Spatial dispersion in finite element models for ion cyclotron resonance heating: Theory and applications for toroidal plasmas

Nuclear fusion can provide large amounts of energy from earth-abundant elements,with no carbon emissions and little radioactive waste. For the nuclei to fuse under earth-relevant conditions, temperatures in excess of 100 000 000 °C are needed. At these temperatures, the fuel is in a plasma state. A common method to heat the plasma is ion cyclotron resonance heating (ICRH), where radiofrequency waves are launched from an antenna on the vessel wall into the plasma to resonate with the gyrating ions. Wave propagation and dissipation in hot magnetized plasmas is a nonlocal process, where the plasma response at a given point depends on the particles' cumulative acceleration along their orbits. To quantify how the plasma is heated, numerical simulations are required. This thesis aims to provide a numerical framework that can simulate the coupling of the wave from the antenna to the plasma, the wave propagation and dissipation inside the plasma, as well as the acceleration of individual ions and how they deposit their energy in the plasma. To this end, an iterative scheme that adds nonlocal effects to an otherwise local finite element (FE) model is developed. FE models are suitable for modeling irregular geometries and wave coupling through the cold scrape-off layer plasma, but not necessarily the hot core plasma. Examples of nonlocal effects that are added iteratively are mode conversion from the fast magnetosonic wave to the ion Bernstein wave (IBW) and up- and downshift of the parallel wavenumber. Further, the wave solver is coupled to a Fokker-Planck solver that evaluates the effect of ICRH on the ion distribution function. The models presented in this thesis are in 1D or 2D axisymmetry, but are not conceptually different from a generalization to 3D. Kärnfusion kan producera stora mängder energi från vanligt förekommande grundämnen på jorden utan att släppa ut koldioxid, och ger endast upphov till små mängder radioaktivt avfall. För att atomkärnor ska slås samman under förhållanden som är relevanta för jorden krävs temperaturer som överstiger 100 000 000 °C. Vid dessa temperaturer befinner sig bränslet i ett plasmatillstånd. En vanlig metod för att värma plasman är jon-cyclotronresonans-uppvärmning (ICRH), där radiovågor skickas från en antenn på kärlets vägg in i plasmat för att resonera med de roterande jonerna. Vågutbredning och dissipation i varma magnetiserade plasman är en ickelokal effekt, där plasmats svar i en given punkt beror på partiklarnas ackum