A burning fusion plasma has a large inwards flux of fuel and outwards flux of ash. Existing impurity transport theories do not account for a steady-state environment of such large fluxes. In this paper, we extend classical transport theory to account for a background of such fluxes. In a mainly two-ion species magnetized plasma, with oppositely directed density gradients maintained by oppositely directed sources of the two species, trace impurity ions are shown to align with the larger mass ions. This unexpected behavior is derived analytically and simulated numerically using the MITNS (Multiple-Ion Transport Numerical Solver) code. The result suggests a potential advantage of edge-fueled p-B11 fusion in extracting high-Z impurities, and possible applications in plasma-based separation methods.
Impurity temperature screening is a favorable neoclassical phenomenon involving an outward radial flux of impurity ions from the core of fusion devices. Quasisymmetric magnetic fields are intrinsically ambipolar and give rise to temperature screening for low enough $η^{-1}\equiv d\ln n/d\ln T$. In contrast, neoclassical fluxes in generic stellarators will depend on the radial electric field, which is predicted to be inward for ion-root plasmas, potentially leading to impurity accumulation. Here we examine the impurity particle flux in a number of approximately quasisymmetric stellarator config…
An impurity hole observed in the Large Helical Device (LHD) is a hollow density profile of an impurity ion species formed in the core plasma where the negative (inward-pointing) ambipolar radial electric field ($E_r$) exists. Although local neoclassical models have predicted the sign of $E_r$ in impurity hole plasmas is negative for the entire minor radius, an experimental measurement of an impurity hole plasma has shown that the $E_r$ changes the sign from negative to positive along the minor radius. In the present work, we investigate neoclassical impurity transport in an impurity hole plasm…
Development and validation of a local neoclassical transport module in NLT with applications to EAST-relevant impurity transport and trapped-electron-mode stability
Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences（中国科学院合肥物质科学研究院等离子体物理研究所）；University of Science and Technology of China（中国科学技术大学）
The turbulence-induced quasi-linear particle flux of a highly-charged, collisional impurity species is calculated from the electrostatic gyrokinetic equation including collisions with the bulk ions and the impurities themselves. The equation is solved by an expansion in powers of the impurity charge number $Z$. In this formalism, the collision operator only affects the impurity flux through the dynamics of the impurities in the direction parallel to the magnetic field. At reactor-relevant collisionality, the parallel dynamics is dominated by the parallel electric field, and collisions have a m…
Avoiding impurity accumulation is a requirement for steady-state stellarator operation. The accumulation of impurities can be heavily affected by variations in their density on the flux-surface. Using recently derived semi-analytic expressions for the transport of a collisional impurity species with high-$Z$ and flux-surface density-variation in the presence of a low-collisionality bulk ion species, we numerically optimize the impurity density-variation on the flux-surface to minimize the radial peaking factor of the impurities. These optimized density-variations can reduce the core impurity d…
In a two-ion-species plasma with disparate ion masses, heavy ions tend to concentrate in the low-temperature region of collisionally magnetized plasma and in the high-temperature region of collisionally unmagnetized plasma, respectively. Moreover, collisional magnetization can be determined as the ratio of the light ion gyrofrequency to the collision frequency of light and heavy ion species, and the behavior of this effect in the intermediate regime of partially magnetized plasma is predominantly dependent on this Hall parameter. Multi-ion cross-field transport has been described before in the…
In toroidal magnetic confinement devices, such as tokamaks and stellarators, neoclassical transport is usually an order of magnitude larger than its classical counterpart. However, when a high-collisionality species is present in a stellarator optimized for low Pfirsch-Schlüter current, its classical transport can be comparable to the neoclassical transport. In this letter, we compare neoclassical and classical fluxes and transport coefficients calculated for Wendelstein 7-X (W7-X) and Large Helical Device (LHD) cases. In W7-X, we find that the classical transport of a collisional impurity is …
The accumulation of impurities in the core of magnetically confined plasmas, resulting from standard collisional transport mechanisms, is a known threat to their performance as fusion energy sources. Whilst the axisymmetric tokamak systems have been shown to benefit from the effect of temperature screening, that is an outward flux of impurities driven by the temperature gradient, impurity accumulation in stellarators was thought to be inevitable, driven robustly by the inward pointing electric field characteristic of hot fusion plasmas. We have shown in Helander et. al. (2017b) that such scree…
In tokamak transport barriers, the radial scale of profile variations can be comparable to a typical ion orbit width, which makes the coupling of the distribution function across flux surfaces important in the collisional dynamics. We use the radially global steady-state neoclassical δf code Perfect to calculate poloidal and toroidal flows, and radial fluxes, in the pedestal. In particular, we have studied the changes in these quantities as the plasma composition is changed from a deuterium bulk species with a helium impurity to a helium bulk with a deuterium impurity, under specific profile s…
A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ITG, TEM and ETG modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the non…
The multi-species plasma of natural or laboratory origin is often considered to host nonlinear ion-acoustic waves. We present calculations of ion fluxes induced by nonlinear ion-acoustic waves in a plasma consisting of multiple ion populations, electrons, and dust. The following plasma models are considered: an electron-ion plasma with cold ions, a bi-ion plasma with two types of warm positively charged ions, and a dusty bi-ion plasma. It is found that in the electron-ion plasma, the wave-induced ion flux is directed oppositely to the phase speed of the nonlinear ion-acoustic wave. In the bi-i…
The drift wave in the presence of impurity ions was investigated numerically in reversed field pinch (RFP) plasmas, using the gyrokinetic integral eigenmode equation. It was found that in RFP plasmas with hollow density profiles, an increase in $k_θρ_s$ increases the growth rate of the ion temperature gradient (ITG). Comparing the results of regular and hollow plasma density profile shows that the ITG mode under the hollow density profile is much harder to be excited. For the impurities' effects, when the impurities' density gradient is opposite to the primary ions, namely when $L_{ez}$ is neg…
We present a numerical study of collisional transport in a tokamak pedestal in the presence of non-trace impurities, using the radially global $δf$ neoclassical solver PERFECT [M. Landreman et al. 2014 Plasma Phys. Control. Fusion 56 045005]. It is known that in a tokamak core with non-trace impurities present the radial impurity flux opposes the bulk ion flux to provide an ambipolar particle transport, with the electron transport being negligibly small. However, in a sharp density pedestal with sub-sonic ion flows the electron transport can be comparable to the ion and impurity flows. Further…
Role of Shafranov shift, zonal structures on the behavior of TAEs, AAEs and microinstabilities in the presence of energetic particles
Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Max-Planck-Institut für Plasmaphysik（马克斯·普朗克等离子体物理研究所）；Université de Lorraine（洛林大学）；De Vinci Higher Education（德文奇高等教育）；University of Warwick（华威大学）
We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic var…
For a plasma with fixed total energy, number of particles, and momentum, the distribution function that maximizes entropy is a Boltzmann distribution. If, in addition, the rearrangement of charge is constrained, as happens on ion-ion collisional timescales for cross-field multiple-species transport, the maximum-entropy state is instead given by the classic impurity pinch relation. The maximum-entropy derivation, unlike previous approaches, does not rely on the details of the collision operator, only on the presence of certain conservation properties.
