Spherical compression of an applied magnetic field in inertial confinement fusion

Abstract

Applying an external magnetic field to laser-driven inertial confinement fusion implosions is a promising approach for enhancing fusion yield. The field is compressed with the plasma, producing a magnetized hotspot that anisotropically suppresses thermal losses and traps alpha particles, making performance sensitive to the compressed field orientation. We derive a simple, readily applicable analytic model that enables rapid evaluation of the compressed field topology and show that ablation into the hotspot amplifies the central field, while the ablated ice near the hotspot edge develops a decaying, radially bent field, with a discontinuity in the field direction. The radially bent field renders thermal insulation at the hotspot edge negligible and largely independent of the applied field strength, whereas insulation in the hotspot core still depends strongly on the applied field. Applying the model to non-axial initial field configurations, we find that an initially applied mirror field provides the greatest suppression, followed by the standard axial field.

Figures (8)

• Figure 1: (Top) Magnetic field profile at peak compression (7.5 ns) resulting from applying the advection-only model (Eq. \ref{['eq:evolutionBcyl']}) to NIF Symcap N210607 with an axial applied field. The inner and outer shell boundaries are marked with orange lines. Field lines are shown in white, with background heatmap showing the field magnitude in kT. (Bottom) Field model variables $R_0/R_f$ (convergence ratio, blue) and $\alpha$ (bending parameter, red) used in the model, determined using a 1D HYDRA simulation. The vertical orange line represents the shell inner boundary.
• Figure 2: Convergence ratio ($R_0/R_f$, left) and field bending parameter ($\alpha$, right) at peak compression from a 1D simulation of DT-layered shot N210808. The vertical lines correspond to the gas/ablated ice interface (purple dashed line) and the hotspot/shell interface (orange solid line).
• Figure 3: Magnetic field profiles at peak compression (9.11 ns) for modeling and simulation of NIF DT-layered shot N210808 with a 26 T applied axial field. The colormap corresponds to the field magnitude (in kT) and streamlines show the field direction. Axis units are in $\mathrm{\mu m}$. Yellow contours show the position of the shell as a contour of the density $\rho_\mathrm{max}/e$. Results correspond to (left) the advection-only analytic model from Eq. \ref{['eq:evolutionBcyl']}, and (right) with feedback on the implosion through the ${\boldsymbol{J}} \times {\boldsymbol{B}}$ force and field evolution from Nernst advection and resistive diffusion. Neither panel includes anisotropic thermal conduction or alpha-particle deposition.
• Figure 4: Magnetic field profiles for N210808-like asymmetrically-compressed implosions, found by numerically integrating Eqs. \ref{['eq:conservationBr']} and \ref{['eq:conservationBtheta']} with prescribed asymmetry given by Eq. \ref{['eq:shellasymmetry']}.
• Figure 5: Magnetic field profiles and coil diagrams for five field topologies explored in this section. Streamlines show the magnetic field direction and are color-coded to the field strength (in T). Fields are superimposed on a N210808-sized hohlraum (black rectangle) and initial capsule (blue circle). Red and green patches correspond to the solenoidal coil locations (radius, height, and position), while the color designates the current flow direction (red for counterclockwise, green for clockwise). For the mirror field, the center coil has 85% the current of the outer coils, and the center coil of the anti-mirror has 200% the current of its outer coils.