Topology and transport

The aim of this page is to introduce and report progress on the activities included in the research project Influence of global flows and their topology on transport in turbulent plasmas, funded by the Spanish Ministry of Science and Innovation through the grant ENE2009-07247. The members of the research team are:

• Iván Calvo (Principal Investigator), Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, Madrid,
• Benjamín Carreras, BACV Solutions Inc., Oak Ridge, Tennessee & University of Alaska,
• Irene Llerena, Universidad de Barcelona,
• Edilberto Sánchez, Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, Madrid,
• Guillermo Sánchez Burillo, Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, Madrid,
• Boudewijn van Milligen, Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, Madrid,

and this is a list of frequent collaborators (whose work is not directly funded by the above grant):

• Francisco Castejón, Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, Madrid,
• Fernando Falceto, Universidad de Zaragoza,
• Luis García, Universidad Carlos III, Madrid,
• Carlos Hidalgo, Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, Madrid,
• M. Ángeles Pedrosa, Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, Madrid,
• Raúl Sánchez, Oak Ridge National Laboratory, Oak Ridge, Tennessee & Universidad Carlos III, Madrid.

The aim of this proposal is to advance the understanding of turbulent transport in magnetically confined fusion plasmas and study the impact of the topology and dynamics of global flows on it. We will tackle concrete problems in three broad research areas of toroidally confined plasmas: topology of structures in the presence of turbulence (or, in short, "the topology of flows"), non-diffusive transport, and transitions to improved confinement regimes. Below, we summarize the concrete objectives in each of the aforementioned research lines, as well as progress made to date.

Topology of flows

Our long-term aim is to develop a set of diagnostics to characterize the topological structures in fluid and particle models of a turbulent plasma. In the frame of this project, and during the next three years, we plan to study the problem in pressure-gradient-driven turbulence, with a possible extension to gyrokinetic models. For this we will make use of Computational Homology. An important tool will be the software developed by the Computational Homology Project (CHomP) which, in particular, computes some topological invariants (the Betti numbers) of three-dimensional spaces. We will investigate the possibility of developing or using other tools which allow to improve the numerical resolution of the calculations.

Non-diffusive transport

Turbulent flows induce non-collisional transport in plasmas. The final goal is to understand in a precise way the origin and implications of the non-Gaussian and non- Markovian character of transport in certain dynamical and topological conditions of those turbulent flows. We will try to make progress in the answer to questions such as: a) The relationship between the topology of flows and the presence of non-diffusive transport. b) The connection between the statistical properties of turbulence and the description by means of stochastic and kinetic equations of particle transport. c) Find out whether there exists a mathematical framework in which one can derive linear, fractional diffusion equations (in particular non-local) from non-linear, partial differential equations (in particular local).

Transitions to improved confinement regimes

The generation of global flows allows to have regimes with enhanced confinement. We will study the importance of the interaction between disparate spatio-temporal scales in the generation of sheared flows and the concomitant turbulence reduction. Our work will be based on recent experimental results in TJ-II. We will use topological techniques in phase space to gain insight into the dynamics of models with multiple states.

• Zonal Flows and long-range correlations in TJ-II

Recent experimental results in the TJ-II stellarator prove the existence of long-distance correlations in the electrostatic potential around the bifurcation point for the emergence of the plasma edge sheared flow layer . Trying to understand these results from a theoretical point of view, we have formulated a phenomenological model based on the paradigm of flow shear generation by Reynolds stress and turbulence suppression by shear. We suggest that the experimental results might be an indirect evidence of the development of poloidally asymmetric zonal flows.