# Non-Iterative Characteristics Analysis for Ramp Loading with a Window

## TL;DR

This paper extends a non-iterative ramp wave analysis method to include measurements through windows, enabling robust, fast, and non-iterative stress-compression analysis in high-pressure ramp loading experiments.

## Contribution

The authors generalize a non-iterative analysis method to handle window measurements, removing the need for uniform velocity sampling and improving robustness over previous free-surface techniques.

## Key findings

- Method now applies to measurements through windows
- Removes need for uniform velocity sampling
- Faster and more robust than iterative analysis

## Abstract

Ramp compression experiment are used to deduce the relation between compression and normal stress in a material, by measuring how a compression wave evolves as it propagates through different thicknesses of the sample material. The compression wave is generally measured by Doppler velocimetry from a surface that can be observed with optical or near-optical photons. For high-pressure ramp loading, the reflectivity of a free surface often decreases as it is accelerated by the ramp wave, and window materials transparent to the probing photons are used to keep the surface flatter and preserve its reflectivity. We previously described a method of analyzing ramp-wave data measured at the free surface which did not require numerical iteration. However, this method breaks down when the pressure at the surface changes and hence cannot be used for data taken with a finite-impedance window. We have now generalized this non-iterative analysis method to apply to measurements taken through a window. Free surfaces can be treated seamlessly, and the need for sampling at uniform intervals of velocity has been removed. These calculations require interpolation of partially-released states using the partially-constructed stress-compression relation, making them slower than the previous free-surface scheme, but they are still much more robust and fast than iterative analysis.