Seminar

Synopsis:

Despite significant development over the last decades, a model able to describe the periphery region of magnetic confinement fusion devices, extending from the edge to the far scrape-off layer, is still missing. The lack of a proper model has undermined our ability to properly simulate the plasma dynamics in this region, which is necessary to predict the heat flux to the vessel wall of future fusion devices, the L-H transition, and ELM dynamics. These are some of the most important issues on the way to a fusion reactor. In this work, a drift-kinetic and a gyrokinetic model able to describe the plasma dynamics in the tokamak periphery are developed, which take into account electrostatic fluctuations at all relevant scales, allowing for comparable amplitudes of background and fluctuating components. In addition, the models implement a full Coulomb collision operator, and are therefore valid at arbitrary collisionality regimes. For an efficient numerical implementation of the models, the resulting kinetic equations are projected onto a Hermite-Laguerre velocity-space polynomial basis, obtaining a moment-hierarchy. The use of systematic closures to truncate the moment-hierarchy equation, such as the semi-collisional closure, allows for the straightforward adjustment of the kinetic physics content of the model. In the electrostatic high collisionality regime, our models are therefore reduced to an improved set of drift-reduced Braginskii equations, which are widely used in scrape-off layer simulations. The first numerical studies based on our models are carried out, shedding light on the interplay between collisional, using the Coulomb collision operator, and collisionless mechanisms. In particular, the dynamics of electron-plasma waves and the drift-wave instability are studied at arbitrary collisionality. A comparison is made with the collisionless limit and simplified collision operators used in state-of-the-art simulation codes, where large deviations in the growth rates and eigenmode spectra are found, especially at the levels of collisionality relevant for present and future magnetic confinement fusion devices.

Synopsis:

In a strong, weakly inhomogeneous magnetic field, charged particles rapidly gyrate around magnetic field lines on the cyclotron timescale. On longer timescales, the center of gyration suffers a slow drift. Computing this long-timescale drift is known as the guiding center problem. The established method for tackling the guiding center problem involves first moving into a perturbed coordinate system that decouples the gyration from the drift. Leveraging this decoupling, standard numerical integration schemes for non-stiff systems are then applied in the new coordinates. The major shortcoming of this approach is that the perturbed coordinates are only known as difficult-to-compute asymptotic series. High-order terms in the series are especially bothersome because they involve high-order derivatives of the magnetic field. In this talk I will describe an alternative solution of the guiding center problem that does not involve asymptotic coordinate transformations. The crux of the new approach is the observation that drift dynamics may be identified with a slow manifold in the phase space for loops entrained in the Lorentz force flow. I will demonstrate that loop dynamics on the slow manifold may be computed efficiently using a fully-implicit energy-conserving integrator for deformable loops coupled with a method for preparing initial conditions on the slow manifold. In particular, I will show that the slow manifold structure may be exploited to cast each implicit timestep as a well-conditioned fixed-point problem.

Synopsis:

In this talk, the energy budget of a collisionless plasma subject to electrostatic fluctuations is studied. In particular, the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion is considered. This excess measures how much thermal energy is “available” for conversion into plasma instabilities, and therefore constitutes a nonlinear measure of plasma stability. The “available energy” defined in this way becomes an interesting and useful quantity in situations where adiabatic invariants impose non-trivial constraints on the plasma motion. For instance, microstability properties of certain stellarators can be inferred directly from the available energy, without the need to solve the gyrokinetic equation. The technique also suggests that an electron-positron plasma confined by a dipole magnetic field could be entirely free from turbulence.

Synopsis:

Tremendous progress has been made on implicit particle-in-cell (PIC) schemes in recent years.  They feature exact energy conservation and have been shown to be more robust to the finite grid instability than their explicit counterparts, making them quite powerful for long-time simulation.  Simultaneously, there has been increasing interest in implicit, full-orbit kinetic simulation that steps over the gyration time-scale as an alternative to gyrokinetics.  Such an approach would have the noteworthy advantage of being able to handle widely varying levels of magnetization within the computational domain.  We present a new full-orbit time integrator at the intersection of these two ideas.  The integrator is built on Crank-Nicolson and preserves the crucial exact energy conservation property of implicit PIC, but it also reproduces all first-order guiding center drifts and the correct gyroradius when stepping over the gyration time-scale, all while converging to the full orbit dynamics for small time-steps.  The key innovations are (1) the ability to capture the grad-B drift and mirror force without breaking energy conservation and (2) a detailed understanding of the time-step restrictions on the scheme along with an adaptive time-stepping strategy that ensures these restrictions are respected.  Results from several test problems are presented that demonstrate the scheme’s effectiveness.  Notably, we are able to predict trapped/passing boundaries, adiabatic invariance of magnetic moment, and behavior when passing through unmagnetized regions much more accurately than previous efforts. 

Notes:

Work performed under the auspices of the U.S. Department of Energy by LLNL and LANL under contracts DE-AC52-07NA27344, DE-AC52-06NA25396, and supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.

Synopsis:

We propose a new reduced fluid model for the study of the drift wave–zonal flow dynamics in
magnetically confined plasmas. Our model can be viewed as an extension of the classic Hasegawa-
Wakatani (HW) model and is based on an improved treatment of the electron dynamics parallel to
the field lines, to guarantee a balanced electron flux on the magnetic surfaces. Our flux-balanced
HW (bHW) model contains the same drift-wave instability as previous HW models, but also has unique features which distinguish it from these models: 1) it converges exactly to the modified Hasegawa-Mima model in the collisionless limit; 2) zonal structures are always present in the flux-balanced model, even for high resistivity, and strongly reduce the level of particle and vorticity flux; 3) the more robust zonal jets also have a higher variability, which is further enhanced when the computational domain is chosen to be elongated in the radial direction.
When the computational domain is elongated in the radial direction, we furthermore observe complex multi-scale dynamics, with multiple jets interacting with one another, and intermittent bursts.

Synopsis:

The Vlasov-Fokker-Planck-Landau (VFP) model is considered a first-principles model for the simulation of collisional plasmas. It has real-world applications in the simulation of many laboratory and natural plasma systems of interest, including the Sun, Earth’s magnetosphere, and thermonuclear fusion experiments. As a mathematical model, however, VFP presents notable challenges for its efficient solution, including high dimensionality (6D+time), nonlinearity, extreme temporal and spatial scale disparity, as well as scale disparity in velocity space due to the presence of multiple species with disparate masses and temperatures. To address these challenges, we propose a novel algorithmic framework in 1D-2V based on implicit timestepping with optimal multigrid-based solvers, spatial and velocity-space adaptivity via mesh motion, and a new discrete treatment of both the collision operator (in the Rosenbluth form) and the Vlasov equation that ensures exact conservation of mass, momentum, and energy. As a result, this new treatment achieves optimal O(N) computational complexities while delivering unprecedented long-term simulation capabilities with moderate computational resources (<1000 cores). We demonstrate the utility of our approach with the simulation of a real Inertial Confinement Fusion (ICF) capsule in spherical geometry, where we show the impact of kinetic effects on the fusion reactivity of the capsule.