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Register a new user$texttt{stella}$: a mixed implicit-explicit, delta-f gyrokinetic code for general magnetic field configurations
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Here we present details of a mixed implicit-explicit numerical scheme for the solution of the gyrokinetic-Poisson system of equations in the local limit. This scheme has been implemented in a new code called $texttt{stella}$, which is capable of evolving electrostatic fluctuations with full kinetic electron effects and an arbitrary number of ion species in general magnetic geometry. We demonstrate the advantages of this mixed approach over a fully explicit treatment and provide linear and nonlinear benchmark comparisons for both axisymmetric and non-axisymmetric magnetic equilibria.
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We are developing a new continuum gyrokinetic code, Gkeyll, for use in edge plasma simulations, and here present initial simulations of turbulence on open field lines with model sheath boundary conditions. The code implements an energy conserving discontinuous Galerkin scheme, applicable to a general class of Hamiltonian equations. Several applications to test problems have been done, including a calculation of the parallel heat-flux on divertor plates resulting from an ELM crash in JET, for a 1x/1v SOL scenario explored previously, where the ELM is modeled as a time-dependent intense upstream source. Here we present initial simulations of turbulence on open field lines in the LAPD linear plasma device. We have also done simulations in a helical open-field-line geometry. While various simplifications have been made at present, this still includes some of the key physics of SOL turbulence, such as bad-curvature drive for instabilities and rapid parallel losses with sheath boundary conditions. This is useful for demonstrating the overall feasibility of this approach and for initial physics studies of SOL turbulence. We developed a novel version of DG that uses Maxwellian-weighted basis functions while still preserving exact particle and energy conservation. The Maxwellian-weighted DG method achieves the same error with 4 times less computational cost in 1v, or 16 times lower cost in the 2 velocity dimensions of gyrokinetics (assuming memory bandwidth is the limiting factor).
An overview of the algorithm and a sampling of plasma applications of the implicit, adaptive high order finite (spectral) element modeling framework, HiFi, is presented. The distinguishing capabilities of the HiFi code include adaptive spectral element spatial representation with flexible geometry, highly parallelizable implicit time advance, and general flux-source form of the partial differential equations and boundary conditions that can be implemented in its framework. Early algorithm development and extensive verification studies of the two-dimensional version of the code, known as SEL, have been previously described [A.H. Glasser & X.Z. Tang, Comp. Phys. Comm., 164 (2004); V.S. Lukin, Ph.D. thesis, Princeton University (2008)]. Here, substantial algorithmic improvements and extensions are presented together with examples of two- and three- dimensional applications of the HiFi framework. These include a Cartesian two-dimensional incompressible magnetohydrodynamic simulation of low dissipation magnetic reconnection in a large system, a two-dimensional axisymmetric simulation of self-similar compression of a magnetic plasma confinement configuration, and a three-dimensional Hall MHD simulation of spheromak tilting and relaxation. Some planned efforts to further improve and expand the capabilities of the HiFi modeling framework are discussed.
Two-fluid Braginskii codes have simulated open-field line turbulence for over a decade, and only recently has it become possible to study these systems with continuum gyrokinetic codes. This work presents a first-of-its-kind comparison between fluid and (long-wavelength) gyrokinetic models in open field-lines, using the GDB and Gkeyll codes to simulate interchange turbulence in the Helimak device at the University of Texas (T. N. Bernard, et. al., Phys. of Plasmas 26, 042301 (2019)). Partial agreement is attained in a number of diagnostic channels when the GDB sources and sheath boundary conditions (BCs) are selected carefully, especially the heat-flux BCs which can drastically alter the temperature. The radial profile of the fluctuation levels is qualitatively similar and quantitatively comparable on the low-field side, although statistics such as moments of the probability density function and the high-frequency spectrum show greater differences. This comparison indicates areas for future improvement in both simulations, such as sheath BCs, as well as improvements in GDB like particle conservation and spatially varying thermal conductivity, in order to achieve better fluid-gyrokinetic agreement and increase fidelity when simulating experiments.
In order to predict and analyze turbulent transport in tokamaks, it is important to model transport that arises from microinstabilities. For this task, quasilinear codes have been developed that seek to calculate particle, angular momentum, and heat fluxes both quickly and accurately. In this tutorial, we present a derivation of one such code known as QuaLiKiz, a quasilinear gyrokinetic transport code. The goal of this derivation is to provide a self-contained and complete description of the underlying physics and mathematics of QuaLiKiz from first principles. This work serves both as a comprehensive overview of QuaLiKiz specifically as well as an illustration for deriving quasilinear models in general.
Curvature-driven turbulence in a helical open-field-line plasma is investigated using electrostatic five-dimensional gyrokinetic continuum simulations in an all-bad-curvature helical-slab geometry. Parameters for a National Spherical Torus Experiment scrape-off-layer plasma are used in the model. The formation and convective radial transport of plasma blobs is observed, and it is shown that the radial particle-transport levels are several times higher than diffusive Bohm-transport estimates. By reducing the strength of the poloidal magnetic field, the profile of the heat flux to the divertor plate is observed to broaden.
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