species, such as carbon $\text{C}^{6+}$ , in the plasma core region where a negative radial electric field ( $E_{r}$ ) is expected to exist. Recent studies have shown that the variation of electrostatic potential on the flux surface, $\unicode[STIX]{x1D6F7}_{1}$ , has significant impact on neoclassical impurity transport. Nevertheless, the effect of $\unicode[STIX]{x1D6F7}_{1}$ has been studied with radially local codes and the necessity of global calculation has been suggested. Thus, we have extended a global neoclassical code, FORTEC-3D, to simulate impurity transport in an impurity hole plasma including $\unicode[STIX]{x1D6F7}_{1}$ globally. Independently of the $\unicode[STIX]{x1D6F7}_{1}$ effect, an electron root of the ambipolar condition for the impurity hole plasma has been found by global simulation. Hence, we have considered two different cases, each with a positive (global) and a negative (local) solution of the ambipolar condition, respectively. Our result provides another support that $\unicode[STIX]{x1D6F7}_{1}$ has non-negligible impact on impurity transport. However, for the ion-root case, the radial $\text{C}^{6+}$ flux is driven further inwardly by $\unicode[STIX]{x1D6F7}_{1}$ . For the electron-root case, on the other hand, the radial particle $\text{C}^{6+}$ flux is outwardly enhanced by $\unicode[STIX]{x1D6F7}_{1}$ . These results indicate that how $\unicode[STIX]{x1D6F7}_{1}$ affects the radial particle transport crucially depends on the profile of the ambipolar- $E_{r}$ , which is found to be susceptible to $\unicode[STIX]{x1D6F7}_{1}$ itself and the global effects.

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Section: Introductionmentioning

confidence: 99%

Global calculation of neoclassical impurity transport including the variation of electrostatic potential

et al. 2020

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“…Assessment of the accuracy of numerical evaluation of Φ 1 is also important for investigating its impact in real plasmas. In addition to the global simulation of impurity transport in LHD including Φ 1 , comparisons between numerical simulation results and available experimental data on Φ 1 profile, such as the radial electric field due to Φ 1 in the TJ-II [16], will be presented in our future publications.…”

Section: Resultsmentioning

confidence: 99%

“…This expression is used in several studies to compute Φ 1 (e.g., [10,11,15]). Some assumptions in the argument above may be questionable, and models based on more relaxed assumptions have also been investigated [12,16]. Yet, the primary purpose of this study is not to make an accurate computation of Φ 1 but to see if and how the global effects make a difference compared with local results.…”

Section: Evaluation Of φmentioning

confidence: 99%

Global Effects on the Variation of Ion Density and Electrostatic Potential on the Flux Surface in Helical Plasmas

Fujita

Satake

Kanno

et al. 2019

Plasma and Fusion Research

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Since the observation of impurity hole in LHD, which contradicts the prediction of the conventional neoclassical transport theory, several attempts have been made to explain the mechanism behind the phenomenon. Consideration of the impact of electrostatic potential variation within the flux surface, Φ 1 , is one of those attempts. However, all of the numerical studies that have investigated the effect of Φ 1 to date have been conducted with local simulation codes, and no global calculation has been performed yet. Here, a global neoclassical simulation code FORTEC-3D is applied to evaluate Φ 1 , including the global effects, for the first time. The global simulation result for a high-temperature low-density plasma, which corresponds to an impurity hole plasma, shows significant difference from the local simulation results in the Φ 1 profile. This indicates that consideration of the global effects is essential for quantitative evaluation of impurity neoclassical transport in an impurity hole plasma.

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“…The next-order terms of the drift-kinetic equation (10) in the ρ z * expansion give an equation for F z1 ,…”

Section: Impurity Drift-kinetic Equationmentioning

confidence: 99%

“…In [4], the calculation is given for the case in which impurities are collisional and the main ions have low collisionality. A considerable part of the recent theoretical effort (see [5,6,7,8,9,10,11]) has been related to the extension of neoclassical theory and, consequently, neoclassical codes, to include the effect of the component of the electric field that is tangent to magnetic surfaces in the calculation of radial impurity fluxes. The determination of the radial and tangential components of the electric field is one of the neoclassical mechanisms by which main ion dynamics affects impurity transport.…”

Section: Introductionmentioning

confidence: 99%

Impact of main ion pressure anisotropy on stellarator impurity transport

Calvo¹,

Parra²,

Velasco³

et al. 2019

Nucl. Fusion

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Main ions influence impurity dynamics through a variety of mechanisms; in particular, via impurity-ion collisions. To lowest order in an expansion in the main ion mass over the impurity mass, the impurity-ion collision operator only depends on the component of the main ion distribution that is odd in the parallel velocity. These lowest order terms give the parallel friction of the impurities with the main ions, which is typically assumed to be the main cause of collisional impurity transport. Next-order terms in the mass ratio expansion of the impurity-ion collision operator, proportional to the component of the main ion distribution that is even in the parallel velocity, are usually neglected. However, in stellarators, the even component of the main ion distribution can be very large. In this article, such next-order terms in the mass ratio expansion of the impurity-ion collision operator are retained, and analytical expressions for the neoclassical radial flux of trace impurities are calculated in the Pfirsch-Schlüter, plateau and 1/ν regimes. The new terms provide a drive for impurity transport that is physically very different from parallel friction: they are associated to anisotropy in the pressure of the main ions, which translates into impurity pressure anisotropy. It is argued that main ion pressure anisotropy must be taken into account for a correct description of impurity transport in certain realistic stellarator plasmas. Examples are given by numerically evaluating the analytical expressions for the impurity flux.

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On-surface potential and radial electric field variations in electron root stellarator plasmas

Cited by 22 publications

References 49 publications

Global calculation of neoclassical impurity transport including the variation of electrostatic potential

Global calculation of neoclassical impurity transport including the variation of electrostatic potential

Global Effects on the Variation of Ion Density and Electrostatic Potential on the Flux Surface in Helical Plasmas

Impact of main ion pressure anisotropy on stellarator impurity transport

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