Gyrokinetic continuum simulations of plasma turbulence in the Texas Helimak

Abstract

The first gyrokinetic simulations of plasma turbulence in the Texas Helimak device, a simple magnetized torus, are presented. The device has features similar to the scrape-off layer region of tokamaks, such as bad-curvature-driven instabilities and sheath boundary conditions on the end plates, which are included in these simulations. Comparisons between simulations and measurements from the experiment show similarities, including equilibrium profiles and fluctuation amplitudes that approach experimental values, but also some important quantitative differences. Both experimental and simulation results exhibit turbulence statistics that are characteristic of blob transport.

Electromagnetic full- gyrokinetics in the tokamak edge with discontinuous Galerkin methods

“…The local limit can be achieved by simulating a helical flux tube with no magnetic shear, which gives a system with constant magnetic curvature that corresponds to ω d = const. This geometry has been previously used for SOL turbulence studies with Gkeyll (Bernard et al 2019;Shi et al 2019), except in this section we take the boundary condition along the field lines to be periodic. We will provide further details about the helical geometry and the coordinates in the next section.…”

“…The present target of the scheme is simulating the edge and SOL of tokamaks, although the scheme could in principle be used for whole-device modelling, including the core. Our scheme has been implemented as part of the gyrokinetics solver (Shi et al 2017(Shi et al , 2019Bernard et al 2019) of the Gkeyll computational plasma framework, which also includes solvers for the Vlasov-Maxwell system (Cagas et al 2017;Juno et al 2018) and multi-moment fluid equations (Wang et al 2015).…”

Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator

“…We now present a benchmark test of the full 5D (long-wavelength) gyrokinetic system, given by (3)- (6). With the moment-conserving GkLBO, we simulated plasma turbulence on helical, open field lines, using a nonorthogonal fieldline-following coordinate system as in [44,45]. In this coordinate system, z is parallel to magnetic field lines, x is the radial coordinate, and y is the "bi-normal" coordinate.…”

Entropy: from thermodynamics to signal processing

“…Actually, the Boltzmann (Gibbs) entropy is the same as Shannon, except for the Boltzmann constant, which has units of J/K, giving the entropy unit J/K. However, it has been shown that this unit is historically connected with the definition of the Kelvin temperature system: the Lagrangian of temperature in statistical mechanics has units of energy (Leff, 1999), and is common in plasma physics to express temperature in eV (Bernard et al, 2018;Bagryansky et al, 2015). In this more generic approach, thermodynamical entropy is dimensionless, and the difference between the Shannon and the Gibbs entropies is merely the Boltzmann's constant.…”

“…The partition function combines state functions, such as temperature and energy for the microstates, and has a central role in statistical mechanics (Bo-sture et al, 1985). Differentiating log Z with respect to λ 2 returns…”