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

At a Glance

Metadata	Details
Publication Date	2023-01-06
Journal	Journal of Plasma Physics
Authors	Patrick Knapp, William Lewis, V. Roshan Joseph, Christopher Jennings, Michael E. Glinsky
Institutions	Georgia Institute of Technology, Sandia National Laboratories
Citations	6
Analysis	Full AI Review Included

Technical Documentation & Analysis: Optimized MPCVD Diamond Detectors for Plasma Diagnostics

Reference Paper: Knapp et al. (2023). Optimizing the configuration of plasma radiation detectors in the presence of uncertain instrument response and inadequate physics. J. Plasma Phys.

Executive Summary

This research validates the critical role of MPCVD Photoconducting Diamond (PCD) detectors in optimizing X-ray spectroscopy for high-energy density physics (HEDP) experiments, such as MagLIF. The findings directly support 6CCVD’s expertise in providing highly customized diamond materials for advanced diagnostics.

Core Application: MPCVD PCD detectors are utilized to estimate physical properties (e.g., electron temperature, X-ray spectrum) of dense plasmas by measuring filtered X-ray radiation.
Methodology: A novel Bayesian Optimization (BO) technique, using Mean Squared Error (MSE) as the metric, was employed to optimize the configuration of a 5-element PCD detector array.
Performance Improvement: The optimized configuration reduced the MSE in the inferred X-ray spectrum by more than two orders of magnitude compared to standard reference configurations (e.g., the “MagLIF” case).
Key Optimization Parameters: The BO successfully determined optimal filter material (Molybdenum, Palladium, Vanadium, Kapton) and precise filter thicknesses (ranging from 4.2 µm to 45 µm) necessary for robust spectral reconstruction.
Uncertainty Reduction: The “Optimum” configuration significantly reduced the variance (credible intervals) and bias in inferred quantities, demonstrating a superior ability to handle instrument response uncertainties and model inadequacies.
6CCVD Value Proposition: 6CCVD specializes in providing the custom-thickness PCD wafers (up to 500 µm) and precision metalization required to replicate and advance these optimized detector designs.

Technical Specifications

The following table summarizes the critical material and performance parameters extracted from the research, focusing on the PCD detector requirements and optimization results.

Parameter	Value	Unit	Context
Detector Material	Photoconducting Diamond (PCD)	N/A	Core diagnostic element
PCD Thickness (LFM)	500	µm	Fixed thickness (0.05 cm) used in the Low Fidelity Model (LFM)
Detector Active Area	0.01	cm²	Used for solid angle calculation ($\Delta\Omega$)
Typical Bias Voltage	~100	V	Applied across the PCD element
Optimized Filter Thickness Range	4.2 to 45	µm	Final optimized values for the 5-detector array
Optimized Filter Materials	Mo, Pd, V, Kapton	N/A	Materials selected by the optimization algorithm
Detector Sensitivity Range (S)	1 x 10^-4 to 25 x 10^-4	A/W	Optimized values for the 5-detector array
MSE Reduction (Optimum vs. Reference)	> 100x	N/A	Reduction in Mean Squared Error (log₁₀(MSE) = -0.22)
Peak Recorded Voltage (Optimum)	14.4	V	Acceptable signal level, demonstrating effective penalty term
Inferred T_e Standard Deviation (Optimum)	22	%	Reduced variance in inferred electron temperature

Key Methodologies

The optimization relied on a sophisticated combination of high-fidelity simulation, simplified modeling, and advanced statistical inference, all centered around the physical response of the PCD detectors.

