Near Stochastic Resonance between Surface Perturbations Could Cause Imploding Shell Breakup of an Inertial Confinement Fusion Target

Bedros Afeyan
Polymath Research, Inc.

To make inertial confinement fusion work, a mm scale spherical thin shell must be imploded at high velocity, driven by shock waves initiated by radiation pressure. The capsule will have tiny yet numerous manufacturing imperfections on its surface which will be amplified in the process of implosion due to a multitude of hydrodynamic instabilities such as Rayleigh-Taylor. While of the order of nanometer height individual bumps or dimples can not cause much damage at the modes with the largest growth factors (which are factors of 40 or more lower in mode number than the scale of the individual bumps), collectively, when there are 100's or 1000's of them scattered around the target, they could cause the shell to break up. This collective behavior is an example of a near stochastic resonance having to do with the location and orientation correlations between the bumps mimicking a significantly enhanced seed of a much lower order mode. The question is how to asses the scaling with number of bumps, N, where purely randomly phased bumps would suggest ~ square root of N scaling, while fully correlated ones an ~ N scaling. We will show how surface-imperfection-capturing phase shifting spherical diffractive interferometric (PSSDI) images of actual shells can be (wavelet) denoised, decluttered and then stitched together (isolating the bump structure) to assess this problem and show how CH shells could be susceptible to breakup far more so than Beryllium and Diamond shells. We will also show how this analysis would lead to erroneous conclusions if the denoising and decluttering steps were skipped (due to the curse of measurement artifacts).

Work sponsored by Lawrence Livermore National Laboratory and General Atomics, and in collaboration with Mathieu Charbonneau-Lefort and Marine Mardirian of PRI, Evan Mapoles and Steve Haan of LLNL and Abbas Nikroo of GA.

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