1 Introduction

The primary cosmic field (PCF) is composed by highly energetic protons and heavier ions of galactic, extragalactic and solar origin. Their interaction with the nuclei of the Earth atmosphere produces a secondary field, which in turn reaches the Earth ground after being attenuated by the atmosphere. This secondary field (cosmic field at ground, CFG) is composed by neutrons, protons, muons, electrons and photons. The solar activity, with its nearly sinusoidal eleven-years cycle, causes time variations in the PCF and consequently in the CFG [1]. A residual modulation with 24-h period is given by the rotation of the Earth in the non-uniform interplanetary magnetic field [2]. These dependences can be perturbed by unpredictable, rare solar events such as the Forbush decrease [3]. The amount of primary cosmic rays entering the atmosphere is affected by the geomagnetic field; thus their flux depends on the geomagnetic latitude. The CFG tends to be more intense at polar latitudes than at equatorial latitudes following a hyperbolic tangent law [4]. Due to the inclination of the geomagnetic field axis with respect to the Earth rotation axis and to the displacement of the dipole center with respect to the Earth’s center, the geomagnetic field has the lowest values of the planet in the South Atlantic Magnetic Anomaly (SAA) region, a vast area of the Atlantic Ocean and South America, where the geomagnetic field can be even 30% lower than other areas with the same altitude and latitude [5], causing a relatively larger flux of cosmic rays. Due to the asymmetry of the geomagnetic field, the SAA is also the region where the distance of the Van Allen Belts from the Earth surface is the lowest. The atmosphere differently shields the different components of the secondary cosmic rays. Thus, their relative importance at ground depends on the penetration into the atmosphere (i.e. on the elevation above the sea). From a radiological protection point of view, the effective dose at sea level is dominated by the muon component, whilst at elevations larger than about 1000 m a.s.l. the neutron component is the most important [6]. According to Sato [7], neutrons account for 20% of the population-weighted annual effective dose due the CFG. However, in countries where citizens reside at high altitude, this fraction can reach 35% (Bolivia) 31% (Perú and Bhutan), 35% (Bolivia), 36% (Kyrgyzstan) up to up to 38% (Andorra). The energy distribution of the CFG neutron component comprises cascade neutrons (20 MeV–GeV), de-excitation evaporation neutrons (MeV), and thermal and epithermal neutrons. The total fluence rate was found to exponentially increases with elevation [8] and to exponentially decrease with the atmospheric pressure [9]. The cascade component is downwards-directed, whilst lower energy components are distributed in the whole solid angle. The typical lethargy distribution includes a cascade peak at about 100 MeV, an evaporation one at 1-2 MeV, an epithermal continuous and a thermal peak. The low-energy portion of the spectrum (E \(\le \) 20 MeV) depends by the interaction of cascade neutrons with materials in the vicinity (tens - hundreds meters) of the measurement point, and is differently affected by surrounding materials. Particularly, it decreases in presence of hydrogenated media like soil moisture and snow. Soil moisture and snow are known to cause an increase in the cascade-to-evaporation peak ratio [10]. The Extended Range Bonner Sphere Spectrometer (ERBSS) [11,12,13] is the most indicated instrument for establishing a common basis for measuring and comparing neutron spectra in the CFG, as it exhibits adequate sensitivity, resolving power and covers the whole energy interval from thermal up to GeV neutrons [14]. Bonner Spheres consist in a set of polyethylene spheres of different diameters with a thermal neutron counter in their centre. As each sphere exhibits a different energy-dependent response, spectrometric information can be obtained by studying the variation of the counting rate as a function of the sphere diameter (unfolding process). Amongst the numerous neutron detection campaigns at different elevations and latitudes starting from the late 1950’s [15], only few included neutron spectra measurement with ERBSS [4, 16,17,18,19,20]. More ERBSS measurements at different elevations and geomagnetic field conditions are needed for space weather, atmosphere science and radiation protection. As a very relevant example, these data are required to validate the computation codes used to estimate radiation exposure of aircrews [21]. The region of the SAA is of particular interest because of the very few available data and its unique geographical position characterized by the low geomagnetic field and a small distance (200 km) from the Van Allen Belts, where protons of energy up to a few GeV are magnetically trapped. Neutron dose rates larger than expected have been reported in Ref. [22] in the SAA area. Measurements in the SAA region are relevant for health protection especially in the region of the Northern Andes, where large populations live at high elevations. In order to contribute filling this data gap, the SAMADHA (South Atlantic Magnetic Anomaly Dosimetry at High Altitude) project of INFN aims to investigate and monitor the neutron fields at high elevation in the SAA using a specially designed ERBSS [23], here called S-ERBSS (SAMADHA Extended Range Bonner Sphere spectrometer). Prior to its installation at 5200 m a.s.l. at the Chacaltaya laboratory (http://www.chacaltaya.edu.bo) in the Bolivian Andes, the S-ERBSS was tested at 3480 m a.s.l. on the Italian western Alps in the Testa Grigia Laboratory (Italy, 45.95\(^\circ \) N, 7.7\(^\circ \) E, vertical rigidity cutoff RV = 4.71 GV in 2015). This laboratory was built in 1947 and is currently hosting experiments in the fields of astrophysics, dosimetry, atmospheric science and medicine [24]. Although neutron dose measurements were performed here in the past [25,26,27], no measurements with ERBSS have been done to date. As Testa Grigia is one of the highest altitude research laboratories, the data provided by this paper are doubly relevant: for testing the S-ERBSS prior to the campaign in the SAA, and to provide new spectrometric data at this high-elevation.

