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Plasma transport in an Eulerian AMR code

A plasma transport model has been implemented in an Eulerian AMR radiation-hydrodynamics code, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions to flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 μm and smaller for viscous effects to appear and 10 μm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more Lagrangian-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an Eulerian computation of complex and dynamically evolving mix regions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Continuum kinetic modelling of cross-separatrix plasma transport in a tokamak edge including self-consistent electric fields

Eulerian kinetic calculations are presented here for the axisymmetric cross-separatrix plasma transport at the edge of a tokamak. The simulations are performed with a high-order finite volume code COGENT, which solves the long-wavelength limit of the full-f ion gyrokinetic equation including the non-linear Fokker–Plank collision model. Self-consistent 2D electrostatic potential variations are obtained from the quasi-neutrality (∇·j = 0) equation coupled to an isothermal fluid electron response. Finally, illustrative solutions presented for parameters characteristic of the DIII-D tokamak show qualitative agreement with experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fully kinetic simulations of strong steady-state collisional planar plasma shocks

We report on simulations of strong, steady-state collisional planar plasma shocks with fully kinetic ions and electrons, independently confirmed by two fully kinetic codes (an Eulerian continuum and a Lagrangian particle-in-cell). While kinetic electrons do not fundamentally change the shock structure as compared with fluid electrons, we find an appreciable rearrangement of the preheat layer, associated with nonlocal electron heat transport effects. The electron heat-flux profile qualitatively agrees between kinetic- and fluid-electron models, suggesting a certain level of “stiffness,” though substantial nonlocality is observed in the kinetic heat flux. We also find good agreement with nonlocal electron heat-flux closures proposed in the literature. Finally, in contrast to the classical hydrodynamic picture, we find a significant collapse in the “precursor” electric-field shock at the preheat layer leading edge, which correlates with the electron-temperature gradient relaxation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Investigating profile stiffness and critical gradients in shaped TCV discharges using local gyrokinetic simulations of turbulent transport

The experimental observation made on the TCV tokamak of a significant confinement improvement in plasmas with negative triangularity ( δ < 0) compared to those with standard positive triangularity has been interpreted in terms of different degrees of profile stiffness (Sauter et al. Phys. Plasmas 21 055906, 2014) and/or different critical gradients. Employing the Eulerian gyrokinetic code GENE (Jenko et al. Phys. Plasmas 7 1904, 2000), profile stiffness and critical gradients are studied under TCV relevant conditions. For the considered experimental discharges, trapped electron modes (TEMs) and electron temperature gradient (ETG) modes are the dominant microinstabilities, with the latter providing a significant contribution to the non-linear electron heat fluxes near the plasma edge. Two series of simulations with different levels of realism are performed, addressing the question of profile stiffness at various radial locations. Retaining finite collisionality, impurities and electromagnetic effects, as well as the physical electron-to-ion mass ratio are all necessary in order to approach the experimental flux measurements. However, flux-tube simulations are unable to fully reproduce the TCV results, pointing towards the need to carry out radially nonlocal (global) simulations, i.e. retaining finite machine size effects, in a future study. Some conclusions about the effect of triangularity can nevertheless be drawn based on the flux-tube results. In particular, the importance of considering the sensitivity to both temperature and density gradient is shown. The flux tube results show an increase of the critical gradients towards the edge, further enhanced when δ < 0, and they also appear to indicate a reduction of profile stiffness towards plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The development of a high-resolution Eulerian radiation-hydrodynamics simulation capability for laser-driven Hohlraums

Hohlraums are hollow cylindrical cavities with high-Z material walls used to convert laser energy into uniform x-ray radiation drives for inertial confinement fusion capsule implosions and high energy density physics experiments. Credible computational modeling of hohlraums requires detailed modeling and coupling of laser physics, hydrodynamics, radiation transport, heat transport, and atomic physics. We report on improvements to Los Alamos National Laboratory's xRAGE radiation-hydrodynamics code in order to enable hohlraum modeling. xRAGE's Eulerian hydrodynamics and adaptive mesh refinement make it uniquely well suited to study the impacts of multiscale features in hohlraums. In order to provide confidence in this new modeling capability, we demonstrate xRAGE's ability to produce reasonable agreement with data from several benchmark hohlraum experiments. We also use xRAGE to perform integrated simulations of a recent layered high density carbon capsule implosion on the National Ignition Facility in order to evaluate the potential impacts of the capsule support tent, mixed cell conductivity methodologies, plasma transport, and cross-beam energy transfer (XBT). We find that XBT, seeded by plasma flows in the laser entrance hole (LEH), causes a slight decrease in energy coupling to the capsule and that all of these impact the symmetry of the x-ray drive such that they have an appreciable impact on the capsule implosion shape.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

