Plasma Physics (physics.plasm-ph)

Abstract: This paper presents the calculation of the bounce-averaged drift of trapped particles in a near-axis framework for axisymmetric and quasisymmetric magnetic fields. This analytic consideration provides important insight on the dependence of the bounce-averaged drift on the geometry and stability properties of the field. In particular, we show that, although the maximum-$\mathcal{J}$ property is unattainable in quasisymmetric stellarators, one may approach it through increased plasma $\beta$ and triangular shaping. The description of trapped particles allows us to calculate the available energy of trapped electrons analytically in two asymptotic regimes, providing insight into the behaviour of this measure of turbulence. It is shown that the available energy is intimately related to MHD-stability, providing a potential synergy between this measure of gyrokinetic turbulence and MHD-stability.

Abstract: This study presents a comprehensive benchmark and convergence analysis of the gyromoment (GM) approach in the gyrokinetic local flux-tube limit, focusing on the cyclone base case (CBC) and the Dimits shift. The GM approach demonstrates its efficacy in accurately capturing the nonlinear dynamics of the CBC with fewer velocity space points compared to the GENE code. Increasing velocity dissipation enhances convergence, albeit with a slight discrepancy in the saturated heat flux value. The GM approach successfully reproduces the Dimits shift and effectively captures its width compared to the ITG threshold. In the collisional case, we obtain a good agreement with previous global PIC results on transport. We report that the choice of collision model has a minimal impact both on the ITG growth rate and on the nonlinear saturated heat flux. We attribute this to the adiabatic electron model that impeaches the electron-ion collisions.

Abstract: Particle-in-cell codes usually represent large groups of particles as a single macroparticle. These codes are computationally efficient but lose information about the internal structure of the macroparticle. To improve the accuracy of these codes, this work presents a method in which, as well as tracking the macroparticle, the moments of the macroparticle are also tracked. Although the equations needed to track these moments are known, the coordinate transformations for moments where the space and time coordinates are mixed cannot be calculated using the standard method for representing moments. These coordinate transformations are important in astrophysical plasma, where there is no preferred coordinate system. This work uses the language of Schwartz distributions to calculate the coordinate transformations of moments. Both the moment tracking and coordinate transformation equations are tested by modelling the motion of uncharged particles in a circular orbit around a black hole in both Schwarzschild and Kruskal-Szekeres coordinates. Numerical testing shows that the error in tracking moments is small, and scales quadratically. This error can be improved by including higher order moments. By choosing an appropriate method for using these moments to deposit the charge back onto the grid, a full particle-in-cell code can be developed.