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Register a new userThe importance of the classical channel in the impurity transport of optimized stellarators
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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-Schluter 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.
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Gyrokinetic simulations of ion temperature gradient mode and trapped electron mode driven impurity transport in a realistic tokamak geometry are presented and compared with results using simplified geometries. The gyrokinetic results, obtained with the GENE code in both linear and non-linear modes are compared with data and analysis for a dedicated impurity injection discharge at JET. The impact of several factors on heat and particle transport is discussed, lending special focus to tokamak geometry and rotational shear. To this end, results using s-alpha and concentric circular equilibria are compared with results with magnetic geometry from a JET experiment. To further approach experimental conditions, non-linear gyrokinetic simulations are performed with collisions and a carbon background included. The impurity peaking factors, computed by finding local density gradients corresponding to zero particle flux, are discussed. The impurity peaking factors are seen to be reduced by a factor of ~2 in realistic geometry compared with the simplified geometries, due to a reduction of the convective pinch. It is also seen that collisions reduce the peaking factor for low-Z impurities, while increasing it for high charge numbers, which is attributed to a shift in the transport spectra towards higher wavenumbers with the addition of collisions. With the addition of roto-diffusion, an overall reduction of the peaking factors is observed, but this decrease is not sufficient to explain the flat carbon profiles seen at JET.
High-Z impurities in magnetic confinement devices are prone to develop density variations on the flux-surface, which can significantly affect their transport. In this paper, we generalize earlier analytic stellarator calculations of the neoclassical radial impurity flux in the mixed-collisionality regime (collisional impurity and low-collisionality bulk ions) to include the effect of such flux-surface variations. We find that only in the homogeneous density case is the transport of highly collisional impurities (in the Pfirsch-Schl{u}ter regime) independent of the radial electric field. We study these effects for a Wendelstein 7-X (W7-X) vacuum field, with simple analytic models for the potential perturbation, under the assumption that the impurity density is given by a Boltzmann response to a perturbed potential. In the W7-X case studied, we find that larger amplitude potential perturbations cause the radial electric field to dominate the transport of the impurities. In addition, we find that classical impurity transport can be larger than the neoclassical transport in W7-X.
A good understanding of the confinement of energetic ions in non-axisymmetric magnetic fields is key for the design of reactors based on the stellarator concept. In this work, we develop a model that, based on the radially-local bounce-averaged drift-kinetic equation, classifies orbits and succeeds in predicting configuration-dependent aspects of the prompt losses of energetic ions in stellarators. Such a model could in turn be employed in the optimization stage of the design of new devices.
We investigate the linear theory of the ion-temperature-gradient (ITG) mode, with the goal of developing a general understanding that may be applied to stellarators. We highlight the Wendelstein 7X (W7-X) device. Simple fluid and kinetic models that follow closely from existing literature are reviewed and two new first-principle models are presented and compared with results from direct numerical simulation. One model investigates the effect of regions of strong localized shear, which are generic to stellarator equilibria. These shear spikes are found to have a potentially significant stabilizing affect on the mode; however, the effect is strongest at short wavelengths perpendicular to the magnetic field, and it is found to be significant only for the fastest growing modes in W7-X. A second model investigates the long-wavelength limit for the case of negligible global magnetic shear. The analytic calculation reveals that the effect of the curvature drive enters at second order in the drift frequency, confirming conventional wisdom that the ITG mode is slab-like at long wavelengths. Using flux tube simulations of a zero-shear W7-X configuration, we observe a close relationship to an axisymmetric configuration at a similar parameter point. It is concluded that scale lengths of the equilibrium gradients constitute a good parameter space to characterize the ITG mode. Thus, to optimize the magnetic geometry for ITG mode stability, it may be fruitful to focus on local parameters, such as the magnitude of bad curvature, connection length, and local shear at locations of bad curvature (where the ITG mode amplitude peaks).
In the present paper the transport of impurities driven by trapped electron (TE) mode turbulence is studied. Non-linear (NL) gyrokinetic simulations using the code GENE are compared with results from quasilinear (QL) gyrokinetic simulations and a computationally efficient fluid model. The main focus is on model comparisons for electron temperature gra- dient driven turbulence regarding the sign of the convective impurity velocity (pinch) and the impurity density gradient R/LnZ (peaking factor) for zero impurity flux. In particular, the scaling of the impurity peaking factors with impurity charge Z and with driving temper- ature gradient is investigated and compared with the results for Ion Temperature Gradient (ITG) driven turbulence. In addition, the impurity peaking is compared to the main ion peaking obtained by a self-consistent fluid calculation of the density gradients corresponding to zero particle fluxes. For the scaling of the peaking factor with impurity charge Z, a weak dependence is obtained from NL GENE and fluid simulations. The QL GENE results show a stronger dependence for low Z impurities and overestimates the peaking factor by up to a factor of two in this region. As in the case of ITG dominated turbulence, the peaking factors saturate as Z increases, at a level much below neoclassical predictions. However, the scaling with Z is weak or reversed as compared to the ITG case. The scaling of impurity peaking with the background temperature gradients is found to be weak in the NL GENE and fluid simulations. The QL results are also here found to significantly overestimate the peaking factor for low Z values. For the parameters considered, the background density gradient for zero particle flux is found to be slightly larger than the corresponding impurity zero flux gradient.
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