The free energy balance equation applied to gyrokinetic instabilities, the effect of the charge flux constraint, and application to simplified kinetic models

The free energy balance equation for gyrokinetic fluctuations is derived and applied to instabilities. An additional term due to electromagnetic sources is included. This can provide a simpler way to compute the free energy balance in practical applications, and is also conceptually clarifying. The free energy balance, by itself, is not sufficient to determine an eigenfrequency. The preceding results are derived in general geometry. The charge flux constraint in gyrokinetics can provide a necessary additional relation, and the combination of these two can be equivalent to a dispersion relation. The charge flux constraint can prevent the appearance of an unstable eigenmode even though the free energy balance would allow strongly growing fluctuations. The application of these concepts to simplified kinetic models in simplified geometry is also indicated.Comment: 5 page

Multi-Scale Interactions of Microtearing Turbulence in the Tokamak Pedestal

Microtearing turbulence in an idealized pedestal scenario is found to saturate via zonal fields, while also exciting strong zonal flows; a concurrent upshift of the non-linear critical gradient is observed. The zonal flows cause electron-temperature-gradient-driven turbulence to be ameliorated. When applying resonant magnetic perturbations, the prompt charge loss off the flux surface erodes the zonal flow, leading to higher electron-scale fluxes, while leaving microtearing saturation physics unaffected.</p

Geometrical Properties of a "Snow-Flake" Divertor

Using a simple set of poloidal field coils, one can reach the situation where the null of the poloidal magnetic field in the divertor region is of a second order, not of the first order as in the usual X-point divertor. Then, the separatrix in the vicinity of the null-point splits the poloidal plane not into four sectors, but into six sectors, making the whole structure looking like a snow-flake (whence a name, [1]). This arrangement allows one to spread the heat load over much broader area than in the case of a standard divertor. A disadvantage of this configuration is in that it is topologically unstable, and, with the current in the plasma varying with time, it would switch either to the standard X-point mode, or to the mode with two X-points close to each other. To avoid this problem, it is suggested to have a current in the divertor coils by roughly 5% higher than in an 'optimum' regime (the one where a snow-flake separatrix is formed). In this mode, the configuration becomes stable and can be controlled by varying the current in the divertor coils in concert with the plasma current; on the other hand, a strong flaring of the scrape-off layer still remains in force. Geometrical properties of this configurations are analyzed for a simple model. Potential advantages and disadvantages of this scheme are discussed

Transport Barriers in Magnetized Plasmas -- General Theory with Dynamical Constraints

A fundamental dynamical constraint -- that fluctuation induced charge-weighted particle flux must vanish -- can prevent instabilities from accessing the free energy in the strong gradients characteristic of Transport Barriers (TBs). Density gradients, when larger than a certain threshold, lead to a violation of the constraint and emerge as a stabilizing force. This mechanism, then, broadens the class of configurations (in magnetized plasmas) where these high confinement states can be formed and sustained. The need for velocity shear, the conventional agent for TB formation, is obviated. The most important ramifications of the constraint is to permit a charting out of the domains conducive to TB formation and hence to optimally confined fusion worthy states; the detailed investigation is conducted through new analytic methods and extensive gyrokinetic simulations

Direct Gyrokinetic Comparison of Pedestal Transport in JET with Carbon and ITER-Like Walls

This paper compares the gyrokinetic instabilities and transport in two representative JET pedestals, one (pulse 78697) from the JET configuration with a carbon wall (C) and another (pulse 92432) from after the installation of JET's ITER-like Wall (ILW). The discharges were selected for a comparison of JET-ILW and JET-C discharges with good confinement at high current (3 MA, corresponding also to low $\rho_*$) and retain the distinguishing features of JET-C and JET-ILW, notably, decreased pedestal top temperature for JET-ILW. A comparison of the profiles and heating power reveals a stark qualitative difference between the discharges: the JET-ILW pulse (92432) requires twice the heating power, at a gas rate of $1.9 \times 10^{22}e/s$, to sustain roughly half the temperature gradient of the JET-C pulse (78697), operated at zero gas rate. This points to heat transport as a central component of the dynamics limiting the JET-ILW pedestal and reinforces the following emerging JET-ILW pedestal transport paradigm, which is proposed for further examination by both theory and experiment. ILW conditions modify the density pedestal in ways that decrease the normalized pedestal density gradient $a/L_n$, often via an outward shift of the density pedestal. This is attributable to some combination of direct metal wall effects and the need for increased fueling to mitigate tungsten contamination. The modification to the density profile increases $\eta = L_n/L_T$ , thereby producing more robust ion temperature gradient (ITG) and electron temperature gradient driven instability. The decreased pedestal gradients for JET-ILW (92432) also result in a strongly reduced $E \times B$ shear rate, further enhancing the ion scale turbulence. Collectively, these effects limit the pedestal temperature and demand more heating power to achieve good pedestal performance

Taming the Heat Flux Problem: Advanced Divertors Towards Fusion Power

The next generation fusion machines are likely to face enormous heat exhaust problems. In addition to summarizing major issues and physical processes connected with these problems, we discuss how advanced divertors, obtained by modifying the local geometry, may yield workable solutions. We also point out that: (1) the initial interpretation of recent experiments show that the advantages, predicted, for instance, for the X-divertor (in particular, being able to run a detached operation at high pedestal pressure) correlate very well with observations, and (2) the X-D geometry could be implemented on ITER (and DEMOS) respecting all the relevant constraints. A roadmap for future research efforts is proposed

Potential Methods for Improving Pedestal Temperatures and Fusion Performance

The physics of the tokamak edge is very complicated, and the scaling of the H-mode transport barrier pedestal has significant uncertainties. Evidence from the largest tokamaks appears to support a model in which the H-mode pedestal width scales linearly with the poloidal gyroradius and the gradient scales with ideal MHD ballooning limits. However, there appears to be significant variability in the data from different tokamaks, including observations on DIII-D that indicate a regime where the pedestal is in second stability and the width is independent of poloidal gyroradius, which would give a more favorable scaling to reactor scales. An important question is the role of the bootstrap current in the pedestal, and another is how far can the improvements in edge stability be p shed with higher triangularity and elongation. Even with the more pessimistic model, where the pedestal width is proportional to the poloidal gyroradius, the results presented here suggest that pedestal temperatures, and thus the fusion performance, may be significantly improved by designs with stronger plasma shaping higher triangularity and elongation, moderate density peaking, and higher magnetic field (and thus reduced size), such as in ARIES-RS, FIRE, and some of the new ITER-RC designs