## 4 Discussions and Conclusions  
The recombination of charge carriers significantly affects the response of gas ionization detectors used for beam monitoring in particle therapy with high-intensity beams. This problem was made even more relevant by the advent of new acceleration technologies, leading to pulsed beams of large instantaneous intensity, and FLASH therapy. In this work, we present the characterization of a detector composed by three gas ionization chambers with different gap widths (multi-gap ionization chamber) developed to test a method for correcting online the non-linearity of the rate of charge collection with the ionization rate. This condition occurs when the chamber is irradiated with very high-intensity beams, leading to a large volume recombination. Figure 11: Calibration curve measured for chamber 1 as a function of \(Q_{2}^{\prime}d_{1}/Q_{1}^{\prime}d_{2}\). Figure 10: (**a**) Average counts per pulse normalized to the Faraday cup measured charge as a function of the bias voltage for 500 \(\upmu\)s pulse width and corresponding fits with the Boag formula for pulsed beams; (**b**) total counts normalized to the detector gap and fit. The method relies on the fact that the charge collection efficiency of a planar ionization chamber decreases, at any given ionization rate, with the increase in the gas gap where the ionization occurs. If the beam crosses two consecutive ionization chambers with different gaps, inducing in both the same volumetric ionization rate, the ratio of the charges collected at the two electrodes, normalized to the gap width, is a direct measurement of the relative efficiency, which is a quantity that can be easily determined online. At first order, for a given beam of varying intensity, this quantity is expected to depend only on the volumetric ionization rate and can be used to parametrize the efficiency of one of the two chambers, which was chosen as the reference. The five different calibration curves measured in this work prove that such a parametrization is not universal as one would expect considering both the different track structure of protons and carbon ions at the microscopic level and the different beam size and transverse distribution of each beam. Indeed, recombination is a complex phenomenon which is expected to depend on the track structures of each particle type, on the beam size and on the time structure of the beam irradiation at a time scale corresponding to the charge collection time in the chamber, typically tens to hundreds of microseconds. Therefore, comprehensive and accurate measurements need to be performed at any given accelerator beam to obtain the specific calibration curve then used online to correct the detector counts. The multi-gap chamber characterization with different charged particle beams (protons and carbon ions) and beam delivery time structure (continuous and pulsed beams) presented in this paper proves that the assumption of working with the same rate of ionization in all the chambers was always satisfied, the experimental efficiency saturation curves obtained changing the bias voltage corroborate the expected behavior predicted by the known models for volumetric charge recombination in parallel plate ionization chambers, and the rate of volumetric ionization increases linearly with the beam intensity. As a final conclusion, the multi-gap ionization chamber represents a possible detector for beam monitoring in particle therapy with high fluence rates, keeping in mind that for each accelerator and for several beam characteristics, optimized gap widths and accurate calibration procedure are mandatory. In particular, the developments presented in this paper can be instrumental toward the solution of the challenging problem of real-time beam monitoring in FLASH radiation therapy. Conceptualization and methodology, R.S., S.G. and L.F.G. ; detector assembly and set up, R.S., S.G., L.F.G. and F.F. ; experimental measurements R.S., S.G., L.F.G., S.B., G.A.P.C., M.D., F.F., F.R., A.V. and R.C. ; data analysis S.G., L.F.G. and F.M.M.