# (U) Boundary Conditions for Ejecta Source Models with Stationary Velocity Distributions

## Abstract

We show that certain apparently universal features of the piezoelectric voltage traces measured in HE-driven tin coupon experiments [1, 2] constrain the functional form of any ejecta source model with a stationary velocity distribution. Building on an analytic formalism that has been extensively documented elsewhere [3, 4, 5, 6, 7], we derive simple expressions for V(t ^{0} _{a}), V'(t ^{0} _{a}), and the discontinuity in V(t _{break}) where t ^{0} _{a} is the time of first ejecta arrival at the sensor and t break is the “depletion” time for the fastest particles arriving at the sensor. These three quantities appear to be zero, or nearly so, in the Vo- gan voltage data [1] (modulo noise and any smoothing effects created by the circuit); however, the predicted voltages for this general class of source models do not automatically achieve these conditions unless special boundary conditions are met. Source models which violate these boundary conditions will produce voltage predictions at odds with the measurements. The RMI+SSVD ejecta source model in its current formulation satisfies none of these boundary conditions, and therefore predictions from a stationary-velocity-distribution approximation to the RMI+SSVD source model deviate significantly from the voltage data. This analysis suggests straightforward methodsmore »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1463572

- Report Number(s):
- LA-UR-18-27420

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Tregillis, Ian Lee.
```*(U) Boundary Conditions for Ejecta Source Models with Stationary Velocity Distributions*. United States: N. p., 2018.
Web. doi:10.2172/1463572.

```
Tregillis, Ian Lee.
```*(U) Boundary Conditions for Ejecta Source Models with Stationary Velocity Distributions*. United States. doi:10.2172/1463572.

```
Tregillis, Ian Lee. Fri .
"(U) Boundary Conditions for Ejecta Source Models with Stationary Velocity Distributions". United States. doi:10.2172/1463572. https://www.osti.gov/servlets/purl/1463572.
```

```
@article{osti_1463572,
```

title = {(U) Boundary Conditions for Ejecta Source Models with Stationary Velocity Distributions},

author = {Tregillis, Ian Lee},

abstractNote = {We show that certain apparently universal features of the piezoelectric voltage traces measured in HE-driven tin coupon experiments [1, 2] constrain the functional form of any ejecta source model with a stationary velocity distribution. Building on an analytic formalism that has been extensively documented elsewhere [3, 4, 5, 6, 7], we derive simple expressions for V(t0a), V'(t0a), and the discontinuity in V(tbreak) where t0a is the time of first ejecta arrival at the sensor and t break is the “depletion” time for the fastest particles arriving at the sensor. These three quantities appear to be zero, or nearly so, in the Vo- gan voltage data [1] (modulo noise and any smoothing effects created by the circuit); however, the predicted voltages for this general class of source models do not automatically achieve these conditions unless special boundary conditions are met. Source models which violate these boundary conditions will produce voltage predictions at odds with the measurements. The RMI+SSVD ejecta source model in its current formulation satisfies none of these boundary conditions, and therefore predictions from a stationary-velocity-distribution approximation to the RMI+SSVD source model deviate significantly from the voltage data. This analysis suggests straightforward methods for potentially improving the predictions of the RMI+SSVD ejecta source model. We test this with a simple adjustment to the SSVD and find, as anticipated, the adjustment corrects three properties of the voltage prediction. Furthermore, the adjusted model’s prediction for ejecta mass accumulation at the sensor exhibits a smoother and more gradual rise from the baseline than that produced by the original source model, thereby improving overall model/data agreement.},

doi = {10.2172/1463572},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {8}

}