A fluid model of internal transport barrier formation in a confined plasma

In this talk we describe the spontaneous formation of an internal transport barrier (ITB), a narrow region of steep zonal temperature gradient with flattened temperature profiles on either side, in a simple two-fluid model of interchange turbulence derived from gyrokinetics. We consider axisymmetric perturbations in an MHD-stable Z-pinch and show that such modes can be unstable due to Hall-MHD effects at small scales (comparable to ion sound radius), even at low beta. Simulations show that the turbulence and heat transport driven by these modes generally exceeds that driven by the electrostatic ion-temperature-gradient (ITG) instabilities that occur at higher parallel wavenumbers (involving adiabatic electrons). We find that these 'Hall-MHD interchange' instabilities give rise to a turbulent state in which an ITB is spontaneously formed. This state is sustained by strong zonal velocity shear in the ITB, which suppresses transport across it. The interplay of different length scales, such as the ion sound radius (the intrinsic length scale in the model) and the diffusive scales, in determining the ITB width is investigated. The emergence of an ITB is accompanied by the radial expulsion of plasma across it. In the broad, flat-temperature regions, the system always drives itself towards a density gradient that is marginally stable for this system and for the ideal MHD interchange. Using numerical simulations, we map out, and explore in detail, the region of parameter space (temperature gradient and collisional diffusivities) in which ITBs form. Outside this region, we observe a transition to non-ITB states. These include suppressed-turbulence "Dimits" regimes with large zonal structures and bursty behaviour, as well as regimes where the turbulence does not saturate, exhibiting a "run-away" usually associated in the literature with "high-beta" regimes.