Quantifying Uncertainties in Radiative Shock Experiments

1. Quantifying Uncertainties in Radiative Shock Experiments Carolyn C. Kuranz CRASH Annual Review Fall 2010

2. Why is it important to understand experimental uncertainty for this project? • Creates realistic input parameter space for predictive studies • Understanding dominant sources of uncertainty can help us to focus on those areas to reduce the uncertainty • Helps us to understand and improve the predictive capability of the model • Important for future experiments

3. Partial list of experimental inputs that have uncertainty associated with them • Diagnostic x-ray signal • Background signal • Source broadening Be disk thickness Be surface roughness Laser energy Laser pulsewidth Laser spot size Xe gas pressure • Target geometry • Angle between Be disk and tube • Angle between tube and diagnostic Observation time Pre and post-shot probability distributions functions (PDFs) for these uncertainties often differ!

4. Summary of the CRASH calculation Calibration Data (D) XH XR XC θC θR CRASH Radiation-Hydrodynamics Simulation Code YHP CRASH Pre-Processor CRASH Post-Processor YC YS NC X - Experiment parameters θ - Physical Constants N - Numerical Parameters YS - Results to be analyzed with data by statistical methods I will be discussing the uncertainties in some of the experimental inputs

5. Types of PDFs for experimental inputs Tails of PDFs are often complex (details and examples to follow)

6. Laser Energy is an example of quasi-Gaussian distribution Mean values of experimental days are within 3% of nominal but standard deviation is ~1% or less on individual day

7. Be disk thickness is an example of a quasi-uniform distribution • Several parameters have a “uniform” distribution with low-amplitude, long tails • In this case, the tails of the distribution correspond to cases in which there is a malfunction of a simple measuring instrument or disregard of measuring procedures

8. Understanding experimental uncertainties is very complex: observation time in Y2 experiment Time Velocity Interferometer Shock breakout Space 548 ps } • Recent experiments measured the amount of time it takes for the shock to move through the Be disk • Each experiment used 3 instruments for the measurement • The most sensitive instrument had 10 ps resolution

9. But these instrumental uncertainties were not the dominant uncertainty Largest uncertainty came from measuring time interval between the drive laser and diagnostic fiducial laser Time t0 Space 548 ps } Diagnostic fiducial Total uncertainty was ± 50 ps even though instrumental uncertainty was smaller

10. Always look behind the curtain… • Often the analysis of experimental data focuses on the detail of these small error bars • The uncertainty in this measurement is dominated by a larger systematic error

11. Conclusions • Understanding and quantifying the uncertainties in our experiments is complex and sometimes surprising • There are 2 types of PDFs for these uncertainties: quasi-Gaussian and quasi-uniform • The tails of these PDFs are often complex • The PDF for a given parameter can be different pre-shot and post-shot • We are continuing to work towards identifying and quantifying uncertainty in our experiments