Layering of inertial confinement fusion targets in microgravity environments

Abstract

A critical concern in the fabrication of targets for inertial confinement fusion is ensuring that the hydrogenic (D2 or DT) fuel layer maintains spherical symmetry. Because of gravitationally induced sagging of the liquid prior to freezing, only relatively thin (<10 μm) layers of solid fuel can be produced by fast refreeze methods. One method to reduce the effective gravitational field environment is free-fall insertion into the target chamber. Another method to counterbalance the gravitational force is to use an applied magnetic field combined with a gradient field to induce a magnetic dipole force (Fm) on the liquid fuel layer. For liquid deuterium, the required B⋅∇B product to counterbalance the gravitational force (Fg) is ∼10 T2/cm. In this paper, we examine the time-dependent dynamics of the liquid fuel layer in a reduced gravitational field environment. We employ an energy method which takes into account the sum of the free energy associated with the surface tension forces, net vertical force [F=Fm−Fg (in the case of magnetic field-assisted microgravity) or FD (the drag force in the case of free fall)], London–van der Waals forces, the kinetic energy of motion and viscous dissipation. By assuming that the motions are incompressible and irrotational, the volume integrals of the free energies over the deformed liquid fuel layer may be converted to surface integrals. With the surface expressed as the sum of Legendre polynomials, rsurface=a+∑al(t)Pl(μ), the perturbed amplitude of the individual modes, al(t) can be obtained. We show that the l=1 vertical shift mode takes the longest to damp out, and may be problematic for free-fall insertion even for thin ∼1 μm overfilled foam targets. For a given liquid fuel layer thickness Δ, the equilibrium value of a1/a (the concentricity of the inner fuel layer) is shown to be dependent on the net vertical force F and layer thickness, i.e., a1∼FΔ5, but independent of the surface tension.