Search NASA⌕ Search

Engineering topics

Daniel, Don

Publications and source records attributed to Daniel, Don.

4 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Turbulent exchanges between near-inertial waves and balanced flows

Wind generated near-inertial waves are ubiquitous in the upper ocean. An improved understanding of near-inertial wave dynamics following their excitation in the ocean and their subsequent interaction with mesoscale geostrophic balanced flows is key to decoding oceanic energy flow pathways. In this regard, multiple oceanic data sets accumulated over the past few decades reveal that the relative strength of near-inertial waves and geostrophic balanced eddy fields is highly variable, both geographically and seasonally. Inspired by these observations, we investigate turbulent interactions and energy exchanges between near-inertial waves and balanced flows using freely evolving numerical simulations of the non-hydrostatic Boussinesq equations. Here, we find accelerated vertical propagation and dissipation of the waves in regimes where balanced and wave fields have comparable strengths. In such regimes we also find that near-inertial waves directly extract energy from balanced flows, with O(10%) being the amount of balanced energy loss. In contrast, we find that near-inertial waves transfer energy to balanced flows in regimes where balance-to-wave energy ratio is small, with the gain in balanced energy being dependent on the relative strength of waves. Furthermore, these regimes are characterized by relatively weaker vertical propagation and dissipation of the near-inertial wave field. One of the key outcomes of this study is the demonstration of the lack of a unique direction for near-inertial wave-balanced flow energy transfers. Depending on the balance-to-wave energy ratio, near-inertial waves can act as an energy sink or energy source for the geostrophic balanced flow.

58 GEOSCIENCES↗
DOE OSTI2020

A fully implicit, scalable, conservative nonlinear relativistic Fokker–Planck 0D-2P solver for runaway electrons

Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic ‘runaway’ electrons (~ MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. As such, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker–Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron–ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham–Lorentz–Dirac reaction term. However, our implementation improves on these earlier studies by (1) ensuring exact conservation properties for electron collisions, (2) strictly preserving positivity, and (3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams–Karney potentials, and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