High Fidelity Model (HFM) Generation: Synthetic X-ray emission data was generated using GORGON magneto hydrodynamics (MHD) simulations of MagLIF implosions, providing time-dependent, spectrally resolved power $P_{\epsilon}(t)$.
Low Fidelity Model (LFM) Development: A simplified, time-integrated model was created for efficient Bayesian inference, focusing on key parameters: electron temperature ($T_{e}$), liner areal density ($\rho R_{e}$), and a scale factor ($C$).
PCD Signal Modeling: The synthetic signal $O_{i}$ for each detector was calculated by integrating the LFM X-ray energy over photon energy, incorporating the transmission of the filter ($T_{\epsilon, filter}$), the absorption of the PCD ($A_{\epsilon, PCD}$), and the detector sensitivity ($S$).
Uncertainty Inclusion: Uncertainties in instrument response characteristics (e.g., detector sensitivity, distance, area) were incorporated as normally distributed random variables ($\xi_{i}$) and marginalized out during posterior sampling.
Optimization Metric (M): The objective function $M$ was defined as $M = \log(\frac{1}{K}\sum_{j=1}^{K} (\text{MSE}^{j} + \lambda L^{j}))$.
- MSE: Mean Squared Error between the posterior distribution of the inferred spectrum and the HFM truth, normalized by the true spectrum.
- Penalty Term ($L’$): An exponential penalty was applied to configurations producing excessively large signals (V_peak > $\alpha V_{bias}$), preventing detector saturation and non-linear compression effects.
Bayesian Optimization (BO): BO was applied to the mixed parameter space (discrete filter material, continuous filter thickness, continuous sensitivity) to efficiently find the optimal configuration that minimized $M$.

6CCVD Solutions & Capabilities

The successful optimization of filtered PCD detectors for HEDP diagnostics requires materials with extreme precision in thickness, purity, and surface preparation. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond components to replicate and extend this critical research.

Applicable Materials

Research Requirement	6CCVD Material Recommendation	Technical Rationale
Photoconducting Diamond (PCD)	High-Purity Polycrystalline Diamond (PCD)	PCD is the material of choice for high-flux X-ray detection due to its wide bandgap and radiation hardness. 6CCVD offers PCD wafers up to 125mm in diameter.
High Uniformity/Low Noise	Optical Grade Single Crystal Diamond (SCD)	For future extensions seeking to minimize the stochastic calibration uncertainties ($\xi_{i}$), SCD offers superior crystalline uniformity and purity, leading to lower inherent noise and more predictable response characteristics.
Electrode Application	Boron-Doped Diamond (BDD)	BDD films can be used for highly conductive, robust electrode contacts or as a base layer for advanced sensor architectures requiring integrated circuitry.

Customization Potential

The optimization process demonstrated that precise control over detector geometry and associated components is paramount. 6CCVD’s in-house capabilities ensure that researchers can obtain materials tailored exactly to their optimized configurations.

Optimization Parameter	6CCVD Customization Service	Specification Match
Detector Thickness	Custom Thickness Growth: SCD and PCD wafers grown to precise specifications.	SCD/PCD: 0.1 µm to 500 µm. Substrates: up to 10 mm. (Matches the 500 µm thickness used in the LFM).
Filter/Electrode Fabrication	Advanced Metalization Services: In-house deposition and patterning.	Au, Pt, Pd, Ti, W, Cu layers available for custom electrode designs and filter integration. (Directly supports the need for Mo, Pd, V, etc., filters and high-voltage contacts).
Surface Quality	Precision Polishing: Chemical-Mechanical Polishing (CMP) services.	SCD: Ra < 1nm. Inch-size PCD: Ra < 5nm. Essential for minimizing surface scattering and ensuring consistent detector response.
Custom Geometry	Precision Laser Cutting & Shaping:	Ability to cut PCD wafers to the exact 0.01 cm² active area or custom array dimensions required for optimized fielding.

Engineering Support

The research highlights the complexity of optimizing instrument configuration in the presence of uncertain instrument response and simplified physics models. 6CCVD’s in-house PhD team provides expert consultation to bridge the gap between theoretical optimization and physical implementation.

Material Selection for HEDP: Our engineers can assist researchers in selecting the optimal diamond grade (SCD vs. PCD) based on expected X-ray flux, required signal-to-noise ratio, and radiation hardness needs for similar Plasma Radiation Detector projects.
Uncertainty Minimization: We provide detailed material characterization data (e.g., defect density, resistivity) to help researchers refine their prior distributions on stochastic calibration values ($\xi_{i}$), thereby reducing the overall uncertainty in their Bayesian inference models.
Global Supply Chain: 6CCVD offers reliable global shipping (DDU default, DDP available) to ensure timely delivery of custom components for time-sensitive experimental campaigns at major facilities like Sandia National Laboratories.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

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

Original Source

DOI: https://doi.org/10.1017/s002237782200126x

References

2006 - Pattern Recognition and Machine Learning
2006 - High Energy Density Physics: Fundamentals, Inertial Fusion, and Experimental Astrophysics