Measuring the Asymptotic Behavior of Self-Generated B Magnetic Fields in a Hohlraum Geometry

John Moody | 17-ERD-084


We used experiments and computational modeling to characterize the self-generated B magnetic fields produced by lasers illuminating a gold cylindrical ring target. Using four laser shots, a ring target oriented with its axis along the laser chamber's axis was illuminated on the inside surface. Protons at 14.7 and 3.1 MeV (generated by imploding a D 3 He spherical capsule) were used to measure the deflection caused by the magnetic and electric fields. The protons were timed to arrive at the ring target at 4 ns and 4.5 ns. Measurements showed magnetic fields of about 1 MG and a significant difference in the proton deflection images for the four shots. Simulations of a gold cylindrical ring target using Hydra computational fluid dynamics code (Marinak et al. 2001) with magnetohydrodynamics (MHD) terms, combined with data obtained from proton simulations, exhibited similarities to the experimental data and indicated that electrical field effects are approximately 1% of the magnetic field effects.

Background and Research Objectives

Energy and particle transport in inertial confinement fusion hohlraums and other laboratory and astrophysical plasmas typically use reduced physics models to simplify computation (Barrios et al. 2018). These computational models use approximations of the laser-generated magnetic fields, non-local thermal transport, turbulence, and instabilities. One simplified thermal transport model uses a flux limiter (f) to generate an approximate model of the non-classical transport physics. These reduced models are successfully generated in some situations but not in others. A strategy for improving the performance of reduced models uses well-defined experiments to adjust and modify the models, making them useful in broader circumstances.

A number of experiments have shown that when mid-intensity lasers are incident upon a solid target, "Biermann" magnetic fields are generated (Rosenberg et al. 2015). In addition, the presence of magnetic induction fields (or "B-fields") in a plasma has been seen (in simulations and experiments) to affect heat transport. Simulations of hohlraum plasmas that include MHD effects show that B-fields in a hohlraum reach the 1-MG level and affect heat transport in a way that significantly modifies the hohlraum plasma conditions (Jones et al. 2017, Strozzi et al. 2017, Farmer et al. 2017). Experiments on the Omega laser (Li et al. 2010) to characterize these fields showed that the geometry caused the proton trajectories to be primarily sensitive to electric fields generated by plasma-density gradients.

Within the context of these results, we proposed to build off of Li's findings (Li et al. 2010) by quantifying the magnitude and topology of laser-generated magnetic fields at later times (2 ns). A key difference in laser-generated magnetic field measurements on the National Ignition Facility (NIF) is that long laser pulses enable measurements of the fields later in time after resistive diffusion and Nernst advection have had time to develop.

The original goal of this project was to use experiments and computational modeling to test the hypothesis that self-generated magnetic field dynamics in a hohlraum-like (i.e., ring) geometry is dominated by Nernst advection rather than frozen-in advection at long periods of time (2 ns). The experimental evidence for this was expected to come from proton deflection images and would show that magnetic fields should concentrate near the walls of the ring. The modeling was planned to provide a way to test the importance of the MHD terms in matching the measurements.

We conducted four NIF experiments that acquired proton deflection data. The first two experiments used a single proton source and an aluminum and a gold ring placed side by side; the timing of the proton flash was changed by about 1 ns between the two experiments. The next two experiments used a single gold ring. These experiments showed significant differences in the proton images for the upper compared to the lower laser illumination. HYDRA-based simulations of aluminum rings with proton backlighting also showed significant differences in the proton images for the upper and lower laser drives. The simulations included self-generated magnetic fields and estimated electrical fields from the electron pressure gradient.

A secondary goal of this project was to investigate the efficiency of amplifying a seed magnetic field using a cylindrical or spherical implosion in a future experiment. The motivation for this was to achieve super-high-intensity magnetic fields for studies of exotic magnetized high-energy-density (HED) plasmas and atomic physics. Magnetized liner inertial fusion simulations show that there is significant magnetic field "leakage" during magnetic field amplification in a cylindrical relative to a spherical geometry. This is important to understand the efficiency of magnetized hohlraum implosions as well as magnetic field amplification. Understanding the physics differences in these two cases could provide an opportunity to characterize the role of resistive diffusion and Nernst advection in magnetic field amplification. Initial design of spherical and cylindrical magnetic field amplification experiments was done, and simulations investigating the cause of high magnetic field leakage in the cylindrical case were also completed. The simulation results will be published in the future.

Impact on Mission

Our research supports the advancement of the science, technology, and engineering competencies that are the foundation of the NNSA missions. It also supports Lawrence Livermore National Laboratory's core competency in HED science. This research has initiated an effort to characterize the amplitude and topology of magnetic fields in cylindrical geometry such as that used in targets for indirect-drive inertial confinement fusion at the NIF. It also adds to our understanding of proton-deflection measurements, which is a key diagnostic technique for magnetic field characterization in HED plasmas.


We intend to propose a second phase of this research that will involve adding an externally applied seed B-field of about 30 to 40 Tesla and measuring the effect of this external field on the development and advection of self-generated B-fields. This seed field is planned to be available on the NIF in early 2019.


Barrios, M. A., et al. 2018. "Developing an Experimental Basis for Understanding Transport in NIF Hohlraum Plasmas." Physical Review Letters 121(9): 095002. doi: 10.1103/PhysRevLett.121.095002.

Farmer, W. A., et al. 2017. "Simulation of Self-Generated Magnetic Fields in an Inertial Fusion Hohlraum Environment." Physics of Plasmas 24(5): 052703. doi: 10.1063/1.4983140.

Jones, O. S., et al. 2017. "Progress Towards a More Predictive Model for Hohlraum Radiation Drive and Symmetry." Physics of Plasmas 24(5): 056312. doi: 10.1063/1.4982693.

Li, C. K., et al. 2010. "Charged-Particle Probing of X-Ray–Driven Inertial-Fusion Implosions." Science 327(5970): 1231–35. doi: 10.1126/science.1185747.

Marinak, M. M. 2001. "Three-Dimensional HYDRA Simulations of National Ignition Facility Targets." Physics of Plasmas 8(5): 2275–80. doi: 10.1063/1.1356740.

Rosenberg, M. J., et al. 2015. "Slowing of Magnetic Reconnection Concurrent with Weakening Plasma Inflows and Increasing Collisionality in Strongly Driven Laser-Plasma Experiments." Physical Review Letters 114(20): 205004. doi: 10.1103/PhysRevLett.114.205004.

Strozzi, D. J., et al. 2017. "Interplay of Laser-Plasma Interactions and Inertial Fusion Hydrodynamics." Physical Review Letters 118(2): 025002. doi: 10.1103/PhysRevLett.118.025002.