LOKI

LOKI is a simulation code that models weakly-coupled plasma evolution using Eulerian kinetic models in four phase space dimensions. The code is useful to understand basic plasma nonlinear plasma physics phenomena - in particular, wave-particle and wave-wave resonances that occur in laser plasma interactions. LOKI can simulate fundamental physical process in low-density plasmas on a scale of hundreds of light wavelengths. It does so by solving the Vlasov and Valsov-Fokker-Planck differential transport equations describing the collision less and low-collisionality evolution of charged particles in electromagnetic fields in two configuration space and two velocity space dimensions. Two principle electromagnetic models are provided: electrostatic (Poisson's Equation) and electromagnetic (Maxwell's equations).

Banks, Jeffrey↗

LOKI

LOKI is a simulation code that models weakly-coupled plasma evolution using Eulerian kinetic models in four phase space dimensions. The code is useful to understand basic plasma nonlinear plasma physics phenomena - in particular, wave-particle and wave-wave resonances that occur in laser plasma interactions. LOKI can simulate fundamental physical process in low-density plasmas on a scale of hundreds of light wavelengths. It does so by solving the relativistic Vlasov and Valsov-Fokker-Planck differential transport equations describing the collision less and low-collisionality evolution of charged particles in electromagnetic fields in two configuration space and two velocity space dimensions. Two principle electromagnetic models are provided: electrostatic (Poisson's Equation) and electromagnetic (Maxwell's equations).

DIMITS, ANDRIS↗

Simulations of radiatively cooled magnetic reconnection driven by pulsed power

Magnetic reconnection is an important process in astrophysical environments, as it reconfigures magnetic field topology and converts magnetic energy into thermal and kinetic energy. In extreme astrophysical systems, such as black hole coronae and pulsar magnetospheres, radiative cooling modifies the energy partition by radiating away internal energy, which can lead to the radiative collapse of the reconnection layer. In this paper, we perform two- and three-dimensional simulations to model the MARZ (Magnetic Reconnection on Z) experiments, which are designed to access cooling rates in the laboratory necessary to investigate reconnection in a previously unexplored radiatively cooled regime. These simulations are performed in GORGON, an Eulerian two-temperature resistive magnetohydrodynamic code, which models the experimental geometry comprising two exploding wire arrays driven by 20 MA of current on the Z machine (Sandia National Laboratories). Radiative losses are implemented using non-local thermodynamic equilibrium tables computed using the atomic code Spk, and we probe the effects of radiation transport by implementing both a local radiation loss model and P 1/3 multi-group radiation transport. The load produces highly collisional, super-Alfvénic (Alfvén Mach number M A ≈ 1.5), supersonic (Sonic Mach number M S ≈ 4–5) strongly driven plasma flows which generate an elongated reconnection layer (Aspect Ratio L/δ≈100 , Lundquist number S L ≈ 400). The reconnection layer undergoes radiative collapse when the radiative losses exceed the rates of ohmic and compressional heating (cooling rate/hydrodynamic transit rate = τ$^{–1}_{cool}$/τ$^{–1}_{H}$ ≈100); this generates a cold strongly compressed current sheet, leading to an accelerated reconnection rate, consistent with theoretical predictions. Lastly, the current sheet is also unstable to the plasmoid instability, but the magnetic islands are extinguished by strong radiative cooling before ejection from the layer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Mixing with applications to inertial-confinement-fusion implosions

Approximate one-dimensional (1D) as well as 2D and 3D simulations are playing an important supporting role in the design and analysis of future experiments at National Ignition Facility. This work is mainly concerned with 1D simulations, used extensively in design and optimization. We couple a 1D buoyancy-drag mix model for the mixing zone edges with a 1D inertial confinement fusion simulation code. This analysis predicts that National Ignition Campaign (NIC) designs are located close to a performance cliff, so modeling errors, design features (fill tube and tent) and additional, unmodeled instabilities could lead to significant levels of mix. The performance cliff we identify is associated with multimode plastic ablator (CH) mix into the hot-spot deuterium and tritium (DT). The buoyancy-drag mix model is mode number independent and selects implicitly a range of maximum growth modes. Our main conclusion is that single effect instabilities are predicted not to lead to hot-spot mix, while combined mode mixing effects are predicted to affect hot-spot thermodynamics and possibly hot-spot mix. Combined with the stagnation Rayleigh-Taylor instability, we find the potential for mix effects in combination with the ice-to-gas DT boundary, numerical effects of Eulerian species CH concentration diffusion, and ablation-driven instabilities. With the help of a convenient package of plasma transport parameters developed here, we give an approximate determination of these quantities in the regime relevant to the NIC experiments, while ruling out a variety of mix possibilities. Plasma transport parameters affect the 1D buoyancy-drag mix model primarily through its phenomenological drag coefficient as well as the 1D hydro model to which the buoyancy-drag equation is coupled.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magnetohydrodynamic MACH Code Used to Simulate Magnetoplasmadynamic Thrusters

