Here we present first results simulating plasma filaments in non-axisymmetric geometries, using a fluid turbulence extension of the \boutxx~framework. This is made possible by the implementation of the Flux Coordinate Independent scheme for parallel derivatives, an extension of the metric tensor components which allows them to vary in three dimensions, and development of grid generation. Tests have been performed to confirm that the extension to three dimensional metric tensors does not compromise the accuracy and stability of the associated numerical operators. Recent changes to the FCI grid generator in \boutxx, including a curvilinear grid system which allows for potentially more efficient computation, are also presented. Initial simulations of seeded plasma filaments in a non-axisymmetric geometry are reported. We characterize filaments propagating in the closed-field-line region of a low-field-period, rotating ellipse equilibrium as inertially-limited by examining the velocity scaling and currents associated with the filament propagation. Finally, it is shown that filaments in a non-axisymmetric rotating ellipse equilibrium propagate in a toroidally nonuniform fashion, and it is determined that the long connection lengths in the scrape-off-layer enable parallel gradients to establish, which has consequences for interpretation of experimental data.
A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented …
The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-$C^1$ code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework of M3D-$C^1$. A $C^1$ coordinate mapping connects the logical domain to the non-axisymmetric physical domain, where we use the M3D-$C^1$ extended MHD models essentially without modifications. We present several numerical verifications on the implementation of this approac…
In this work, the first nonlinear particle-in-cell simulations carried out in a stellarator with the global gyrokinetic code EUTERPE using realistic plasma parameters are reported. Several studies are conducted with the aim of enabling reliable nonlinear simulations in stellarators with this code. First, EUTERPE is benchmarked against ORB5 in both linear and nonlinear settings in a tokamak configuration. Next, the use of noise control and stabilization tools, a Krook-type collision operator, markers weight smoothing and heating sources is investigated. It is studied in detail how these tools i…
Several fast methods for computing stellarator coil shapes are compared, including the classical NESCOIL procedure [Merkel, Nucl. Fusion 27, 867 (1987)], its generalization using truncated singular value decomposition, and a Tikhonov regularization approach we call REGCOIL in which the squared current density is included in the objective function. Considering W7-X and NCSX geometries, and for any desired level of regularization, we find the REGCOIL approach simultaneously achieves lower surface-averaged and maximum values of both current density (on the coil winding surface) and normal magneti…
In the linear collisionless limit, a zonal potential perturbation in a toroidal plasma relaxes, in general, to a non-zero residual value. Expressions for the residual value in tokamak and stellarator geometries, and for arbitrary wavelengths, are derived. These expressions involve averages over the lowest order particle trajectories, that typically cannot be evaluated analytically. In this work, an efficient numerical method for the evaluation of such expressions is reported. It is shown that this method is faster than direct gyrokinetic simulations performed with the GENE and EUTERPE codes. C…
Wendelstein 7-X core fueling is primarily achieved through pellet injection. The trajectory of plasmoids from an ablating pellet is an ongoing research question, which is complicated by the complex magnetic geometry of W7-X; curvature drive varies significantly toroidally, including a change in the drift drive direction. Here we use the Hermes model in BOUT++ to simulate cold plasma filaments in slab geometries where the magnetic drift drive is non-uniform along the field line. It is shown that if the field-line-averaged curvature drive is non-zero, a filament will propagate coherently in the …
The Dimits shift, an upshift in the onset of turbulence from the linear instability threshold, caused by self-generated zonal flows, can greatly enhance the performance of magnetic confinement plasma devices. Except in simple cases, using fluid approximations and model magnetic geometries, this phenomenon has proved difficult to understand and quantitatively predict. To bridge the large gap in complexity between simple models and realistic treatment in toroidal magnetic geometries (e.g. tokamaks or stellarators), the present work uses fully gyrokinetic simulations in Z-pinch geometry to invest…
Electromagnetic turbulence is addressed in tokamak and stellarator plasmas with the global gyrokinetic particle-in-cell codes ORB5 [E. Lanti et al, Comp. Phys. Comm, vol. 251, 107072 (2020)] and EUTERPE [V. Kornilov et al, Phys. Plasmas, vol. 11, 3196 (2004)]. The large-aspect-ratio tokamak, down-scaled ITER, and Wendelstein 7-X geometries are considered. The main goal is to increase the plasma beta, the machine size, the ion-to-electron mass ratio, as well as to include realistic-geometry features in such simulations. The associated numerical requirements and the computational cost for the ca…
