Controlling the cross-field transport of energy and momentum has become one of the central goals of the fusion sciences program. Specifically inducing the formation of transport barriers both at the plasma edge and in the core has become a primary means of limiting plasma transport across most of the confinement domain of modern fusion experiments. The formation of these barriers is considered central to the achievement of peak performance in future experiments such as ITER and therefore understanding the full physics of barrier formation, development and structure becomes a central goal of the fusion program. It is only the recent development of finite-β gyrokinetic models which has made it possible to study the formation of these barriers in the plasma core — the strong pressure gradients that are associated with a fully developed barrier locally distort the magnetic surfaces, profoundly impacting the local MHD and kinetic stability. Neglecting such effects rendered models based on electrostatic gyrokinetics unjustifiable.

Even with a fully operational electromagnetic, gyrokinetic code the study of transport barrier formation and structure is a challenging task. The number of known parameters that influence the dynamics of barriers includes the shape of the magnetic surfaces, the local plasma β, the local magnetic shear, the plasma rotation profiles and local pressure gradients. The multiplicity of control parameters combined with the relatively long time required for the full development of the barrier challenges the modeler. For this reason, this project will take place in three distinct phases. In the first phase, we will prepare for the barrier calculation by

• Adding non-periodic radial boundary conditions to GS2, and
• Developing the appropriate coarse-graining operators to allow GS2 to be embedded in a multiscale transport calculation.

It is critical to address the first topic early because of the peculiar property of instabilities that are driven by sheared ExB flows - like the Kelvin-Helmholtz instability, many are unstable only in the presence of an inflection point in the radial profile of the flow. Since a periodic radial domain forces all but non-trivial flows to have an inflection point, this property implies that a strongly sheared flow in a periodic domain will generically be more unstable than it should be. This is clearly unsatisfactory for the investigation of transport barriers. The second item is straightforward and can be accomplished immediately. In the course of the first phase, we will also accelerate the implicit algorithms used in GS2 with a new iterative algorithm that bypasses the need for the implicit fields solver.

In the second phase, we wrap the gaptooth and projective integration techniques into a new toolkit which can act as a controller for transport-time-scale gyrokinetic turbulence simulations. A bird's-eye view of how this project will proceed is described elsewhere.

In the third phase, having established the appropriate lifting and restriction operators for the gyrokinetic transport problem, we will use the bifurcation toolkit of Kevrekidis and Gear to perform a bifurcation analysis. (This is essentially the infinite time limit of a projective integrator.) This analysis will yield conditions under which transport barrier formation could begin with and without significant ExB shear, magnetic shear and strong plasma shaping.

Once we have demonstrated the capability to create transport barriers in the simulations, we will then be able to explore for the first time their formation, structure and stability in a realistic, self-consistent numerical system. A major practical focus of this study, central to the effectiveness of ITER and other devices which depend upon transport barriers for effective operation, will be on the factors that govern the height and width of the barriers, and steepness of the plasma profiles within them. Some of the most basic questions regarding the barrier structure are at present not well understood. For example, in the case of internal transport barriers, do MHD instability limits play a role, or are such modes eliminated by second-stability effects? In the case of the edge pedestal, what is the physical nature of ELMs, and what are the impacts of ExB shear and diamagnetic effects on pedestal stability? In addition to such MHD instabilities, microinstability-driven transport is likely to be another key factor governing the observed structure of transport barriers. It is not at present clear, however, what the dominant modes are that drive such transport or what the factors are that control them. Candidates include local and non-local drift-wave modes, modes driven by the electron and ion temperature gradients, parallel and perpendicular velocity-shear driven modes, tearing modes, curvature-driven modes and possibly others. With a self-consistent barrier available for study in a numerical simulation, such as we propose to create, this important question can be directly answered.

Such transport-generating modes, and their parameter dependence, are also likely to play a key role in another major issue, namely, in the triggering of transport barrier formation or destruction. For example, the onset of barrier formation might be associated with the suppression of strong transport (e.g., in the case of the edge pedestal, the finite-β suppression of drift waves.) It has also been proposed that barrier formation is associated with the onset of ExB-generating secondary modes.

In summary, the structure and formation of transport barriers are likely to depend on an array of interrelated phenomena involving MHD and non-MHD stability as well as transport. Given the complexity of this problem, it seems likely a reliable, physics-based model for barrier formation will eventually emerge from detailed study of self-consistent numerical simulations such as those proposed here.