The On-Board Propulsion program at the NASA Glenn Research Center is utilizing a state of-the-art numerical simulation to model the performance of high-power electromagnetic plasma thrusters. Such thrusters are envisioned for use in lunar and Mars cargo transport, piloted interplanetary expeditions, and deep-space robotic exploration of the solar system. The experimental portion of this program is described in reference 1. This article describes the numerical modeling program used to guide the experimental research. The synergistic use of numerical simulations and experimental research has spurred the rapid advancement of high-power thruster technologies for a variety of bold new NASA missions. From its inception as a U.S. Department of Defense code in the mid-1980's, the Multiblock Arbitrary Coordinate Hydromagnetic (MACH) simulation tool has been used by the plasma physics community to model a diverse range of plasma problems--including plasma opening switches, inertial confinement fusion concepts, compact toroid formation and acceleration, z-pinch implosion physics, laser-target interactions, and a variety of plasma thrusters. The MACH2 code used at Glenn is a time-dependent, two-dimensional, axisymmetric, multimaterial code with a multiblock structure. MACH3, a more recent three-dimensional version of the code, is currently undergoing beta tests. The MACH computational mesh moves in an arbitrary Lagrangian-Eulerian (ALE) fashion that allows the simulation of diffusive-dominated and dispersive-dominated problems, and the mesh can be refined via a variety of adaptive schemes to capture regions of varying characteristic scale. The mass continuity and momentum equations model a compressible viscous fluid, and three energy equations are used to simulate nonthermal equilibrium between electrons, ions, and the radiation field. Magnetic fields are modeled by an induction equation that includes resistive diffusion, the Hall effect, and a thermal source for magnetic fields. Various models of plasma resistivity are included, along with ablation models and multiport circuit solvers. The set of equations is closed using either an ideal gas or real equation of state.

Mikellides, Pavlos G.↗

Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry

Tenth-order compact difference code Miranda is utilized to perform large-eddy simulation (LES) of a hydrogen gas–plastic mixing layer in a spherical geometry. Once the mixing layer has achieved self-similar growth, it is heated to 1 keV, and the second-order arbitrary Lagrangian-Eulerian (ALE) code Ares is used to simulate mixing layer evolution as it undergoes thermonuclear (TN) burn. Both premixed (in which deuterium and tritium are initially present in the gas) and nonpremixed (in which deuterium is initially present only in the plastic) variants are considered at Atwood numbers 0.05 and 0.50. The effect of turbulent mixing on mean TN reaction rate is examined, and a four-equation k – L – a – V Reynolds-averaged Navier-Stokes (RANS) model is presented. The k – L – a – V model, which represents an extension of the k – L – a model [Morgan and Wickett, Phys. Rev. E 91, 043002 (2015)] by the addition of a transport equation for the scalar mass fraction variance, is then applied in one-dimensional simulations of the reacting mixing layer under consideration. Excellent agreement is gained between LES and RANS in total TN neutron production when fluctuations in reaction cross-section can be neglected.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Hot electron preheat effects in two-photon polymerization plastic lattice laser-driven shock-tube experiments on the OMEGA laser

We present simulations of Omega shock tube experiments designed to investigate hot electron preheat effects in 3D-printed, two-photon polymerization (2PP) plastic lattices. Preheat is inferred in the experiments from the expansion of a plastic witness disk embedded in the lattice. Using the Eulerian radiation-hydrodynamics code xRAGE, we model shock propagation and preheat from both radiative and hot electron energy sources to evaluate their relative impact. To simulate the transport of laser-generated hot electrons, the nonlocal electron heat transport model proposed by Schurtz, Nicolaï, and Busquet (SNB) is extended with a hot electron source term and an energy cascade algorithm. We explore how variations in ablator, lattice geometry, and laser drive affect the shock velocity and witness disk expansion. Simulations show that the inclusion of a 5 μm gold layer reduces shock pressure by 60% and shock speeds by 30%–40% but does not significantly reduce the hot electron preheat, and that different lattice geometries lead to enhanced shock velocities—up to 40% faster than in homogeneous foams. However, radiative and conductive preheat from classical mechanisms alone fail to match experiment. By including a hot electron source term, we reproduce experimental observables such as disk expansion rates and spatial radiographic features. We find that a hot electron population corresponding to 4%–8% of the incident laser energy with T hot = 50 keV produces expansion which agrees with the experimental data, suggesting hot electron preheat is the most plausible explanation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