Global effects on neoclassical transport in the pedestal with impurities

We present a numerical study of collisional transport in a tokamak pedestal in the presence of non-trace impurities, using the radially global $\delta f$ 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. Furthermore, the neoclassical particle transport is not intrinsically ambipolar, and the non-ambipolarity of the fluxes extends outside the pedestal region by the radial coupling of the perturbations. The neoclassical momentum transport, which is finite in the presence of ion orbit-width scale profile variations, is significantly enhanced when impurities are present in non-trace quantities, even if the total parallel mass flow is dominated by the bulk ions

Consistent multiphase-field theory for interface driven multidomain dynamics

We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We first analyze previous multiphase-field theories, and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a new way of constructing the free energy surface, and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism; reduces (or extends) naturally to lower (or higher) number of fields on the level of both the free energy functional and the dynamic equations; enables the use of arbitrary pairwise equilibrium interfacial properties; penalizes multiple junctions increasingly with the number of phases; ensures non-negative entropy production, and the convergence of the dynamic solutions to the equilibrium solutions; and avoids the appearance of spurious phases on binary interfaces. The new approach is tested for multi-component phase separation and grain coarsening

Turbulent transport of impurities and their effect on energy confinement

By presenting linear and nonlinear gyrokinetic studies, based on a balanced neutral beam injection deuterium discharge from the DIII-D tokamak, we demonstrate that impurities alter the scaling of the transport on the charge and mass of the main species, and even more importantly, they can dramatically change the energy transport even in relatively small quantities. A poloidally varying equilibrium electrostatic potential can lead to a strong reduction or sign change of the impurity peaking factor due to the combined effect of the in-out impurity density asymmetry and the EXB drift of impurities. We present an approximate expression for the impurity peaking factor and demonstrate that impurity peaking is not significantly affected by impurity self-collisions.Comment: Accepted for publication in Plasma Physics and Controlled Fusio

Impurity transport in trapped electron mode driven turbulence

Trapped electron mode turbulence is studied by gyrokinetic simulations with the GYRO code and an analytical model including the effect of a poloidally varying electrostatic potential. Its impact on radial transport of high-Z trace impurities close to the core is thoroughly investigated and the dependence of the zero-flux impurity density gradient (peaking factor) on local plasma parameters is presented. Parameters such as ion-to-electron temperature ratio, electron temperature gradient and main species density gradient mainly affect the impurity peaking through their impact on mode characteristics. The poloidal asymmetry, the safety factor and magnetic shear have the strongest effect on impurity peaking, and it is shown that under certain scenarios where trapped electron modes are dominant, core accumulation of high-Z impurities can be avoided. We demonstrate that accounting for the momentum conservation property of the impurity-impurity collision operator can be important for an accurate evaluation of the impurity peaking factor.Comment: 30 pages, 10 figure

Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model

The Euler-Lagrange equation of the phase-field crystal (PFC) model has been solved under appropriate boundary conditions to obtain the equilibrium free energy of the body centered cubic crystal-liquid interface for 18 orientations at various reduced temperatures in the range $\epsilon\in\left[0,0.5\right]$. While the maximum free energy corresponds to the $\left\{ 100\right\}$ orientation for all $\epsilon$ values, the minimum is realized by the $\left\{ 111\right\}$ direction for small $\epsilon\,(<0.13)$, and by the $\left\{ 211\right\}$ orientation for higher $\epsilon$. The predicted dependence on the reduced temperature is consistent with the respective mean field critical exponent. The results are fitted with an eight-term Kubic harmonic series, and are used to create stereographic plots displaying the anisotropy of the interface free energy. We have also derived the corresponding Wulff shapes that vary with increasing $\epsilon$ from sphere to a polyhedral form that differs from the rhombo-dodecahedron obtained previously by growing a bcc seed until reaching equilibrium with the remaining liquid

Edge momentum transport by neutrals: an interpretive numerical framework

Due to their high cross-field mobility, neutrals can contribute to momentum transport even at the low relative densities found inside the separatrix and they can generate intrinsic rotation. We use a charge-exchange dominated solution to the neutral kinetic equation, coupled to neoclassical ions, to evaluate the momentum transport due to neutrals. Numerical solutions to the drift-kinetic equation allow us to cover the full range of collisionality, including the intermediate levels typical of the tokamak edge. In the edge there are several processes likely to contribute to momentum transport in addition to neutrals. Therefore, we present here an interpretive framework that can evaluate the momentum transport through neutrals based on radial plasma profiles. We demonstrate its application by analysing the neutral angular momentum flux for an L-mode discharge in the ASDEX Upgrade tokamak. The magnitudes of the angular momentum fluxes we find here due to neutrals of 0.6 – 2 Nm are comparable to the net torque on the plasma from neutral beam injection, indicating the importance of neutrals for rotation in the edge.Vetenskapsrådet and Marie Sklodowska Curie Actions, Cofund, Project INCA 60039

The importance of the classical channel in the impurity transport of optimized stellarators

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-Schl\"uter 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 comparable to the neoclassical transport for all radii, while it is negligible in the LHD cases, except in the vicinity of radii where the neoclassical transport changes sign. In the LHD case, electrostatic potential variations on the flux-surface significantly enhance the neoclassical impurity transport, while the classical transport is largely insensitive to this effect in the cases studied.Comment: 10 pages, 2 figure