Professor Felix Parra Diaz

Abstract:

The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a 𝑍-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations (Dimits et al., Phys. Plasmas, vol. 7, 2000, 969). A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear (van Wyk et al., J. Plasma Phys., vol. 82, 2016, 905820609). The breakup of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system – the Reynolds stress and the advection of the diamagnetic flow by the 𝐸×𝐵 flow. By analysing the linear ion-temperature-gradient modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.

Abstract:

Main ions influence impurity dynamics through a variety of mechanisms; in particular, via impurity-ion collisions. To lowest order in an expansion in the main ion mass over the impurity mass, the impurity-ion collision operator only depends on the component of the main ion distribution that is odd in the parallel velocity. These lowest order terms give the parallel friction of the impurities with the main ions, which is typically assumed to be the main cause of collisional impurity transport. Next-order terms in the mass ratio expansion of the impurity-ion collision operator, proportional to the component of the main ion distribution that is even in the parallel velocity, are usually neglected. However, in stellarators, the even component of the main ion distribution can be very large. In this article, such next-order terms in the mass ratio expansion of the impurity-ion collision operator are retained, and analytical expressions for the neoclassical radial flux of trace impurities are calculated in the Pfirsch-Schl\"uter, plateau and $1/\nu$ regimes. The new terms provide a drive for impurity transport that is physically very different from parallel friction: they are associated to anisotropy in the pressure of the main ions, which translates into impurity pressure anisotropy. It is argued that main ion pressure anisotropy must be taken into account for a correct description of impurity transport in certain realistic stellarator plasmas. Examples are given by numerically evaluating the analytical expressions for the impurity flux.

Abstract:

The magnetic presheath is a boundary layer occurring when magnetized plasma is in contact with a wall and the angle α between the wall and the magnetic field B is oblique. Here, we consider the fusion-relevant case of a shallow-angle, α 1, electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for α/√τ + 1 √me/mi, where me is the electron mass, mi is the ion mass, τ = Ti/ZTe,Te is the electron temperature, Ti is the ion temperature and Z is the ionic charge state. The thickness of the magnetic presheath is of the order of a few ion sound Larmor radii ρs = √mi(ZTe + Ti)/ZeB, where e is the proton charge and B = |B| is the magnitude of the magnetic field. We study the dependence on τ of the electrostatic potential and ion distribution function in the magnetic presheath by using a set of prescribed ion distribution functions at the magnetic presheath entrance, parameterized by τ . The kinetic model is shown to be asymptotically equivalent to Chodura’s fluid model at small ion temperature, τ 1, for |ln α| > 3|ln τ | 1. In this limit, despite the fact that fluid equations give a reasonable approximation to the potential, ion gyroorbits acquire a spatial extent that occupies a large portion of the magnetic presheath. At large ion temperature, τ 1, relevant because Ti is measured to be a few times larger than Te near divertor targets of fusion devices, ions reach the Debye sheath entrance (and subsequently the wall) at a shallow angle whose size is given by √α or 1/√τ, depending on which is largest.