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6CCVD Research

Optimizing the configuration of plasma radiation detectors in the presence of uncertain instrument response and inadequate physics

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2023-01-06
JournalJournal of Plasma Physics
AuthorsPatrick Knapp, William Lewis, V. Roshan Joseph, Christopher Jennings, Michael E. Glinsky
InstitutionsGeorgia Institute of Technology, Sandia National Laboratories
Citations6
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”
  • Core Value Proposition: A general methodology was developed for optimizing experimental diagnostic configurations to minimize both uncertainty (variance) and systematic error (bias) in inferred physical quantities.
  • Methodology: The technique integrates Bayesian Inference (BI) to handle uncertainties in instrument response with Bayesian Optimization (BO) to efficiently search the configuration space.
  • Optimization Metric: The objective function minimizes the Mean Squared Error (MSE) of the inferred posterior distribution of the X-ray spectrum relative to a High Fidelity Model (HFM).
  • Bias Mitigation: The optimization metric uses the time-integrated X-ray spectrum (Q) as the comparison metric, circumventing ambiguities arising from the inadequate physics contained in the Low Fidelity Model (LFM).
  • Constraint Handling: A domain-specific penalty term was introduced to the metric to prevent configurations that would drive detector signals into non-linear or saturation regimes (e.g., peak voltage > Vbias).
  • Performance Improvement: The optimized configuration reduced the average log10(MSE) of the inferred X-ray spectrum on the validation set from 2.13 (standard MagLIF setup) to -0.22, an improvement of over an order of magnitude.
  • Inferred Quantities: The optimized setup significantly reduced the standard deviation (variance) in inferred quantities like electron temperature (Te) and total radiated energy, leading to tighter credible intervals.

Technical Specifications

Section titled “Technical Specifications”

Detector and Experimental Parameters

Section titled “Detector and Experimental Parameters”
ParameterValueUnitContext
Detector TypePhotoconducting Diamond (PCD)N/AUsed for X-ray power measurement.
Typical Bias Voltage (Vbias)~100VApplied across the PCD element.
Source-to-Detector Distance (d)170cmFixed geometry parameter.
Detector Active Area (A)0.01cm2Fixed geometry parameter.
Detector Thickness0.05cmFixed parameter (diamond element).
Synthetic Noise (Std Dev)50mVGaussian noise added to synthetic observations.
Electron Temperature (Te) PriorN(4, 3)keVNormal distribution used in Bayesian inference.
Liner Areal Density (rho*Re) PriorN(1, 1)g/cm2Normal distribution used in Bayesian inference.
Optimization Hyperparameter (lambda)0.15N/AWeight of the penalty term (L’) in the metric M.
Optimization Hyperparameter (alpha)0.25N/AVoltage threshold factor for penalty term.
Maximum Recorded Vpeak (Optimized)14.4VMax voltage across validation set (resulting in ~11% signal compression).

Optimized Detector Configuration (5 PCD Elements)

Section titled “Optimized Detector Configuration (5 PCD Elements)”
Detector IndexFilter MaterialThicknessSensitivity (S)
1Molybdenum4.7 ”m1 x 10-4 A/W
2Palladium18.1 ”m25 x 10-4 A/W
3Vanadium26 ”m25 x 10-4 A/W
4Vanadium4.2 ”m1 x 10-4 A/W
5Kapton45 ”m1 x 10-4 A/W

Performance Metrics Comparison (Validation Dataset)

Section titled “Performance Metrics Comparison (Validation Dataset)”
Configurationlog10(MSE)Peak Voltage (V)Te Std Dev (sigmaT)Total Output Std Dev (sigmaY)
MagLIF (Reference)2.1335.355 %22 %
Expert (Reference)2.515.639 %12.5 %
Optimum-0.2214.422 %12.2 %

Key Methodologies

Section titled “Key Methodologies”

  1. Model Hierarchy Establishment:

    • High Fidelity Model (HFM): GORGON Magneto Hydrodynamics (MHD) simulations of MagLIF implosions were used to generate the “true” synthetic X-ray emission data (time-dependent, spatially resolved).
    • Low Fidelity Model (LFM): A simplified, analytic, time-independent model assuming uniform deuterium plasma (bremsstrahlung emission) was used for the computationally efficient Bayesian inference step.

