The Parallel Boundary Condition for Turbulence Simulations in Low Magnetic Shear Devices

Flux tube simulations of plasma turbulence in stellarators and tokamaks typically employ coordinates which are aligned with the magnetic field lines. Anisotropic turbulent fluctuations can be represented in such field-aligned coordinates very efficiently, but the resulting non-trivial boundary conditions involve all three spatial directions, and must be handled with care. The standard "twist-and-shift" formulation of the boundary conditions [Beer, Cowley, Hammett \textit{Phys. Plasmas} \textbf{2}, 2687 (1995)] was derived assuming axisymmetry and is widely used because it is efficient, as long as the global magnetic shear is not too small. A generalization of this formulation is presented, appropriate for studies of non-axisymmetric, stellarator-symmetric configurations, as well as for axisymmetric configurations with small global shear. The key idea is to replace the "twist" of the standard approach (which accounts only for global shear) with the integrated local shear. This generalization allows one significantly more freedom when choosing the extent of the simulation domain in each direction, without losing the natural efficiency of field-line-following coordinates. It also corrects errors associated with naive application of axisymmetric boundary conditions to non-axisymmetric configurations. Simulations of stellarator turbulence that employ the generalized boundary conditions require much less resolution than simulations that use the (incorrect, axisymmetric) boundary conditions. We also demonstrate the surprising result that (at least in some cases) an easily implemented but manifestly incorrect formulation of the boundary conditions does {\it not} change important predicted quantities, such as the turbulent heat flux

Optimization of Nonlinear Turbulence in Stellarators

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasisymmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using T3D to evaluate the changes in the macroscopic profiles

Highly Volcanic Exoplanets, Lava Worlds, and Magma Ocean Worlds:An Emerging Class of Dynamic Exoplanets of Significant Scientific Priority

Highly volcanic exoplanets, which can be variously characterized as 'lava worlds', 'magma ocean worlds', or 'super-Ios' are high priority targets for investigation. The term 'lava world' may refer to any planet with extensive surface lava lakes, while the term 'magma ocean world' refers to planets with global or hemispherical magma oceans at their surface. 'Highly volcanic planets', including super-Ios, may simply have large, or large numbers of, active explosive or extrusive volcanoes of any form. They are plausibly highly diverse, with magmatic processes across a wide range of compositions, temperatures, activity rates, volcanic eruption styles, and background gravitational force magnitudes. Worlds in all these classes are likely to be the most characterizable rocky exoplanets in the near future due to observational advantages that stem from their preferential occurrence in short orbital periods and their bright day-side flux in the infrared. Transit techniques should enable a level of characterization of these worlds analogous to hot Jupiters. Understanding processes on highly volcanic worlds is critical to interpret imminent observations. The physical states of these worlds are likely to inform not just geodynamic processes, but also planet formation, and phenomena crucial to habitability. Volcanic and magmatic activity uniquely allows chemical investigation of otherwise spectroscopically inaccessible interior compositions. These worlds will be vital to assess the degree to which planetary interior element abundances compare to their stellar hosts, and may also offer pathways to study both the very young Earth, and the very early form of many silicate planets where magma oceans and surface lava lakes are expected to be more prevalent. We suggest that highly volcanic worlds may become second only to habitable worlds in terms of both scientific and public long-term interest.Comment: A white paper submitted in response to the National Academy of Sciences 2018 Exoplanet Science Strategy solicitation, from the NASA Sellers Exoplanet Environments Collaboration (SEEC) of the Goddard Space Flight Center. 6 pages, 0 figure

Towards continuum gyrokinetic study of high-field mirrors

High-temperature superconducting (HTS) magnetic mirrors under development exploit strong fields with high mirror ratio to compress loss cones and enhance confinement, and may offer cheaper, more compact fusion power plant candidates. This new class of devices could exhibit largely unexplored interchange and gradient-driven modes. Such instabilities, and methods to stabilize them, can be studied with gyrokinetics given the strong magnetization and prevalence of kinetic effects. Our focus here is to: a) determine if oft-used gyrokinetic models for open field lines produce the electron-confining (Pastukhov) electrostatic potential; b) examine and address challenges faced by gyrokinetic codes in studying HTS mirrors. We show that a one-dimensional limit of said models self-consistently develops a potential qualitatively reaching the analytical Pastukhov level. Additionally, we describe the computational challenges of studying high mirror ratios with open field line gyrokinetic solvers, and offer a force softening method to mitigate small time steps needed for time integration in colossal magnetic field gradients produced by HTS coils, providing a 19X speedup