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CMA-Unfold A Covariance Matrix Adaptation unfolding algorithm for stacked calorimeter detectors

G. Fauvel, A. Arefiev, M. Manuel, K. Tangtartharakul, S. Weber, F. P. Condamine

Abstract

Stacking calorimeters also refered as bremsstrahlung cannons widely used in inertial confinement fusion and ultra-intense laser plasma experiments have become essential diagnostics for characterizing short bursts of high-energy photons and charged particles. Extracting the underlying energy spectrum from these detectors requires solving an ill-posed inverse problem, often complicated by noise, secondary particle contamination, and uncertainties in the detector response. In this work, we introduce an open-source unfolding framework available under the username ggfauvel under CMA-unfold based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), designed to reconstruct photon spectra directly from depth-dose profiles without imposing restrictive parametric assumptions. The algorithm demonstrates high robustness, accurately recovering complex spectral shapes while tolerating percent-level deviations in individual detector layers. This approach provides a flexible and noise-resilient tool for the analysis of stacking calorimeter data, with particular relevance for bremsstrahlung diagnostics in inertial confinement fusion and high-intensity laser applications.

CMA-Unfold A Covariance Matrix Adaptation unfolding algorithm for stacked calorimeter detectors

Abstract

Stacking calorimeters also refered as bremsstrahlung cannons widely used in inertial confinement fusion and ultra-intense laser plasma experiments have become essential diagnostics for characterizing short bursts of high-energy photons and charged particles. Extracting the underlying energy spectrum from these detectors requires solving an ill-posed inverse problem, often complicated by noise, secondary particle contamination, and uncertainties in the detector response. In this work, we introduce an open-source unfolding framework available under the username ggfauvel under CMA-unfold based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), designed to reconstruct photon spectra directly from depth-dose profiles without imposing restrictive parametric assumptions. The algorithm demonstrates high robustness, accurately recovering complex spectral shapes while tolerating percent-level deviations in individual detector layers. This approach provides a flexible and noise-resilient tool for the analysis of stacking calorimeter data, with particular relevance for bremsstrahlung diagnostics in inertial confinement fusion and high-intensity laser applications.
Paper Structure (16 sections, 10 equations, 10 figures, 1 table)

This paper contains 16 sections, 10 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Covariance Matrix Adaptation Evolution Strategy (CMA-ES)
  3. Covariance Matrix Adaptation Evolution Strategy (CMA-ES) working principle
  4. Minimization function
  5. Response Matrix
  6. Residuals
  7. Smoothing factor
  8. Calibration factors
  9. Computer generated data
  10. Unfolding from known distributions
  11. Double type of particles
  12. Noisy unfolding
  13. Adaptive smoothing factor
  14. Typical computing time
  15. Detector designed at ELI-Beamlines and experimental measure
  16. ...and 1 more sections

Figures (10)

  • Figure 1: CMA-ES principle flowing chart.
  • Figure 2: Unfolding of a numerically generated Bremsstrahlung distribution leading to "peak" solutions.
  • Figure 3: Unfolding of a numerically generated synchrotron distribution.
  • Figure 4: Unfolding of a numerically generated Gaussian distribution of mean 10 MeV and standard deviation 1 MeV.
  • Figure 5: Unfolding of a numerically generated bremsstrahlung distribution.
  • ...and 5 more figures