Listening to pulses of radiation: design of a submersible thermoacoustic sensor

Nowadays, various collaborations are creating immense machines to try to track and understand the origin of high-energy cosmic particles (e.g., IceCube, ANTARES, Baikal-GVD, P-ONE). The detection mechanism of these sophisticated experiments relies mainly on an optical signal generated by the passage of charged particles on a dielectric medium (Čerenkov radiation). Unfortunately, the dim light produced by passing particles cannot travel too far until it fades away, creating the necessity to instrument large areas with short spacing between sensors. The range limitation of the optical technique has created a fertile ground for experimenting on the detection of acoustic signals generated by radiation—thermoacoustics. Despite the increased use of the thermoacoustic technique, the instrumentation to capture the faint acoustic signals is still scarce. Therefore, this work has the objective to contribute with information on the critical stages of an affordable submersible thermoacoustic sensor: namely the piezoelectric transducer and the amplifying electronics. We tested the sensor in a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$170\,{\textit{l}}$$\end{document}170l non-anechoic tank using an infrared (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda =1064\,\hbox {nm}$$\end{document}λ=1064nm) Q-switched Nd:YAG laser as a pulsed energy source to create the characteristic signals of the thermoacoustic phenomena. In accordance with the thermoacoustic model, a polarity inversion of the pressure signal was observed when transiting from temperatures below the point of maximum density of water to temperatures above it. Also, the amplitude of the acoustic signal displayed a linear relationship with pulse energies up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(51.1 \pm 1.7)\,\hbox {mJ}$$\end{document}(51.1±1.7)mJ (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2 \sim 0.98$$\end{document}R2∼0.98). Despite the use of cost-effective parts and simple construction methods, the proposed sensor design is a viable instrument for experimental thermoacoustic investigations on high-energy particles.

. Illustration of the experiment location, at Urca beach in Rio de Janeiro (22 • 56 51.1 S, 43 • 9 49.3 W). The acoustic source (pinger) and the thermoacoustic sensor were installed 170 m apart. The red surfaces represent the acoustic wavefronts propagating away from the pinger (1 s intervals) until they reach the sensor. The top box is the spectrogram of a 2.2 s snippet of the sensor recording, clipped between 35.5 kHz and 38.5 kHz, when the pinger was active in the water. The blue dots, around 37 kHz, are points of high acoustic intensity and spacing close to 1 s.
The computed spectrogram for an audio snippet of 2.2 s from the recorded data (see supplementary material for the recorded audio file: underwater_pinger_audio_10s.wav) indicates intense pulses, when compared to the surrounding spectrum, centered at ∼37.0 kHz and intervals of ∼1 s (Figure 1, top box). Therefore, the pinger acoustic signal on the data stream was a positive indication of the TA sensor operational capabilities.

Detection range estimative
The flux of particles with ultra-high energies can be very low 4 . For instance, the flux of cosmic rays with energies of 10 19 eV is ∼1/km 2 year [5] . To better detect these rare events, it is important to understand the sensing range 6-10 of the thermoacoustic sensor developed in this work.
Once the energy from a cosmic particle is transferred to the water, the rapid expansion of the volume generates an acoustic pulse. This pulse will propagate through the water volume until it reaches a listening sensor or vanishes away. During the transit of an acoustic wave in the water, it will be attenuated mainly by the effects of divergence, or geometric spreading, and absorption, by molecular relaxation (in seawater strongly dominated by MgSO 4 and H 3 BO 3 ) 11,12 . The work of Volovik et al. (1979) 13 presents an expression for the maximum pressure p max (in Pa), at a distance r (in m), caused by a particle with energy E = 10 16 eV to 10 21 eV, which takes into account the transmission loss, The factor φ (r) adjusts the result for the deviation of a cylindrical spreading to the distance 14 .
As previously discussed, the advantage of the acoustic method, over the optical, is its increased detection range. Neutrino oceanic observatories optical-modules are spaced in distances shorter than the light absorption length, that for blue light (λ ∼ 426 nm) it is ∼50 m to 55 m [15] . What would be the acoustic signal amplitude for a range ten times bigger than the blue light absorption length, d = 500 m? Using Eq. 1, the amplitude of a sonic signal generated by a particle with energy E = 10 19 eV at a distance of 500 m (φ =0.28) will be 55.1 mPa.
The resulting electrical signal, found through the thermoacoustic sensor sensitivity (M h = −168.9 dB re 1V/µPa = 3.59 nV/µPa), is equal to 197.8 µV. Now, this small captured signal can be processed by following amplifying stages until reaching appropriate levels for the Analog-to-Digital converter (ADC).
We must note that the ultimate sensitivity of the system will be dictated by the ambient noise level. Ocean noise is a complex subject, the following literature has a wide coverage on the topic: 12,16,17 .

Temporal accuracy
We conducted an experiment to estimate the temporal accuracy of the sensor. Using a small acoustic tank, described in the Section "Experimental Setup", a waterproofed 35 mm piezoelectric disk was fixated at a depth of h ∼ 18.5 cm, and excited by a signal generator (Agilent 33250A) with a burst of 5 cycles of a sinus at f = 120 kHz and amplitude of 10 Vpp.
The thermoacoustic sensor was installed in the extremity of a rigid rod attached to a robotic linear actuator (Daedal MD-2303), with a displacement resolution of 50 µm/step. The linear actuator was connected to a laptop able to issue moving commands. Before commencing the experiment, the sensor was placed 14.18 cm from the sound source, and its position was adjusted in 40 steps of 50 mm until reaching a total distance of 34.18 cm.
At each position, an average of 256 acoustic pulses, that traveled through the tank and reached the thermoacoustic sensor, was acquired through a digital oscilloscope with a sampling frequency of f s = 350 MHz (Tektronix MSO-4034). The acoustic pulse propagation time was then calculated as the difference between the instant of signal injection on the piezoelectric disc and the time of arrival at the sensor.
Calculating the time difference between two consecutive measurements, we can have 40-time measurements over the same, precise, 50 mm distance. The resulting average propagation time ist = 3.39 µs, and a standard-deviation σ t = 0.19 µs, which can be considered as the temporal uncertainty of the device for this specific experimental setup. With the value of the sound-speed in water c s = 1504.6 m/s (T w = 28.0 • C) [18] , the position uncertainty can be estimated through δ = c s · σ t = 0.286 mm (an error of ∼0.57% over the distance of 50 mm).