2 The SAMADHA ERBSS (S-ERBSS)

Fig. 1
figure 1

The SAMADHA extended range Bonner Sphere spectrometer (S-ERBSS) installed in the Testa Grigia Station

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The S-ERBSS (see Fig. 1) was especially designed to operate unattended and to discriminate genuine neutron events from spurious ones in a low counting rate scenario (typ. 0.03 s\(^{-1}\)). In addition to the neutron fluence rate, its energy distribution and the ambient dose equivalent, the S-ERBSS computes arrival time distribution of the events. Although the S-ERBSS is described in details elsewhere [23], its constituents are briefly recalled here to improve readability. The system is composed of the following:

  • six polyethylene spheres with diameter 80, 100, 120, 150, 170 and 200 mm, plus two extended range spheres with diameter 200 mm and including lead or iron inserts;

  • Cylindrical \(^{3}\)He (VacuTec type 70 060) proportional counters [28] with effective volume 2.8 cm\(^{3}\), effective length 40 mm and gas pressure 10 bar. To minimize the vulnerability to electromagnetic interferences, all detectors were cabled using triaxial cables and double grounded. The detectors are biased at 850 V. To prevent non-neutron (or false positive) signals arising from conducted interferences, a 7 \(\mu \)F capacitor filter was interposed between the high-voltage generator and the detectors. A remotely controlled switch allows the high-voltage generator to charge the capacitor for 60 s every 6 h. Consequently, the detectors are permanently isolated from the AC line, except for the very short charging intervals. The stability of the 220 V AC supply is guaranteed by an un-interruptible power supply.

  • The eight detectors are simultaneously acquired and the pulses are shaped in Gaussian form (shaping time 8 \(\mu \)s) by a dedicated multi-input analog board with gain 0.9 V MeV\(^{-1}\). A genuine neutron pulse is shown in Fig. 2.

  • Real-time data processing: the waveform from the analog board is digitized by a 2 MS s\(^{-1}\) chn\(^{-1}\) commercial digitizer (National Instrument 6366) programmed in LabVIEW.

In order to eliminate the non-neutron events, the following filters are applied in real-time by the software:

  1. 1)

    Gamma events are rejected by applying a lower threshold in pulse amplitude, set to 0.3 MeV.

  2. 2)

    Small discharges in the detector may occur due to electronegative impurities in the filling gas or imperfections in the insulating materials. These discharges, resulting in pulses with amplitude higher than 1 V, are rejected by applying an upper threshold in pulse amplitude. An example of discharge event, saturating the shaper amplifier, is shown in Fig. 2 (event C).

  3. 3)

    As the high-voltage system is insulated from the AC supply, residual spurious events due to conducted interferences from the low-voltage supply or the computer are very rare (less than 10\(^{-3}\) s\(^{-1}\)), see Fig. 2, event B. These are eliminated by comparing the shape of the candidate event with that of the “reference one” in terms of power spectra in the Fourier domain. For each genuine event (see Fig. 2, event A) a string is written in a detector-specific data file, including the arrival time (with resolution of 2 \(\mu \)s) and the pulse amplitude. The software also manages the recharge cycles of the high voltage capacitor filter.

