István Pusztai

Neoclassical plateau regime transport in a tokamak pedestal

In tokamak pedestals with subsonic flows the radial scale of plasma profiles can be comparable to the ion poloidal Larmor radius, thereby making the radial electrostatic field so strong that the E × B drift has to be retained in the ion kinetic equation in the same order as the parallel streaming. The modifications of neoclassical plateau regime transport—such as the ion heat flux and the poloidal ion and impurity flows—are evaluated in the presence of a strong radial electric field. The altered poloidal ion flow can lead to a significant increase in the bootstrap current in the pedestal where the spatial profile variation is strong because of the enhanced coefficient of the ion temperature gradient term near the electric field minimum. Unlike the banana regime, orbit squeezing does not affect the plateau regime results.

Poloidal asymmetries due to ion cyclotron resonance heating

The poloidal density asymmetry of impurity ions in ion cyclotron resonance heated (ICRH) discharges is calculated. The link between the asymmetry strength and ICRH and plasma parameters is quantified. The main parameter governing the asymmetry strength is identified to be the minority ion temperature anisotropy. Through numerical simulations with the full-wave TORIC code coupled to the Fokker–Planck quasilinear solver SSFPQL, the dependence of the anisotropy on various parameters, such as ICRH power, background density and temperature, minority and impurity concentration and toroidal wavenumber has been investigated. An approximate expression for the poloidal asymmetry of impurities as a function of plasma parameters, resonance location and ICRH power is given. A quantification of the link of the impurity asymmetry and ICRH heating is valuable not only for understanding the changes in the cross-field transport but also for the possibilities to use the asymmetry measurements as diagnostics.

Isotope mass and charge effects in tokamak plasmas

The effect of primary ion species of differing charge and mass - specifically, deuterium, hydrogen, and helium - on instabilities and transport is studied in DIII-D plasmas through gyrokinetic simulations with GYRO [J. Candy and E. Belli, General Atomics Technical Report No. GA-A26818, 2010]. In linear simulations under imposed similarity of the profiles, there is an isomorphism between the linear growth rates of hydrogen isotopes, but the growth rates are higher for Z > 1 main ions due to the appearance of the charge in the Poisson equation. On ion scales the most significant effect of the different electron-to-ion mass ratio appears through collisions stabilizing trapped electron modes. In nonlinear simulations, significant favorable deviations from pure gyro-Bohm scaling are found due to electron-to-ion mass ratio effects and collisions. The presence of any non-trace impurity species cannot be neglected in a comprehensive simulation of the transport; including carbon impurity in the simulations caused a dramatic reduction of energy fluxes. The transport in the analyzed deuterium and helium discharges could be well reproduced in gyrokinetic and gyrofluid simulations while the significant hydrogen discrepancy is the subject of ongoing investigation.

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 driven by ion temperature gradient turbulence in tokamak plasmas

Impurity transport driven by electrostatic turbulence is analyzed in weakly collisional tokamak plasmas using a semianalytical model based on a boundary layer solution of the gyrokinetic equation. Analytical expressions for the perturbed density responses are derived and used to determine the stability boundaries and the quasilinear particle fluxes. For moderate impurity charge number Z, the stability boundaries are very weakly affected by the increasing impurity charge for constant effective charge, while for lower impurity charge the influence of impurities is larger, if the amount of impurities is not too small. Scalings of the mode frequencies and quasilinear fluxes with charge number, effective charge, impurity density scale length, and collisionality are determined and compared to quasilinear gyrokinetic simulations with GYRO resulting in very good agreement. Collisions do not affect the mode frequencies, growth rates, and impurity fluxes significantly. The eigenfrequencies and growth rates depend only weakly on Z and Zeff but they are sensitive to the impurity density gradient scale length. An analytical approximate expression of the zero-flux impurity density gradient is derived and used to discuss its parametric dependencies.

Three-dimensional modeling of beam emission spectroscopy measurements in fusion plasmas

One of the main diagnostic tools for measuring electron density profiles and the characteristics of long wavelength turbulent wave structures in fusion plasmas is beam emission spectroscopy (BES). The increasing number of BES systems necessitated an accurate and comprehensive simulation of BES diagnostics, which in turn motivated the development of the Rate Equations for Neutral Alkali-beam TEchnique (RENATE) simulation code that is the topic of this paper. RENATE is a modular, fully three-dimensional code incorporating all key features of BES systems from the atomic physics to the observation, including an advanced modeling of the optics. Thus RENATE can be used both in the interpretation of measured signals and the development of new BES systems. The most important components of the code have been successfully benchmarked against other simulation codes. The primary results have been validated against experimental data from the KSTAR tokamak.

Numerical characterization of bump formation in the runaway electron tail

Runaway electrons are generated in a magnetized plasma when the parallel electric field exceeds a critical value. For such electrons with energies typically reaching tens of MeV, the Abraham–Lorentz–Dirac (ALD) radiation force, in reaction to the synchrotron emission, is significant and can be the dominant process limiting electron acceleration. The effect of the ALD force on runaway electron dynamics in a homogeneous plasma is investigated using the relativistic finite-difference Fokker–Planck codes LUKE (Decker and Peysson 2004 Report EUR-CEA-FC-1736, Euratom-CEA), and CODE (Landreman et al 2014 Comput. Phys. Commun. 185 847). The time evolution of the distribution function is analyzed as a function of the relevant parameters: parallel electric field, background magnetic field, and effective charge. Under the action of the ALD force, we find that runaway electrons are subject to an energy limit, and that the electron distribution evolves towards a steady-state. In addition, a bump is formed in the tail of the electron distribution function if the electric field is sufficiently strong. The mechanisms leading to the bump formation and energy limit involve both the parallel and perpendicular momentum dynamics; they are described in detail. An estimate for the bump location in momentum space is derived. We observe that the energy of runaway electrons in the bump increases with the electric field amplitude, while the population increases with the bulk electron temperature. The presence of the bump divides the electron distribution into a runaway beam and a bulk population. This mechanism may give rise to beam-plasma types of instabilities that could, in turn, pump energy from runaway electrons and alter their confinement.

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 E × B 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.