Simulation of self-generated magnetic fields in an inertial fusion hohlraum environment

Abstract

We present radiation-hydrodynamic simulations of self-generated magnetic field in a hohlraum, which show an increased temperature in large regions of the underdense fill. Non-parallel gradients in electron density and temperature in a laser-heated plasma give rise to a self-generated field by the “Biermann battery” mechanism. Here, HYDRA simulations of three hohlraum designs on the National Ignition Facility are reported, which use a partial magnetohydrodynamic (MHD) description that includes the self-generated source term, resistive dissipation, and advection of the field due to both the plasma flow and the Nernst term. Anisotropic electron heat conduction parallel and perpendicular to the field is included, but not the Righi-Leduc heat flux. The field strength is too small to compete significantly with plasma pressure, but affects plasma conditions by reducing electron heat conduction perpendicular to the field. Significant reductions in heat flux can occur, especially for high Z plasma, at modest values of the Hall parameter, Ωeτei≲1, where Ωe=eB/mec and τei is the electron-ion collision time. The inclusion of MHD in the simulations leads to 1 keV hotter electron temperatures in the laser entrance hole and high-Z wall blowoff, which reduces inverse-bremsstrahlung absorption of the laser beam. This improves propagation of the inner beams pointed at the hohlraum equator, resulting in a symmetry shift of the resulting capsule implosion towards a more prolate shape. The time of peak x-ray production in the capsule shifts later by only 70 ps (within experimental uncertainty), but a decomposition of the hotspot shape into Legendre moments indicates a shift of P2/P0 by ∼20%. This indicates that MHD cannot explain why simulated x-ray drive exceeds measured levels, but may be partially responsible for failures to correctly model the symmetry.

Extended-magnetohydrodynamics in under-dense plasmas

“…By changing the laser spot radius and keeping the intensity constant, the experiment could be scaled into the non-local transport regime, increasing the relevance of the measurements to laser-plasma interaction regimes in ICF drive 5,6,26 and MagLIF pre-heat 1 . A further investigation of this transition will be the subject of a further publication comparing kinetic and MHD results.…”

“…Even initially unmagnetised ICF configurations can be affected by extended-MHD phenomena, with self-generated fields growing through the Biermann battery process. Simulation studies have found the Nernst (magnetic fields moving down temperature gradients) and Righi-Leduc (heat-flow deflected by the magnetic field) terms to change plasma properties in hohlraums (increasing the temperature of the hohlraum gas fill 5 ), direct-drive ablation fronts (changing the perturbation growth 6 ) and at the compressed fusion-fuel edge (modifying the cooling process 7 ). In addition to a) Electronic mail: c.walsh14@imperial.ac.uk ICF, extended-MHD affects laboratory astrophysics experiments, such as the measurement of magnetic fields generated around laser-foil interactions 8,9 and are anticipated to also affect 2-spot magnetic reconnection 10 .…”

Developing an Experimental Basis for Understanding Transport in NIF Hohlraum Plasmas

“…We conclude that under simplified conditions, nonlocality can in principle account for the observations, but in reality it may play a complementary role and other contributing processes should be considered, most notably magnetic fields [7,8]. MHD simulations suggest the ∇n e × ∇T e mechanism will generate magnetic fields strong enough to inhibit heat flow between the dots.…”

“…Highly averaged atomic models for calculating ionization balance provide results of comparable accuracy to detailed models but at much lower computational cost [6]. Magnetohydrodynamic (MHD) effects are generally modeled using a fluid expression of Ohm's law [7,8] but models which include both MHD and flux-limited heat transport are not readily available or tested. The lack of experimental data available for testing each of these reduced models presents a significant need in HED physics.…”

“…We find that the three temperature measurements are initially consistent with classical (SH) heat transport; later in time, the higher temperature region near the laser entrance hole (LEH) indicates reduced heat transport. We discuss the role of kinetic effects (non-local transport [5]), laser-generated magnetic fields [7] and instabilities [15] in accounting for the observations. Figure 1 (a) shows a sketch of the gold (Au) "View-Factor" hohlraum [16] used for measurements with the shows the streaked spectral data for the dot on film experiment; the labels indicate Mn and Co w (1s2p 1 P1 -1s 2 1 S0), y (1s2p 3 P1 -1s 2 1 S0) and Lyα (2p…”