G.D. Kerbel

Three-dimensional HYDRA simulations of National Ignition Facility targets*

The performance of a targets designed for the National Ignition Facility (NIF) are simulated in three dimensions using the HYDRA multiphysics radiation hydrodynamics code. [M. Marinak et al., Phys. Plasmas 5, 1125 (1998)] In simulations of a cylindrical NIF hohlraum that include an imploding capsule, all relevant hohlraum features and the detailed laser illumination pattern, the motion of the wall material inside the hohlraum shows a high degree of axisymmetry. Laser light is able to propagate through the entrance hole for the required duration of the pulse. Gross hohlraum energetics mirror the results from an axisymmetric simulation. A NIF capsule simulation resolved the full spectrum of the most dangerous modes that grow from surface roughness. Hydrodynamic instabilities evolve into the weakly nonlinear regime. There is no evidence of anomalous low mode growth driven by nonlinear mode coupling.

Toroidal gyro‐Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes

The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyrokinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro‐Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel three‐dimensional (3‐D) nonlinear ballooning mode representation. The representation is a Fourier transform of a field line following basis (ky’,kx’,z’) with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky’ = 0, kx’ ≠ 0) ‘‘radial modes’’ in s...

Kinetic theory and simulation of multispecies plasmas in tokamaks excited with electromagnetic waves in the ion‐cyclotron range of frequencies

A description of a bounce‐averaged Fokker–Planck quasilinear model for the kinetic description of tokamak plasmas is presented. The nonlinear collision and quasilinear resonant diffusion operators are represented in a form conducive to numerical solution with specific attention to the treatment of the boundary layer separating trapped and passing orbit regions of velocity space. The numerical techniques employed are detailed insofar as they constitute significant departure from those used in the conventional uniform magnetic field case. Examples are given to illustrate the combined effects of collisional and resonant diffusion.

Edge Gyrokinetic Theory and Continuum Simulations

The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five-dimensional (3d2v) gyrokinetic continuum edge-plasma code. (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential and mirror ratio, and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regime with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth–Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the plateau regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL.

Performance of indirectly driven capsule implosions on the National Ignition Facility using adiabat-shaping

A series of indirectly driven capsule implosions has been performed on the National Ignition Facility to assess the relative contributions of ablation-front instability growth vs. fuel compression on implosion performance. Laser pulse shapes for both low and high-foot pulses were modified to vary ablation-front growth and fuel adiabat, separately and controllably. Three principal conclusions are drawn from this study: (1) It is shown that reducing ablation-front instability growth in low-foot implosions results in a substantial (3-10X) increase in neutron yield with no loss of fuel compression. (2) It is shown that reducing the fuel adiabat in high-foot implosions results in a significant (36%) increase in fuel compression together with a small (10%) increase in neutron yield. (3) Increased electron preheat at higher laser power in high-foot implosions, however, appears to offset the gain in compression achieved by adiabat-shaping at lower power. These results taken collectively bridge the space between t...

Hydrodynamics simulations of 2ω laser propagation in underdense gasbag plasmas

Recent 2ω laser propagation and stimulated Raman backscatter (SRS) experiments performed on the Helen laser have been analyzed using the radiation-hydrodynamics code HYDRA [M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, Phys. Plasmas 8, 2275 (2001)]. These experiments utilized two diagnostics sensitive to the hydrodynamics of gasbag targets: a fast x-ray framing camera (FXI) and a SRS streak spectrometer. With a newly implemented nonlocal thermal transport model, HYDRA is able to reproduce many features seen in the FXI images and the SRS streak spectra. Experimental and simulated side-on FXI images suggest that propagation can be explained by classical laser absorption and the resulting hydrodynamics. Synthetic SRS spectra generated from the HYDRA results reproduce the details of the experimental SRS streak spectra. Most features in the synthetic spectra can be explained solely by axial density and temperature gradients. The total SRS backscatt...

ICRF fusion reactivity enhancement in tokamaks

A systematic study of ICRF fusion reactivity enhancement has been conducted, using a new bounce-averaged two-dimensional Fokker-Planck code. Second-harmonic heating of deuterium in a 50–50 DT plasma is assumed, and the results are obtained as a function of background plasma density and temperature. An enhancement factor of ten is achieved at low Q (= fusion power/RF power), which is important for ion-tail diagnostics, but at Q = 0.5 the enhancement is 2. Significant poloidal variations in ion density (up to 14%) and in fusion reactivity (by a factor up to 2.5) are found.

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications

Three models for nonlocal electron thermal transport are here compared against Vlasov-Fokker-Planck (VFP) codes to assess their accuracy in situations relevant to both inertial fusion hohlraums and tokamak scrape-off layers. The models tested are (i) a moment-based approach using an eigenvector integral closure (EIC) originally developed by Ji, Held, and Sovinec [Phys. Plasmas 16, 022312 (2009)]; (ii) the non-Fourier Landau-fluid (NFLF) model of Dimits, Joseph, and Umansky [Phys. Plasmas 21, 055907 (2014)]; and (iii) Schurtz, Nicolai, and Busquets [Phys. Plasmas 7, 4238 (2000)] multigroup diffusion model (SNB). We find that while the EIC and NFLF models accurately predict the damping rate of a small-amplitude temperature perturbation (within 10% at moderate collisionalities), they overestimate the peak heat flow by as much as 35% and do not predict preheat in the more relevant case where there is a large temperature difference. The SNB model, however, agrees better with VFP results for the latter problem if care is taken with the definition of the mean free path. Additionally, we present for the first time a comparison of the SNB model against a VFP code for a hohlraum-relevant problem with inhomogeneous ionisation and show that the model overestimates the heat flow in the helium gas-fill by a factor of ?2 despite predicting the peak heat flux to within 16%.

Three-dimensional simulations of electron cyclotron heating

Many heating problems in tokamaks are inherently three-dimensional, involving the velocity coordinates parallel and perpendicular to the ambient magnetic field and the plasma radial coordinate. We will describe a new three-dimensional, Fokker-Planck/rf quasilinear code. This code is based upon a two-dimensional in velocity space Fokker-Planck code which solves for the distribution evaluated at the outer equatorial plane (π = 0) of each flux surface in radial mesh. The rf energy density ϵk satisfies the transport equation ▿·(νgϵk)= −Pabs , where νg is the group velocity of the ordinary or extraordinary wave and pABS is power absorption obtained using results of the Fokker-Planck code. The rf quasilinear operator is a functional of the wave polarization. Warm plasma relations are used for the group velocity and polarizations. With knowledge of Pabs, the transport equation is employed to obtain ϵk, which is used update the quasilinear diffusion coefficients and resume the Fokker-Planck calculation on the various flux surfaces. The procedure of alternately solving the Fokker-Planck equation and the transport equation is repeated to steady state.

Three‐dimensional model of electron cyclotron heating

To address heating problems in tokamaks, we have implemented a 3‐D Fokker‐Planck/rf code. This code uses a 2‐D bounce‐averaged Fokker‐Planck package to solve for the distribution on a radial mesh. The rf energy density ξk is determined as a solution to a transport equation involving the local power absorption and the group velocity of the wave. Once ξk is determined it is used to update the quasi‐linear diffusion coefficients and resume the Fokker‐Planck calculation. A fast procedure for simulating a tokamak diagnostic, the soft‐x‐ray analyzer, is presented.