∎

e1e-mail<EMAIL_ADDRESS>
11institutetext: Centro de Astropartículas y Física de Altas Energías (CAPA),
Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
22institutetext: Laboratorio Subterráneo de Canfranc, Paseo de los Ayerbe s/n,
22880 Canfranc Estación, Huesca, Spain 33institutetext: AEMET, Delegación
Territorial de AEMET en Aragón, Paseo del Canal 17, 50007 Zaragoza, Spain
44institutetext: Fundación ARAID, Avenida de Ranillas 1D, 50018 Zaragoza,
Spain 55institutetext: Laboratorio de Bajas Actividades (LABAC), Universidad
de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain 66institutetext: EUPLA,
Calle Mayor 5, 50100 La Almunia de Doña Godina, Zaragoza, Spain

# Long term measurement of the 222Rn concentration in the Canfranc Underground
Laboratory

J. Amaréaddr1,addr2  I. Bandacaddr2  A. Blancasaddr1  S. Borjabadaddr2  S.
Buisánaddr3  S. Cebriánaddr1,addr2,addr5  D. Cintasaddr1,addr2  I.
Coarasaaddr1,addr2  E. Garcíaaddr1,addr2,addr5  M. Martínezaddr1,addr2,addr4
R. Núñez–Lagosaddr5  M.A. Olivánaddr1  Y. Ortigozaaddr5,addr6  A. Ortiz de
Solórzanoaddr1,addr2,addr5  C. Pérezaddr1,addr2,addr5  J.
Puimedóne1,addr1,addr2,addr5  S. Rodríguezaddr5  A. Salinasaddr1,addr2  M.L.
Sarsaaddr1,addr2  P. Villaraddr1

(Received: date / Accepted: date)

###### Abstract

We report the results of six years (2013-2018) of measurements of 222Rn air
concentration, relative humidity, atmospheric pressure and temperature in the
halls A, B and C of the Canfranc Underground Laboratory (LSC). We have
calculated all the Pearson correlation coefficients among these parameters and
we have found a positive correlation between the 222Rn concentration and the
relative humidity. Both correlated variables show a seasonal periodicity. The
joint analysis of laboratory data and four years (2015-2018) of the
meteorological variables outside the laboratory shows the correlation between
the 222Rn concentration and the outside temperature. The collected information
stresses the relevance of designing good Rn-mitigation strategies in current
and future experiments at LSC; in particular, we have checked for two years
(2017-2018) the good performance of the mitigation procedure of the ANAIS–112
experiment. Finally, in another measurement (2019-2021) for two years of live
time, we report an upper limit to the residual 222Rn content of the radon-free
air provided by the radon abatement system installed in the laboratory.

††journal: Eur. Phys. J. C

##  1 Introduction

Monitoring the level of 222Rn in laboratories of low activity measurements
and, in particular, in underground laboratories is essential to ensure the
safety of the workers inside the laboratory. The main remediation action is a
correct ventilation Arpesella1997healthp ; BASSIGNANI1997rm ;
LESKO2015taup2013 ; liu2018arxiv  to evacuate the radon emanation from the
rock and to keep a concentration similar to that of the open air, that usually
is < 100 Bq m-3 Euratlas . The posterior actions to provide a very low
radioactive background to the experiments in the laboratory depend on their
requirements. The experiments can be purged with nitrogen (from compressed
nitrogen or evaporated from a liquid nitrogen dewar) or with radon-free air
provided that the laboratory has an adequate system to satisfy this demand,
see for instance perezperez2021radon . Monitoring the 222Rn level is also very
important to avoid the plate-out of the 222Rn daughter, specially 210Pb and
its descendants, during the assembly of the components of an experiment
STEIN2018nima . The seasonal modulation of the 222Rn concentration affects in
particular to experiments aiming at the study of the annual modulation
expected in the interaction rate of the galactic halo dark matter particles
modulacion_Drukier1986 . Because of that, these experiments lee2011radon ;
prd-minos-cogent  are specifically isolated from the laboratory air and
conveniently purged with radon free gas.

We address three items in this article: monitoring the 222Rn concentration
inside the LSC and its correlation with the internal and external temperature,
pressure and relative humidity; the measurement of the residual 222Rn
concentration of the evaporated nitrogen that was used to purge the ANAIS–112
experiment during 2017-2018 Amare:2018sxx ; Amare2021prd  and, finally, a
similar measurement of the air provided by the radon abatement system
perezperez2021radon  that supplies radon-free air to the experiments in the
LSC DarT_Garcia_2020 ; cross_Bandac2020 ; next_Adams2021 ; Castel2019 ;
BabyIaxo2021 ; clyc2018 ; HENSA-ANAIS_TAUP2021 . Our data add very useful
information to the published results of other background sources at LSC: the
rock radioactivity rock-LSC-taup2005 , the neutron flux CARMONA2004523 ;
neutrons_LSC-2013  and the cosmic-ray muon flux muons_LSC-2019 .

##  2 Description of the Canfranc Underground Laboratory

The Canfranc Underground Laboratory, LSC111Detailed information at www.lsc-
canfranc.es. (Laboratorio Subterráneo de Canfranc) is a Spanish scientific
installation located in Aragón, in the village Canfranc-Estación (Huesca) at
1120 m above sea level (geographical coordinates: 42º 46’ 30” N; 0º 31’ 42”
W). Its laboratories and rooms have been excavated in the rock at 800 meters
depth, below the Tobazo Mountain, at the Spanish Pyrenees between the Somport
road tunnel, which links Spain with France, and the parallel railway tunnel
today in disuse.

