An in-flight radiography platform to measure hydrodynamic instability growth in inertial confinement fusion capsules at the National Ignition Facility

We note that high fuel–ablator mix was seen in many, but not all, of the NIC implosions.

We have run simulations with the cone down to 150 μm capsule radius, CR ∼ 7.

These (unpublished) modeling studies by N. Meezan et al. suggest this higher sensitivity in the picket is roughly the same for the low- and high-foot pulses, and is believed to be related to processes which occur before the laser spot reaches the hohlraum wall, such as ablation of the plastic window covering the hohlraum laser entrance hole (LEH). The basic correctness of this prescription has been empirically verified by one of us (H. F. Robey) through extensive post-shot modeling studies of VISAR targets.

Shock timing experiments without liquid deuterium have been recently fielded using the same coating strategy to protect from M-band radiation, discussed below. See Ref. 103.

The idea is that optical depths much greater than 2 are equally opaque to the detector. For example, if the average OD is 1.5, we design the perturbation so that the amplitude of the first harmonic at the experiment time is less than 0.5.

A typical outer surface roughness profile is shown in Fig. 3 of Ref. 18. The measured power spectral density of a typical target at mode 60 is around 0.3 nm², corresponding to a characteristic amplitude $4π(0.3)∼2 nm$⁠. The ignition specification for the mode 60 power is 1 nm², for an amplitude of about 3.5 nm. The amplitude (OD) versus time for these initial values may be inferred from Fig. 10 by simply scaling the amplitude of the (3/64) μm curve, which is in the linear regime at 21 ns. For example, if an initial amplitude of (3/64) μm ≈ 47 nm reaches an amplitude (OD) of 0.1 at 21 ns, the amplitude of a 3 nm initial perturbation will have grown to (0.1)(3)/(47) ≈ 0.006, which is below the noise value of 0.01. Also, extrapolating the curves, one can infer that the 3 nm perturbation will be linear for most of the acceleration, even allowing for considerable uncertainty in the growth factor. For instance, even if the growth factor is off by a factor of 15, so that the 3 nm growth is actually represented by the 47 nm calculation, the curves indicate the growth will still be linear until just before peak velocity at 22 ns.

In this example, we simply generate the density profile by simulating a 2xSi capsule, which we then post-process for the different ablator cases. However, in order to actually generate the same density profile with different layered ablators, the drives would need to be different.

We have been unable, so far, to force either mode 60 or 90 to invert in low-foot simulations by simply modifying the simulation in physically reasonable ways. This may be related to our measurement that shows the modes actually do grow positively (see Fig. 14(c)). Following a suggestion by R. Tipton, we are able to force inversion by dropping a number of terms in the radiation diffusion equations, which does not have any physical justification, but is a different way of generating radiographs of inverting scenarios. We have tested the analysis procedure against the radiographs produced from such simulations, as well as simulations using different mode numbers that actually are predicted to invert, in addition to what is discussed in the text.

Because, in this example, the wavelengths of modes 60, λ₆₀ and 90, λ₉₀, are related by λ₆₀ = (3/2)λ₉₀, the distance between markers in Fig. 25 is also consistent with two wavelengths of mode 90, which would imply both modes have grown positively and that the mode 60 marker line is the connection joint. However, this possibility is ruled out if in addition to just the distance between markers, we also examine the spike pattern in between.