Fig. 2
figure 2

Events examined in real-time by the software: A genuine neutron event; B spurious event due to conducted interference; C spurious event due to a discharge in the detector

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Post-processing: the time-to-next-event distributions (TNED) of the pulses in the detectors are studied to search for periodical interferences or high-frequency noise. In Fig. 3, the TNED is shown for the detector in 100 mm diameter sphere, having average count rate (3.56±0.08)\(\times \) 10\(^{-2}\) s\(^{-1}\). For events governed by a Poisson distribution the TNED is exponential. This is the case of Fig. 3: here the best estimation of the average count rate on the basis of an exponential model is (4.0±0.5) \(\times \)10\(^{-2}\) s\(^{-1}\). Very similar distributions are observed for the other spheres.

Fig. 3
figure 3

TNED for the detector in 100 mm diameter sphere

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3 Measurements and discussion

The S-ERBSS was exposed at the Testa Grigia station for 15 h starting from 13th July 2022 at 18:00. The station is on a glacier with a large snow cover. According to Brall [10], the CFG neutron fluence decreases with the snow cover, down to a factor of about 2.5 as compared to a soil without snow. Correspondingly, the cascade-to-evaporation peak ratio increases. The spectrometer was installed in a 3 m \(\times \) 6 m room inside a one-floor building. The infrastructure includes internet access, which allows remote control of all parameters of the system. Various meteorological parameters are being measured on a routine basis, including the air pressure. The air pressure varied of less than 0.2% during the measurement time, with an average value of 681.9 hPa. Figure 4 compares the trends of the air pressure and the counts recorded every hour in the 200 mm diameter sphere. Poisson fluctuations appear to be the only source of variability for the counts.

Fig. 4
figure 4

200 mm sphere: counts collected every hour Vs. air pressure. Data are normalized to their average

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Fig. 5
figure 5

Average count rates of the S-ERBSS as a function of the diameter / sphere configuration

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The average count rates of the S-ERBSS are reported in Fig. 5 as a function of the diameter. As explained in Ref. [29], the smooth shape of this curve indicates that the measurements were performed under “stable conditions, using the right monitors, and are not affected by supplementary uncertainties of unexplained origin”. This serves as a “consistency check”, prior to the unfolding process. The shape of the plot contains the spectrometric information and is typical of the spectrum of secondary neutrons from cosmic radiation [19]. The count rates of Fig. 5 were unfolded with the FRUIT unfolding code [30] in special gradient mode (FRUIT-SGM) [31, 32], using the previously derived S-ERBSS response matrix. The response functions were assumed to be affected by the following uncertainties:

  • ± 3% [23] for the polyethylene spheres, mainly responding below 20 MeV where the cross sections are well-known.

  • ± 10% for the extended range spheres, mainly responding above 20 MeV where the cross sections are generated by model and affected by larger uncertainties [33, 34].

Different guess-spectra were used to verify the robustness of the solution. As the presence of snow is recognized to be the main responsible for the shape of the spectrum, two unfolding sessions were conducted, using two guess spectra calculated by Brall et al. [10] in “extreme” snow conditions and shown in Fig. 6:

  • “Minimal snow cover (1 cm of snow water equivalent (SWE) )”: due to minimal hydrogenated material in the surroundings, the evaporation peak is larger than the cascade peak.

  • “Saturation snow cover (20 cm SWE)”: As the amount of hydrogenated material (snow cover) increases, the evaporation peak is gradually attenuated. The cascade-to-evaporation peak ratio increases with the snow cover till a saturation value at 15–20 cm SWE [10].

Fig. 6
figure 6

Two guess spectra calculated by Brall et al [10] under “extreme” snow conditions and used to verify the robustness of the unfolding solution. Spectra are normalized to the unit fluence and in lethargy representation

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Fig. 7
figure 7

Results of two unfolding sessions using guess spectra with SWE = 1 cm and SWE = 20 cm. Spectra are normalized to the unit fluence and in lethargy representation

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As demonstrated in Fig. 7, the spectra obtained in the two separate unfolding sessions do not depend on the specific guess spectrum and provide the same output spectrum within unfolding uncertainties. This unfolded spectrum has a large cascade-to-evaporation peak ratio which is coherent with a large snow cover at the measurement site. The uncertainties in Fig. 7 are specified on a bin-per-bin basis and are obtained by propagating uncertainties on the input quantities (response matrix and sphere counts) through the unfolding process [31, 32]. Interestingly, the uncertainties in the thermal region are large (about 30-40%). Indeed, the S-ERBSS does not include small spheres (30 to 50 mm diameter) that are more sensitive in this region. For practical reasons the number of detectors was limited to eight at design stage, and preference was given to larger spheres to emphasise the resolving power in the more interesting energy region above 10 keV. The thermal peak is only determined by the materials in the vicinity of the system, and is not used to study the properties of the CFG. Nevertheless it is interesting to note that the unfolding process correctly considers the lack of resolving power in this domain by attributing a higher uncertainty to the fluence in the related energy intervals. As expected, the agreement between the two unfolding solutions improves in the epithermal and evaporation regions, where the resolving power is higher and bin-per-bin uncertainties are lower (10-20%). In the cascade region the uncertainties are in the order of ±20% or higher and are mainly due to the larger input uncertainties (± 10%) associated to the response of the extended range spheres. These numbers well agree with relevant literature on high-energy response of extended range Bonner Spheres [34]. Table 1 reports the spectrum-integrated quantities (average between the two solutions of Fig. 7). These data have been corrected:

