DDI 3.3: High-gain wetted-foam target design Progress with high-resolution AMR wetted-foam simulations. • Two issues are central: the role of density fluctuations at the ablation surface, shock speed. • The new material tracking routines show a short mixing length. • Simulations modeling the CH ablator show agreement with Rankine-Hugoniot jump conditions.
A single fiber is subject to the Richtmyer-Meshkov and Kelvin-Helmholtz instabilities • The primary instability is Richtmyer-Meshkov, which generates a pair of vortices as the shock passes the fiber.
A lone fiber is “destroyed” in ~13 ps, or about 3 fiber-crossing times. • A characteristic hydrodynamic time scale is the shock-crossing time tc of the fiber. • The fiber is accelerated to the speed of the DT in about ~2tc, or ~8 ps. • 75% of the fiber mass lies outside its original boundaries after ~3tc, or ~13 ps.
The fiber destruction time depends on the ratio of fiber density to fluid density • For a larger density ratio: • the Atwood number is higher and the Richtmyer-Meshkov instability is increased • The velocity shear between the fiber and DT is greater, resulting in greater Kelvin-Helmholtz instability 40:1 density ratio
Identification of the CH as a second material type provides a measure of mixing
Tagging a single fiber as a third material shows the degree of mixing • Any cell with over 10 mg/cc of the “tagged” material is colored red.
Fourier decomposition of the tracer mass fraction shows a mixing length of ~1.3 mm • The average e-folding distance for decay of the mass-fraction fluctuations is ~1.3 mm.
Shocks reflected from the fibers raise the pressure, elevating the post-shock pressure • The higher pressure results in an elevated shock speed relative to a shock in a uniform field of the same average density, with the same inflow pressure.
When the CH ablator is included, the Rankine-Hugoniot jump conditions are satisfied • These targets will be fabricated with a thin plastic overcoat. • The post-shock conditions are the same as in the average case with the same pusher. • On average the Rankine-Hugoniot conditions are obeyed, and the shock speeds are the same. • An average treatment of density, as in LILAC, is accurate.
The fiber destruction time depends on the ratio of the fiber density to the fluid density 4 ps 8 ps 12 ps 40:1 4:1
The fiber-resolved simulations behave, on average, like the equivalent 1-D simulation
Shocks reflected from the foam fibers elevate the post-shock pressure. • The main shock is partially reflected off the foam fibers. • The reflected shocks make their way though the mix region, eventually crossing the ablation surface and entering the corona. • Conservation of mass requires the density in the mix region match the post-shock speed. • Since a ~ log(p / r5/3), the post-shock adiabat is higher by dp / p ~ ??.
The fiber destruction time depends on the ratio of fiber density to fluid density • For a larger density ratio: • the Atwood number is lower and the Richtmyer-Meshkov instability is increased • The velocity shear between the fiber and DT is greater, resulting in greater Kelvin-Helmholtz instability
Artificial viscosity is modeled in BEARCLAW by splitting the contact discontinuity • The Riemann problem at a cell boundary is solved with three waves: shock, rarefaction (collapsed to a midpoint line) and contact discontinuity (CD). • Eulerian codes are subject to the growth of noise due to discretization. • These are eliminated in BEARCLAW by splitting the CD from a sharp transition to a smooth transitional region. • For appropriate values of the artificial viscosity, the shock speed is not affected.