Progress report on analytic and numerical studies of x-ray-induced impulse
In a variety of high-energy-density (HED) systems, x-rays of a given energy are used to generate shockwaves, bulk motion, and impulse in materials. As radiation energy is deposited within the material, the material is heated. The number of photons of a certain wavelength absorbed is determined by the spectral intensity of the radiation and the material’s opacity evaluated at that wavelength. This heating results in a pressure increase dictated by the material’s equation of state. Depending on the intensity of the absorbed radiation, it may also cause the material to change phase into a liquid, gas, or plasma. The increased pressure drives the heated surface layer to blow off, imparting impulse and sending a compressive wave into the bulk of the material. Additionally, the compression wave interacts with the solid boundary of the material, resulting in a tensile wave that may cause the material to spall. The impulse generated by the deposition of x-ray energy within the sample can be modeled using purely analytical methods, e.g. the Bethe, Bade, Averell, and Yost (BBAY) model. However, the blow-off process is rather complicated, and proper modeling efforts must account for material ejected by spallation, vaporization, jetting, and plasma ablation. For this reason, analytical models have an unclosed term describing the final energy of the blown-off material Ef(z). Prior modeling efforts have arbitrarily fixed this at some value or modeled it using a limiting set of thermodynamic assumptions. The work we are currently performing uses validated simulations using sophisticated photon transport, equation of state, and strength models/data to provide a fit for Ef(z) that is useful for predictive calculation of impulse. We will apply our methodology and show results for different materials and x-ray sources. This work is particularly useful for the design of experiments studying x-ray impulse generation. The present report is outlined as follows. Section 1.2 describes a series of HED experiments investigating x-ray-generated impulse in materials. Section 1.3 describes the computational approach we employ in this study, and presents validation results against the aforementioned experiments. Section 1.4 introduces analytical models for impulse generation, as well as our method for utilizing impulse from simulations to close the models. We discuss the concept of impulse-spectrum sensitivity, it’s application to uncertainty quantification, and derive a very useful analytical expression for it in 1.5. We then summarize recent progress in this project and discuss future work in section 1.6.