Charge collection efficiency of thimble ionization chambers exposed to ultra-high dose per pulse

TL;DR

This work addresses the nonlinearity in charge collection efficiency (CCE) of thimble ionization chambers under ultra-high dose per pulse (DPP) beams, driven by volume recombination and polarity effects. The authors combine a targeted experimental campaign at PTB with a novel finite-element 1D/2D numerical model (including guard rings) to reproduce CCE and time-resolved current behavior, and they benchmark against Fenwick's analytical framework for cylindrical geometries. Key findings show a strong polarity effect at high DPPs, with CCE higher when electrons are collected toward the central electrode; guard rings substantially modify CCE and the polarity correction factor $k_{pol}$, making 2D geometry essential for PP3D accuracy. The study demonstrates that, in the absence of guard rings, the CCE of thimble ICs can be approximated by a volume-weighted mix of spherical and cylindrical geometries, and that intercomparison across chambers can be guided by the geometrical parameter to bias-voltage ratio $g/U$, enabling improved metrology in ultra-high-DPP contexts.

Abstract

Background: Commercially available ionization chambers (ICs) exposed to ultra-high dose per pulse (DPP) exhibit deviations from a linear dose response due to volume recombination. In the last years, phenomenological and simulation models have been developed to describe the charge collection efficiency (CCE) focused on parallel-plate ICs. Methods: The response of two PinPoint3D T31022 (PP3D) and two PinPoint T31023 (PP) ICs was investigated experimentally at the national metrology institute of Germany (PTB). The ICs were irradiated using the ultra-high-DPP reference electron beam with an energy of 20 MeV and DPPs between 0.1 Gy up to 9.3 Gy. The bias voltage supplied to the ICs was varied between +/- 200 V up to +/- 500 V. Additionally, the time-resolved signal of the ICs was recorded using an oscilloscope. To simulate the response of the chambers, a novel finite element code capable of simulating 1D and 2D geometries was developed. Three different geometries were considered to describe the investigated ICs: a cylindrical 1D geometry, a simplified 2D geometry and a complete 2D geometry including the conductive guard ring of the ICs. Conclusions: Thimble ICs exposed to ultra-high-DPP exhibit a large polarity effect due to the different distribution and recombination of the charge carriers whether the free electrons drift toward the central or outer electrode. Although the two thimble ICs studied have a similar sensitive volume, the PP shows a greater CCE due to its smaller external radius. A numerical model based on the finite element method is able to satisfactory reproduce the actual CCE for these two chambers. For the PP3D, the inclusion of the guard ring in the simulation geometry is mandatory to obtain accurate results. At large DPPs, thimble ICs should be used with caution due to their large polarity effect.

Figures (7)

• Figure 1: Simplified diagrams of the different IC geometries considered in this study. $r_1$ corresponds to the inner radius and $r_2$ to the outer radius of the IC cavity. All the geometries assume a cylindrical symmetry around the vertical axis. In the complete 2D geometry the guard ring is assumed to be a perfect conductor. Gray lines shows the electric field lines and the dead volume is highlighted in blue.
• Figure 2: Comparison between the CCE calculated using the numerical model and the analytical model of Fenwick et al.Fenwick_Collection_2024 as a function of the DPP for a PinPoint3D T31022 IC to illustrate the polarity and electric field perturbation effects. For this calculation the chamber is idealized as a tip-less cylindrical geometry biased at 300 V. The simulation assumes: i) no electric field perturbation, ii) charge released instantaneously in the active volume (zero pulse duration) and iii) electrons are collected immediately after the release of the charge. Positive (negative) charge corresponds to positive (negative) polarity using external polarization.
• Figure 3: Comparison of the CCE and $k_{\rm pol}$ simulations using a 1D cylindrical geometry ($f_{\rm cyl}$), a 1D spherical geometry ($f_{\rm sph}$), a volume-weighted average model ($f_{\rm w}$) a simplified 2D geometry ($f_{\rm 2D}$) and the complete 2D geometry with guard ring ($f_{\rm 2D+gR}$) for a PinPoint3D T31022 IC as a function of the DPP. Calculations were conducted using a pulse duration of 1.9 $\upmu$s, a bias voltage of 300 V and ion mobilities from Boissonnat et al.Boissonnat_Measurement_2016
• Figure 4: Comparison between experimental and simulated CCE (left side) and polarity effect correction factor (right side) using the complete 2D geometry for the PinPoint3D T31022 SN 152986 (top, panel A) and the PinPoint T31023 SN 170313 IC (bottom, panel B) as a function of the DPP for different bias voltages. The pulse duration is 1.9 $\upmu$s. The results from simulations are shown with a spline interpolation for a better visualization while the detailed residuals with respect to the experimental data are reported in the lower panels. Simulations were performed using ion mobilities from Boissonnat et al.Boissonnat_Measurement_2016 together with a volume recombination coefficient of 1.4$\times$10$^{-12}$ m$^3$ s$^{-1}$.
• Figure 5: Impact of the pulse duration on the CCE and $k_{\rm pol}$ for the PinPoint T31023 (SN 170293) and the PinPoint3D T31022 ICs (SN 153056) using 1.0 $\upmu$s and 1.9 $\upmu$s at 500 V bias voltage.