Validating a quasi-linear transport model versus nonlinear simulations

Abstract

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.

Quasilinear transport modelling at low magnetic shear

“…This choice of k-space spectrum is in agreement with nonlinear simulations and observations. 4,11 Fluxes computed by QuaLiKiz have been compared with GYRO non-linear simulations, and agreement for both heat and particle fluxes have been obtained in R=L T ; Z eff ; T i =T e , and collisionality scans around GA-standard case parameters. 4 Extensive GYRO non-linear simulations consisting of q-profile and magnetic shear scans have previously been carried out.…”

“…4,11 Fluxes computed by QuaLiKiz have been compared with GYRO non-linear simulations, and agreement for both heat and particle fluxes have been obtained in R=L T ; Z eff ; T i =T e , and collisionality scans around GA-standard case parameters. 4 Extensive GYRO non-linear simulations consisting of q-profile and magnetic shear scans have previously been carried out. 13 In Figure 1, the R=L T scan comparison is reproduced, and q-profile and magnetic shear scans around the GA standard case have been added.…”

“…4,10 The model for the saturated electrostatic potential-a critical ingredient in evaluating the turbulent fluxes-consists of a mixing length rule weighted by a k-space spectral function validated against both non-linear simulations and experimental observations. 4,11 The saturated potential frequency spectral shape is taken as a Lorentzian, with a width equal to the linear growth rate. This assumption has been shown to agree with non-linear simulations and experimental observations at transport relevant wavelengths.…”

“…Fluxes computed by QuaLiKiz have been validated by non-linear GYRO 2,3 simulations over a wide range of parameter space. 4 However, significant discrepancies between QuaLiKiz and non-linear simulations have been observed at low magnetic shear.…”

“…The primary motivation of this work is thus to understand the physics behind the low magnetic shear discrepancy between the QuaLiKiz model as formulated in Casati et al, 4 and non-linear simulations. To this end, the assumptions made in the QuaLiKiz model are systematically examined at low magnetic shear.…”