  • For the atmospheric pressure, assuming 671 hPa as a reference pressure for the site;

  • For the solar activity, usually represented by the pressure-corrected count rate of the Oulu neutron monitor (http://cosmicrays.oulu.fi/) [35]. 6400 min\(^{-1}\) was assumed as reference count rate for the Oulu monitor.

Comparing the measured neutron fluence rate with literature values requires prior elaboration. As mentioned before, the total fluence rate at the same site may vary up to a factor of 2.5 depending on the presence of hydrogenated media as snow. The low-energy portion of the spectrum (E \(\le \) 20 MeV) is especially affected by this factor of influence. Therefore the cascade fluence rate (E \(\ge \) 20 MeV) is the most indicated for the comparison. To this aim, literature neutron spectra measured at various elevations but similar latitudes of the Testa Grigia station were elaborated to extract the cascade fluence rate. This was further corrected for the atmospheric pressure and the solar activity, assuming 6400 min\(^{-1}\) of the Oulu monitor as reference parameter to represent the solar activity. Figure 8 reports the corrected cascade fluence rate values as a function of the elevation. The latitude of the sites ranges from 41° 54’ (Rome) to to 47° 25’ (Zugspitze), corresponding to a vertical geomagnetic rigidity cutoff in the interval \(\simeq \) 4.1\(-\)6.3 GV. Coherently with the results of this work and with relevant literature [34], the fluence rate values were assumed to be affected by a ±20% uncertainty. The experimental values can be fitted by an exponential law of the form

$$\begin{aligned} \dot{\phi }_{C}(z) = \dot{\phi }_{0} \times e^{\alpha z} \end{aligned}$$
(1)

where \(\phi (0)\)= (2.90 ± 0.20) \(\times \) 10\(^{-3}\) cm\(^{-2}\) s\(^{-1}\) and \(\alpha \) = (8.4 ± 0.5) \(\times \) 10\(^{-4}\) m\(^{-1}\) Model-based values obtained with the EXPACS code [36] are also reported in Fig. 8. Interestingly, they closely agree with the exponential fit. Similar exponential curves were derived by Kowatari et al. [8] and Cheminet et al. [20] but they are expressed in terms of total neutron fluence rate, so they can only describe data taken in sites with similar local conditions, especially in terms of amount of hydrogenated media. By contrast, the curve derived in this work can be regarded as “universal” for sites at similar geomagnetic latitudes.

Table 1 Spectrum-integrated quantities for the neutron component of the CFG at Testa Grigia station after correction for the atmospheric pressure and the solar activity
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Fig. 8
figure 8

Corrected cascade fluence rate as a function of the elevation. Letters correspond to: A: Rome at sea level [37], B Pic-du-Midi at elevations 518 m, 1067 m and 2885 m [20]; C Zugspitze at 2650 m [18]; D Zugspitze at 2650 m [38]; E This work at 3480 m; F Jungfrau at 3475 m and 3585 m [39]

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4 Conclusions

The cosmic neutron spectrometry campaign at 3480 m a.s.l. in the Testa Grigia Station was successful as it reached the primary objective of validating the extended range Bonner Sphere Spectrometer that will be used by the SAMADHA project to measure neutron fields in the SAA. Secondarily, it contributed to increase the available sets of measured neutron spectra at high-elevation sites. These measured data are important because they are used to validate computational models such as those for aircrew dosimetry. The high-energy neutron fluence rate from this work was compared with literature values measured at various elevations but similar latitudes. An exponential fitting law was found to relate the experimental data with the elevation and, very interestingly, this fitting curve well agrees with results from the model-based EXPACS code. As the cascade component is not influenced by the materials surrounding the measurement site, this curve can be regarded as “universal” for a given geomagnetic latitude. Flux variations are expected during the most active phases of the Sun, due the geomagnetic field perturbations or solar proton events, which will be addressed by the future measurements in the Andes within the SAMADHA project.