  2. Synthetic Data Generation:

    • HFM output (Pepsilon(t)) was integrated over time and passed through the diagnostic response function (Equation 3.3) to simulate the observed voltage signals (Oi).
    • Uncertainties in instrument characteristics (sensitivity, distance, area) were incorporated using normal prior distributions.

  3. Bayesian Inference (BI):

    • Markov Chain Monte Carlo (MCMC) sampling (using pymc3) was employed to estimate the posterior distribution p(theta|O) of the LFM parameters (Te, rho*Re, C) and derived quantities (q).

  4. Optimization Metric (M) Definition:

    • The metric M was defined as: M = log( (1/K) * Sumj=1K [MSEj + lambda * L’j] ).
    • MSE Component: Calculated using the full posterior distribution of the inferred time-integrated X-ray spectrum (Q) relative to the HFM true spectrum (Y), ensuring the optimization targets the fundamental observable quantity.
    • Penalty Term (L’): An exponential function L’ = exp(max(Vpeak,i) / (alpha * Vbias)) - 1 was used to penalize configurations that produce peak voltages (Vpeak) exceeding a safe threshold (alpha * Vbias), thus avoiding detector saturation.

  5. Bayesian Optimization (BO) Implementation:

    • The optimization was performed using the GPyOpt framework.
    • BO utilized a Gaussian Process (GP) to model the expensive objective function M, balancing exploration (searching high-variance regions) and exploitation (searching high-mean regions) to find the global optimum configuration (filter material, thickness, sensitivity).

  6. Hyperparameter Tuning:

    • A small scan was performed to empirically set the penalty hyperparameters (lambda = 0.15, alpha = 0.25) to ensure the penalty term functioned as intended, balancing signal quality against voltage limitations.

Commercial Applications

Section titled “Commercial Applications”
  • Fusion Energy Diagnostics: Essential for designing optimal X-ray and radiation detector arrays for next-generation fusion reactors (e.g., ITER, DEMO) where diagnostics must operate reliably under high uncertainty and harsh conditions.
  • High Energy Density Physics (HEDP): Direct application in optimizing diagnostics for large pulsed-power facilities (like Sandia’s Z machine) or laser facilities (like NIF) to improve the precision of inferred plasma metrics (temperature, mix, pressure).
  • Advanced Sensor Network Design: Applicable to any field requiring the optimal configuration of sensor arrays where individual sensor response is uncertain and the underlying physical model used for interpretation is simplified (e.g., environmental monitoring, non-destructive testing).
  • Uncertainty Quantification (UQ) in Engineering: Provides a robust framework for experimental design, allowing engineers to quantitatively assess the trade-offs between instrument cost/complexity and the resulting reduction in uncertainty of key performance indicators (QOIs).
  • Black-Box Optimization: The BO methodology is generally useful for optimizing expensive, gradient-free simulation or experimental processes involving mixed continuous and discrete parameters.
View Original Abstract

We present a general method for optimizing the configuration of an experimental diagnostic to minimize uncertainty and bias in inferred quantities from experimental data. The method relies on Bayesian inference to sample the posterior using a physical model of the experiment and instrument. The mean squared error (MSE) of posterior samples relative to true values obtained from a high fidelity model (HFM) across multiple configurations is used as the optimization metric. The method is demonstrated on a common problem in dense plasma research, the use of radiation detectors to estimate physical properties of the plasma. We optimize a set of filtered photoconducting diamond detectors to minimize the MSE in the inferred X-ray spectrum, from which we can derive quantities like the electron temperature. In the optimization we self-consistently account for uncertainties in the instrument response with appropriate prior probabilities. We also develop a penalty term, acting as a soft constraint on the optimization, to produce results that avoid negative instrumental effects. We show results of the optimization and compare with two other reference instrument configurations to demonstrate the improvement. The MSE with respect to the total inferred X-ray spectrum is reduced by more than an order of magnitude using our optimized configuration compared with the two reference cases. We also extract multiple other quantities from the inference and compare with the HFM, showing an overall improvement in multiple inferred quantities like the electron temperature, the peak in the X-ray spectrum and the total radiated energy.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2006 - Pattern Recognition and Machine Learning
  2. 2006 - High Energy Density Physics: Fundamentals, Inertial Fusion, and Experimental Astrophysics

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