A new model for electron temperature gradient (ETG) modes is developed as a component of the Multi-Mode anomalous transport module [T. Rafiq \textit{et al.,} Phys Plasmas \textbf{20}, 032506 (2013)] to predict a time dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, $\beta$ and gradient of $\beta$ $(\betap)$, collisionality, safety factor, and toroidicity, where $\beta$ is the ratio of plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.
Sharma, A. Y.; Cole, M. D. J.; Görler, T.; Chen, Y.; Hatch, D. R.; Guttenfelder, W.; Hager, R.; Sturdevant, B. J.; Ku, S.; Chang, C. S.
Abstract:
Plasma shaping may have a stronger effect on global turbulence in tight-aspect-ratio tokamaks than in conventional-aspect-ratio tokamaks due to the higher toroidicity and more acute poloidal asymmetry in the magnetic field. In addition, previous local gyrokinetic studies have shown that it is necessary to include parallel magnetic field perturbations in order to accurately compute growth rates of electromagnetic modes in tight-aspect-ratio tokamaks. In this work, the effects of elongation and triangularity on global, ion-scale, linear electromagnetic modes are studied at NSTX aspect ratio and high plasma beta using the global gyrokinetic particle-in-cell code XGC. The effects of compressional magnetic perturbations are approximated via a well-known modification to the particle drifts that was developed for flux-tube simulations [N. Joiner et al., Phys. Plasmas 17, 072104 (2010)], without proof of its validity in a global simulation. Magnetic equilibria are re-constructed for each distinct plasma profile that is used. Coulomb collision effects are not considered. Within the limitations imposed by the present study, it is found that linear growth rates of electromagnetic modes (collisionless microtearing modes and kinetic ballooning modes) are significantly reduced by NSTX-like shaping. For example, growth rates of kinetic ballooning modes at high beta are reduced to the level of that of collisionless trapped electron modes.
Non-axisymmetric magnetic fields arising in a tokamak either by external or internal perturbations can induce complex non-ideal MHD responses in their resonant surfaces while remaining ideally evolved elsewhere. This layer response can be characterized in a linear regime by a single parameter called the inner-layer Delta, which enables outer-layer matching and the prediction of torque balance to non-linear island regimes. Here, we follow strictly one of the most comprehensive analytic treatments including two-fluid and drift MHD effects and keep the fidelity of the formulation by incorporating the numerical method based on the Riccati transformation when quantifying the inner-layer Delta. The proposed scheme reproduces not only the predicted responses in essentially all asymptotic regimes but also with continuous transitions as well as improved accuracies. In particular, the Delta variations across the inertial regimes with viscous or semi-collisional effects have been further resolved, in comparison with additional analytic solutions. The results imply greater shielding of the electromagnetic torque at the layer than what would be expected by earlier work when the viscous or semi-collisional effects can compete against the inertial effects, and also due to the intermediate regulation by kinetic Alfven wave resonances as rotation slows down. These are important features that can alter the nonaxisymmetric plasma responses including the field penetration by external fields or island seeding process in rotating tokamak plasmas.
The engineering limits of plasma facing components (PFCs) constrain the allowable operational space of tokamaks. Poorly managed heat fluxes that push the PFCs beyond their limits not only degrade core plasma performance via elevated impurities, but can also result in PFC failure due to thermal stresses or melting. Simple axisymmetric assumptions fail to capture the complex interaction between 3D PFC geometry and 2D or 3D plasmas. This results in fusion systems that must either operate with increased risk or reduce PFC loads, potentially through lower core plasma performance, to maintain a nominal safety factor. High precision 3D heat flux predictions are necessary to accurately ascertain the state of a PFC given the evolution of the magnetic equilibrium. A new code, the Heat flux Engineering Analysis Toolkit (HEAT), has been developed to provide high precision 3D predictions and analysis for PFCs. HEAT couples many otherwise disparate computational tools together into a single open source python package. Magnetic equilibrium, engineering CAD, finite volume solvers, scrape off layer plasma physics, visualization, high performace computing, and more, are connected in a single web-based user interface. Linux users may use HEAT without any software prerequisites via an appImage. This manuscript introduces HEAT, discusses the software architecture, presents first HEAT results, and outlines physics modules in development.
