Quantifying Uncertainties in Radiative Shock Experiments

Carolyn C. Kuranz

CRASH Annual Review

Fall 2010

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

Partial list of experimental inputs that have uncertainty associated with them

Laser energy

Laser pulsewidth

Laser spot size

Observation time

Be disk thickness

Be surface roughness

Xe gas pressure

Diagnostic x-ray signalBackground signalSource broadening

Target geometryAngle between Be disk and tubeAngle between tube and diagnostic

Pre and post-shot probability distributions functions (PDFs) for these

uncertainties often differ!

Summary of the CRASH calculation

X - Experiment parametersθ - Physical ConstantsN - Numerical ParametersYS - Results to be analyzed with data by statistical methods

CRASHPre-Processor

XH

CalibrationData (D)

CRASHRadiation-Hydrodynamics

Simulation Code

XCθC

NC

YHP YC YS

CRASHPost-Processor

XRθR

I will be discussing the uncertainties in some of the experimental inputs

Types of PDFs for experimental inputs

Tails of PDFs are often complex (details and examples to follow)

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

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

Understanding experimental uncertainties is very complex: observation time in Y2 experiment

Recent experiments measured the amount of time it takes for the shock to move through the Be diskEach experiment used 3 instruments for the

measurement The most sensitive instrument had 10 ps resolution

Time

Spa

ce

VelocityInterferometer

}548 ps

Shock breakout

But these instrumental uncertainties were not the dominant uncertainty

-0.5 0.5 1.50

200000000000000

400000000000000

600000000000000

800000000000000

Time (ns)

Las

er I

rrad

ian

ce

(W/c

m2)

t0

Time

Spa

ceDiagnostic fiducial

Total uncertainty was ± 50 ps even though instrumental uncertainty was smaller

Largest uncertainty came from measuring time interval between the drive laser and diagnostic fiducial laser

}548 ps

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

ConclusionsUnderstanding and quantifying the uncertainties in our

experiments is complex and sometimes surprisingThere are 2 types of PDFs for these uncertainties: quasi-

Gaussian and quasi-uniformThe 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