Quasilinear Transport Model Research Articles

Characterizing turbulent transport in ASDEX Upgrade L-mode plasmas via nonlinear gyrokinetic simulations

The nature and level of turbulent transport in the outer core of low-confinement (L-mode) discharges performed at the ASDEX Upgrade tokamak [Kallenbach et al., Nucl. Fusion 51, 094012 (2011)] are examined. Previously, it was found that for an L-mode discharge of the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] gyrokinetic simulations were unable to reproduce the experimental ion heat flux, underestimating it by almost an order of magnitude. In the present work, employing the GENE gyrokinetic turbulence code, an extensive nonlinear study is performed for L-mode discharges of ASDEX Upgrade in order to cross-check this observation. It is shown that no systematic underprediction can be found in these simulations—instead, discrepancies with respect to experimental transport levels are small enough to be resolved within the uncertainties of the experimental profiles. Moreover, it is shown that some turbulence properties resemble closely those of the underlying linear microinstabilities at least out to 90% of the minor radius, so that quasilinear transport models remain, in principle, applicable even for these parameters, provided that appropriate nonlinear saturation rules can be developed.

Quasilinear transport modelling at low magnetic shear

Accurate and computationally inexpensive transport models are vital for routine and robust predictions of tokamak turbulent transport. To this end, the QuaLiKiz [Bourdelle et al., Phys. Plasmas 14, 112501 (2007)] quasilinear gyrokinetic transport model has been recently developed. QuaLiKiz flux predictions have been validated by non-linear simulations over a wide range in parameter space. However, a discrepancy is found at low magnetic shear, where the quasilinear fluxes are significantly larger than the non-linear predictions. This discrepancy is found to stem from two distinct sources: the turbulence correlation length in the mixing length rule and an increase in the ratio between the quasilinear and non-linear transport weights, correlated with increased non-linear frequency broadening. Significantly closer agreement between the quasilinear and non-linear predictions is achieved through the development of an improved mixing length rule, whose assumptions are validated by non-linear simulations.

Validating a quasi-linear transport model versus nonlinear simulations

In order to gain reliable predictions on turbulent fluxes in tokamak plasmas, physics based transport models are required. Nonlinear gyrokinetic electromagnetic simulations for all species are still too costly in terms of computing time. On the other hand, interestingly, the quasi-linear approximation seems to retain the relevant physics for fairly reproducing both experimental results and nonlinear gyrokinetic simulations. Quasi-linear fluxes are made of two parts: (1) the quasi-linear response of the transported quantities and (2) the saturated fluctuating electrostatic potential. The first one is shown to follow well nonlinear numerical predictions; the second one is based on both nonlinear simulations and turbulence measurements. The resulting quasi-linear fluxes computed by QuaLiKiz (Bourdelle et al 2007 Phys. Plasmas 14 112501) are shown to agree with the nonlinear predictions when varying various dimensionless parameters, such as the temperature gradients, the ion to electron temperature ratio, the dimensionless collisionality, the effective charge and ranging from ion temperature gradient to trapped electron modes turbulence.

A new gyrokinetic quasilinear transport model applied to particle transport in tokamak plasmas

The scope of this paper is to present and benchmark the first version of a quasilinear calculation, QuaLiKiz, based on a fast linear gyrokinetic code, Kinezero [C. Bourdelle, X. Garbet, G. T. Hoang, J. Ongena, and R. V. Budny, Nucl. Fusion 42, 892 (2002)] accounting for all unstable modes and summing over a wave-number spectrum. The fluctuating electrostatic potential frequency and wave-number spectra are chosen based on turbulence measurements and nonlinear simulations results. A peculiar focus on particle transport is developed. The directions of compressibility and thermodiffusion convections of ions and electrons are analytically derived for passing and trapped particles in both ion and electron turbulence. Also, the charge and mass dependence of trace heavy impurity convection is analytically estimated. These results are compared with quasilinear simulations done by QuaLiKiz. Finally, the impact of accounting for all unstable modes and of summing over the wave-number spectrum is shown to reverse in some cases the direction of particle fluxes.

Transport modelling

Linear and quasi-linear transport models for core transport of a tokamak plasma are reviewed. The dependence of the modelled transport on the main plasma parameters is discussed. The comparison of the models with the experiment is reviewed both directly in terms of the predicted stored energy as well as indirectly discussing key physics ingredients of the models. To cite this article: A.G. Peeters et al., C. R. Physique 7 (2006).

Quasi-linear transport model for mirror machines

A quasi-linear model to describe the evolution of a mirror plasma is presented. It is shown that, as in the 2XIIB mirror experiment, a plasma stream sufficiently reduces rf turbulence so that a high density steady state mirror plasma can be sustained by a neutral beam. The scaling law for this plasma configuration is derived. The energy lifetime is found to be the Spitzer electron-ion drag time even when electron thermal conduction to the external plasma can be neglected.