Sara Moradi

Effect of poloidal asymmetry on the impurity density profile in tokamak plasmas

The effect of poloidal asymmetry of impurities on impurity transport driven by electrostatic turbulence in tokamak plasmas is analyzed. It is found that if the density of the impurity ions is poloidally asymmetric then the zero-flux impurity density gradient is significantly reduced and even a sign change in the impurity flux may occur if the asymmetry is sufficiently large. This effect is most effective in low shear plasmas with the impurity density peaking on the inboard side and may be a contributing factor to the observed outward convection of impurities in the presence of radio frequency heating.

Effect of poloidal asymmetries on impurity peaking in tokamaks

Poloidal impurity asymmetries are frequently observed in tokamaks. In this paper, the effect of poloidal asymmetry on electrostatic turbulent transport is studied, including the effect of the E×B drift. Collisions are modeled by a Lorentz operator, and the gyrokinetic equation is solved with a variational approach. The impurity transport is shown to be sensitive to the magnetic shear and changes sign for s≳0.5 in the presence of inboard accumulation. The zero-flux impurity density gradient (peaking factor) is shown to be rather insensitive to collisions in both ion temperature gradient and trapped electron mode driven cases. Our results suggest that the asymmetry (both the location of its maximum and its strength) and the magnetic shear are the two most important parameters that affect the impurity peaking.

A possible mechanism responsible for generating impurity outward flow under radio frequency heating

The effect of poloidal asymmetry of impurities on impurity transport driven by electrostatic turbulence in tokamak plasmas is analyzed. It is found that in the presence of in–out asymmetric impurity populations the zero-flux impurity density gradient (the so-called peaking factor) is significantly reduced. A sign change in the impurity flux may occur if the asymmetry is sufficiently large. This may be a contributing reason for the observed outward convection of impurities in the presence of radio frequency heating. This paper extends a previous work (Fulop and Moradi 2011 Phys. Plasmas 18 030703), by including the effect of ion parallel compressibility on the peaking factor, which is found to have a significant contribution in the presence of poloidal asymmetry. It is shown here that in the ion temperature gradient mode dominated plasmas the presence of an in–out poloidal asymmetry can lead to a negative impurity peaking factor, and it becomes more negative in regions with larger ion temperature gradients. In the trapped electron mode dominated plasmas an in–out poloidal asymmetry results in a strong reduction of the peaking factor; however, it remains positive for typical experimental parameters. Furthermore, it is shown that an up–down asymmetry reduces the peaking factor while an out–in asymmetry increases it.

Microtearing modes in spherical and conventional tokamaks

The onset and characteristics of microtearing modes (MTM) in the core of spherical (NSTX) and conventional tokamaks (ASDEX Upgrade and JET) are studied through local linear gyrokinetic simulations with GYRO (Candy and Belli 2011 General Atomics Report GA-A26818). For experimentally relevant core plasma parameters in the NSTX and ASDEX Upgrade tokamaks, in agreement with previous works, we find MTMs as the dominant linear instability. Also, for JET-like core parameters considered in our study an MTM is found as the most unstable mode. In all of these plasmas, finite collisionality is needed for MTMs to become unstable and the electron temperature gradient is found to be the fundamental drive. However, a significant difference is observed in the dependence of the linear growth rate of MTMs on electron temperature gradient. While it varies weakly and non-monotonically in JET and ASDEX Upgrade plasmas, in NSTX it increases with the electron temperature gradient.

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.

Impurity transport due to electromagnetic drift wave turbulence

Finite β effects on impurity transport are studied through local linear gyrokinetic simulations with GYRO [J. Candy and E. Belli, General Atomics Report No. GA-A26818, 2011]; in particular, we investigate the parametric dependences of the impurity peaking factor (zero-flux density gradient) and the onset of the kinetic ballooning modes (KBMs). We find that electromagnetic effects even at low β can have significant impact on the impurity transport. The KBM instability threshold depends on the plasma parameters, particularly strongly on plasma shape. We have shown that magnetic geometry significantly influences the results, and the commonly used s-α model overestimates the KBM growth rates and ITG stabilization at high β. In the β range, where the KBM is the dominant instability the impurity peaking factor is strongly reduced, with very little dependence on β and the impurity charge.

Modelling of JET hybrid scenarios with GLF23 transport model: E???B shear stabilization of anomalous transport

The E???B shear stabilization of anomalous transport in JET hybrid discharges is studied via self-consistent predictive modelling of electron and ion temperature, ion density and toroidal rotation velocity performed with the GLF23 model. The E???B shear stabilization factor (parameter ?E in the GLF23 model) is adjusted to predict accurately the four simulated quantities under different experimental conditions, and the uncertainty in ?E determined by 15% deviation between simulated and measured quantities is estimated. A correlation of ?E with toroidal rotation velocity and E???B shearing rate is found in the low density plasmas, suggesting that the turbulence quench rule may be more complicated than assumed in the GLF23 model with constant ?E. For the selected discharges the best predictive accuracy is obtained by using weak/no E???B shear stabilization (i.e. ?E???0) at low toroidal angular frequency (?? ?100?krad?s?1). Interestingly, a weak E???B shear stabilization of anomalous transport is found in the medium density strongly rotating discharge. An importance of linear ?e stabilization in this discharge is estimated and compared to the low density discharge with equally high ?e. The toroidal rotation velocity is well predicted here by assuming that the momentum diffusion coefficient is a fraction of thermal ion diffusivity. Taking into account the ?E and Prandtl number with their uncertainties determined in the modelling of JET hybrid discharges, the performance of ITER hybrid scenario with optimized heat mix (33?MW of NBI and 20?MW of ECCD) is estimated showing the importance of toroidal rotation for achieving Q?>?5.

A fractional Fokker-Planck model for anomalous diffusion

In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Levy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.

A theory of non-local linear drift wave transport

Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated through a Fokker-Planck equation with fractional velocity derivatives. A dispersion relation for density gradient driven linear drift modes is derived including the effects of the fractional velocity derivative in the Fokker-Planck equation. It is found that a small deviation (a few percent) from the Maxwellian distribution function alters the dispersion relation such that the growth rates are substantially increased and thereby may cause enhanced levels of transport.

Importance of collisions with the main plasma components for impurity anomalous transport

The problem of impurity transport in fusion plasmas is of extraordinary importance and has been intensively studied for a long time. Nevertheless the experimentally found behaviour of impurity transport characteristics, such as diffusivity and pinch-velocity and, in particular, their dependence on the impurity ion charge, Z, has not been completely understood yet. In this paper the model for the impurity anomalous transport is developed further by taking into account the effects of impurity ion collisions with the main plasma components which become more and more important with increasing impurity charge. In linearized transport equations these effects are included as friction, thermal forces and collision energy exchange, affecting the perturbations of impurity ion parallel velocity and temperature, correspondingly. New terms can provide significant Z-dependence of the impurity anomalous convection and the density peaking factor. A numerical assessment is done for plasma parameters typical in the tokamak JET, with anomalous transport due to the ion temperature gradient/trapped electron unstable modes.