Fig. 1. Schematic top view of the experimental setup (not to scale) with all components relevant for this study; in addition, a picture of the I-BEAT 3D detector is shown with the circular entrance window being visible in the centre of the detector. The laser (magenta) is focused onto a thin foil target (black) from which protons are accelerated (grey). One energy selective solenoid S1 focuses the protons to a spot in air. The protons pass either an aperture equipped with a time-of-flight spectrometer (TOF, pink) and an ionization chamber (IC, yellow), or a collimator with a variable diameter (green). Finally, the protons reach the I-BEAT 3D detector, which is positioned on a linear stage. I-BEAT 3D consists of a water reservoir (turquoise) surrounded by four ultrasonic transducers (brown, three are visible). The ions enter the water through a thin Kapton entrance foil (ochre).

Fig. 2. Exemplary ionoacoustic signal recorded with the (a) axial transducer and (b) the right lateral transducer. Curves represent the lowpass filtered data (red, cut-off frequencies: MHz for the axial transducer and MHz for the right transducer) and the signal envelope (black). The read-out positions for the deduction of the bunch properties from the signal envelope are marked by dashed lines. For the axial transducer, the arrival time difference between the first and the third maxima corresponds to twice the proton bunch range , the pulse width is related to the width of the BP and the amplitude reveals the bunch particle number. For the lateral transducers, the position of the maximum is used to define the lateral bunch position and the pulse width relates to the lateral bunch diameter.

Fig. 3. (a) Estimated mean energy and range as a function of the solenoid magnetic field for I-BEAT 3D (black) and TOF (blue). (b) I-BEAT 3D signal width as a function of the determined I-BEAT 3D mean energy. A fit of the I-BEAT 3D data dots according to Equation (2) is shown in green.

Fig. 4. (a) I-BEAT 3D result of the bunch position in dependence of the stage position. The resolution limit is shown in red. (b) Measured lateral signal size in dependence of the collimator size along with a fit according to Equation (3) for the top and the right transducers. The minimal measurable pulse width is found to be mm for the right transducer and mm for the top transducer.

Fig. 5. The amplitude of the ionoacoustic signal envelope generated in the I-BEAT 3D entrance window is displayed in dependence of charge measured with the ionization chamber for various bunch particle numbers. In addition to the black data dots, the linear correlation curve is shown in green.