## 1 Introduction  
**Compact accelerators for Charged Particle Therapy are being investigated and developed to reduce the costs and the dimensions of new facilities** **[**1,2**]****. In parallel, new beam delivery time structures will allow new therapeutic features as faster treatments, different dose rates, fast energy change for range modulation and FLASH irradiations [3].  
The temporal structure of the future beams will drastically change and will provide instantaneous beam currents three orders of magnitude larger than the present beams, which are supplied continuously by common cyclotrons, and in beam spills by synchrotrons. Meanwhile, the emerging and fascinating FLASH therapy [4; 5] has to cope with similar issues to treat tumors with an average dose rate greater than 40 Gy/s, while the conventional dose rate is around 0.1 Gy/s.  
The expected beam delivery conditions feature short pulses (1-10 \(\upmu\)s) at a wide range of repetition rates (0.1-1 kHz), and the resulting high instantaneous flux rate (up to 10\({}^{14}\) protons/s) is a challenge for online beam monitors worldwide based on parallel-plate gas ionization chambers (ICs).  
Due to the increased charge recombination probability, to compensate for the charge losses, online correction methods are needed such as the one proposed by [PERSON] et al. [6] to correct the charge measured by arrays of ionization chambers irradiated with time-varying dose rates. In parallel, the detector efficiency can be maximized, reducing as much as possible the gap width as successfully performed by [PERSON] et al. [7] and by [PERSON] et al. [8] to investigate if thin and ultra-thin parallel plate ionization chambers are suitable for the dosimetric characterization of FLASH therapy beams.  
In this work, we present a prototype of multi-gap detector (MGD) composed of three parallel-plate ICs in series along the beam, each one featuring a different gap width. The prototype is designed to measure in real time the beam fluence at flux rates characterized by large charge volume recombination, exploiting a correction method described in the following. The correction method is based on the different rates of charge recombination among the three ICs because of their different gaps when exposed to the same ionization density. Indeed, for a given ionization density, deviation from the proportionality of different ICs mainly depends on the gap width and bias voltage. Thus, from the measurement of the charges collected in each of the three gaps, a procedure is described and experimentally verified to evaluate the amount of deviation and determine the total ionization charge through a calibration curve, which is characteristic of the specific measurement conditions.  
In order to explore a wide range of ionization densities, this work presents measurements performed with three different accelerators exploiting different particles (protons and carbon ions). In addition, two beam delivery time structures are considered which can be studied using two different analytical models for charge recombination. If the beam is delivered continuously or in spills (macropulses) of a duration much larger than the charge collection time, and the underlying time intervals between micropulses are much shorter than the same quantity, the charge recombination can be described by the continuous beam model (continuous beam). If the delivery is composed of pulses with duration much shorter than the detector charge collection time and with a time interval large enough for all the charge being collected before the arrival of the next pulse, the charge recombination can be described by the pulsed beam model (pulsed beam). Finally, to fill the lack of high-intensity beams, the MGD was operated at low bias voltage to reproduce the rates of charge recombination expected with instantaneous beam currents orders of magnitude larger than the available ones.