Absolute Energy Calibration of X-ray TESs with 0.04 eV Uncertainty at 6.4 keV in a Hadron-Beam Environment

TL;DR

This paper demonstrates highly precise absolute energy calibration of superconducting TES X-ray detectors in a hadron-beam environment, achieving 0.04 eV uncertainty at 6.4 keV by accounting for non-Gaussian responses and pile-up effects.

Contribution

It introduces a calibration method that achieves unprecedented energy accuracy for TESs in particle beam environments, considering complex detector response effects.

Findings

Achieved 5.2 eV FWHM energy resolution at 6.9 keV without beam.

Demonstrated absolute energy uncertainty of ±0.04 eV at 6.4 keV.

Validated calibration method in a high-rate pion beam environment.

Abstract

A performance evaluation of superconducting transition-edge sensors (TESs) in the environment of a pion beam line at a particle accelerator is presented. Averaged across the 209 functioning sensors in the array, the achieved energy resolution is 5.2 eV FWHM at Co $K_{\alpha}$ (6.9 keV) when the pion beam is off and 7.3 eV at a beam rate of 1.45 MHz. Absolute energy uncertainty of $\pm$0.04 eV is demonstrated for Fe $K_{\alpha}$ (6.4 keV) with in-situ energy calibration obtained from other nearby known x-ray lines. To achieve this small uncertainty, it is essential to consider the non-Gaussian energy response of the TESs and thermal cross-talk pile-up effects due to charged-particle hits in the silicon substrate of the TES array.