Professor Felix Parra Diaz

Abstract:

Strong gradient regions in tokamaks, such as the pedestal or internal transport barriers, are regions of reduced turbulence where neoclassical transport can play a dominant role. However, standard neoclassical transport theory assumes that the gradient length scales of density, temperature, and potential are of the order of the system size. In the pedestal, gradient length scales are much shorter and are measured to be of the order of the ion poloidal gyroradius. We present an extension of neoclassical theory that is applicable in transport barriers of large aspect ratio tokamaks. We show that particle and momentum transport are connected in such a way that a source of parallel momentum can drive a significant neoclassical ion particle flux. In strong gradient regions, density, electric potential, mean parallel flow, and ion temperature are shown to no longer be flux functions. Instead, they have a small but important poloidally varying piece that modifies the transport equations to lowest order. This introduces a nonlinearity in the transport problem through the coupling with quasineutrality that yields multiple co-existing solutions when solving for the plasma profiles. The different solutions could be connected to low and high transport states and jumps between solutions could provide a new neoclassical explanation for H-L back-transitions.

Abstract:

Recent nonlinear gyrokinetic simulations have shown that impurities can strongly modify the turbulent heat flux in stellarator plasmas. Here, the ion-temperature-gradient (ITG) dispersion relation in a plasma containing impurities is analytically solved in certain limits and an expression for the modification of the ITG growth rate by impurities is derived. The analytical expression is the sum of three terms corresponding to three different physical causes (impurity density gradient, impurity temperature gradient and dilution) of the change in the growth rate. The scalings predicted analytically for the modification of the growth rate are shown to be reproduced by linear gyrokinetic simulations. The conditions for reduction or increase of the ITG growth by impurities are also correctly predicted by the analytical solution to the dispersion relation. Finally, a remarkable correlation is found between the analytical expression for the modification of the growth rate and the modification of the turbulent heat flux obtained from nonlinear gyrokinetic simulations.

Abstract:

The toroidal geometry of tokamaks and stellarators is known to play a crucial role in the linear physics of zonal flows (ZFs), leading to e.g. the Rosenbluth–Hinton residual and geodesic acoustic modes. However, descriptions of the nonlinear ZF growth from a turbulent background typically resort to simplified models of the geometry. We present a generalised theory of the secondary instability to model the ZF growth from turbulent fluctuations in toroidal geometry, demonstrating that the radial magnetic drift substantially affects the nonlinear ZF dynamics. In particular, the toroidicity gives rise to a new branch of propagating ZFs, the toroidal secondary mode, which is nonlinearly supported by the turbulence. We present a theory of this mode and compare the theory against gyrokinetic simulations of the secondary mode. The connection with other secondary modes—the ion-temperature-gradient and Rogers–Dorland–Kotschenreuther secondary modes—is also examined.

Abstract:

Strongly driven ion-scale turbulence in tokamak plasmas is shown to be regulated by a new propagating zonal flow mode, the toroidal secondary mode, which is nonlinearly supported by the turbulence. The mode grows and propagates due to the combined effects of zonal flow shearing and advection by the magnetic drift. Above a threshold in the turbulence level, small-scale toroidal secondary modes become unstable and shear apart turbulent eddies, forcing the turbulence level to remain near the threshold. This threshold condition is used to derive scaling laws for the turbulent heat flux, fluctuation spectra, and zonal flow amplitude, which are validated in nonlinear gyrokinetic simulations and explain previous experimental observations.

Abstract:

We introduce a new approach to measure the magnetic pitch angle profile in tokamak plasmas with Doppler backscattering (DBS), a technique traditionally used for measuring flows and density fluctuations. The DBS signal is maximised when its probe beam’s wavevector is perpendicular to the magnetic field at the cutoff location, independent of the density fluctuations (Hillesheim et al 2015 Nucl. Fusion 55 073024). Hence, if one could isolate this effect, DBS would then yield information about the magnetic pitch angle. By varying the toroidal launch angle, the DBS beam reaches cutoff with different angles with respect to the magnetic field, but with other properties remaining similar. Hence, the toroidal launch angle which gives maximum backscattered power is thus that which is matched to the pitch angle at the cutoff location, enabling inference of the magnetic pitch angle. We performed systematic scans of the DBS toroidal launch angle for repeated DIII-D tokamak discharges. Experimental DBS data from this scan were analysed and combined with Gaussian beam-tracing simulations using the Scotty code (Hall-Chen et al 2022 Plasma Phys. Control. Fusion 64 095002). The pitch-angle inferred from DBS is consistent with that from magnetics-only and motional-Stark-effect-constrained (MSE) equilibrium reconstruction in the edge. In the core, the pitch angles from DBS and magnetics-only reconstructions differ by one to two degrees, while simultaneous MSE measurements were not available. The uncertainty in these measurements was under a degree; we show that this uncertainty is primarily due to the error in toroidal steering, the number of toroidally separated measurements, and shot-to-shot repeatability. We find that the error of pitch-angle measurements can be reduced by optimising the poloidal launch angle and initial beam properties. Since DBS has high spatial and temporal resolutions, is non-perturbative, does not require neutral beams, and is likely robust to neutron damage of and debris on the first mirrors, using DBS to measure the pitch angle in future fusion energy systems is especially appealing.