The underground infrastructure has a total surface of about 1600 m2 divided in
LAB780 (two small experimental rooms at 260 meters depth), LAB2400 and LAB2500
(both at 800 meters depth), named according to the distance in meters from
each location to the Spanish entrance of the railway tunnel (780, 2400 and
2500 m, respectively). This work has focused on the main experimental area
(LAB2400) that consists of a large room, hall A, 40$\times$15$\times$12
(height) m3 and a smaller volume of 15$\times$10$\times$8 (height) m3 divided
into two contiguous rooms, halls B and C (Figure 1).

Figure 1: Scheme (not to scale) of the Canfranc Underground Laboratory
facilities

The ventilation provides around 11000 m${}^{3}~{}$h-1 of fresh air. The flow
of fresh air is taken from the mountain at 1400 m altitude and then reaches an
intermediate ventilation room at 1120 m through a ventilation shaft and a
ventilation gallery excavated in the rock. From there it is sent to the air
conditioning room by a forced ventilation duct, where it joins 14000
m${}^{3}~{}$h-1 of the returned air and its final temperature is regulated by
the air conditioning system. The fresh air flow guarantees the total renewal
of the laboratory air once per hour Radiopro2014 .

##  3 222Rn concentration in six years of data

The here reported measurements of the 222Rn concentration in air (Rni), the
temperature (Ti), the atmospheric pressure (Pi) and the relative humidity
(RHi) have been obtained using three Genitron (now BERTIN) ALPHAGUARD P30™
monitors from 2013 to 2018. The measurements were taken continuously by a
dedicated software that recorded every 10 minutes the values of the four
variables and the statistical uncertainty of the 222Rn concentration.

The calibration uncertainties quoted in the data sheet are 3% for the 222Rn
concentration activity, 1.5 °C for the temperature, 3 hPa for the atmospheric
pressure and 3% for the relative humidity. In order to check for small
variations, each monitor measured in the same hall for the six years. The
calibrations of the monitors were tested by an interlaboratory comparison in
2015 laruc2015 . The mean departure of our monitors was a 9% with respect to
the 222Rn concentrations measured by the reference monitor of the comparison.

The 222Rn annual average activity concentrations in the three halls are listed
in Table 1; their statistical uncertainties are about 0.07% because the
response of the monitor is (5 counts per minute)/(100 Bq m-3). The radon
annual level is independent of the hall (within the 3% instrument calibration
uncertainty), it complies with the European directive on radon in workplaces
directive_euratom , with the ICRP recommendations icrp103  and it is well
below the 600 Bq m-3 allowed by Spanish legislation csn11-04 .

Table 1: Annual average activity concentration of 222Rn (Bq m-3) from 2013 to 2018. Their statistical uncertainties are approximately 0.07% whereas the instrument calibration error is 3%. The last column is the annual average for the 6 years of data Room | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2013-8
---|---|---|---|---|---|---|---
Hall A | 87.5 | 82.4 | 82.8 | 80.4 | 80.8 | 82.9 | 82.8
Hall B | 89.1 | 83.8 | 84.0 | 82.8 | 84.8 | 87.0 | 85.2
Hall C | 89.2 | 82.7 | 86.1 | 82.9 | 83.3 | 84.4 | 84.8

###  3.1 Correlations between the variables inside the laboratory

The relations between meteorological parameters and levels of 222Rn have been
studied before at shallow depth, see for instance Pujol_Garcia-Tobar_2014 . In
this section, we give the results for all possible correlations between every
pair of the monthly averages at LSC (222Rn concentration, temperature,
atmospheric pressure and relative humidity). Table 2 shows the values of the
Pearson correlation coefficient, $r$, for the monthly averages of all the
pairs of parameters measured at halls A, B and C.

Table 2: Values of Pearson correlation coefficient (2013-18) for all pairs of the measured monthly averaged parameters inside the LSC |  | Radon | Temperature | Pressure | Relative humidity
---|---|---|---|---|---
|  | Hall A | Hall B | Hall C | Hall A | Hall B | Hall C | Hall A | Hall B | Hall C | Hall A | Hall B | Hall C
| Hall A | 1.00 |  |  |  |  |  |  |  |  |  |  |
Rni | Hall B | 0.98 | 1.00 |  |  |  |  |  |  |  |  |  |
| Hall C | 0.96 | 0.94 | 1.00 |  |  |  |  |  |  |  |  |
| Hall A |  $-$0.13 |  $-$0.07 |  $-$0.16 | 1.00 |  |  |  |  |  |  |  |
Ti | Hall B | 0.09 | 0.18 | 0.05 | 0.53 | 1.00 |  |  |  |  |  |  |
| Hall C |  $-$0.02 | 0.09 |  $-$0.03 | 0.32 | 0.86 | 1.00 |  |  |  |  |  |
| Hall A | 0.11 | 0.13 | 0.11 | 0.14 | 0.12 | 0.06 | 1.00 |  |  |  |  |
Pi | Hall B | 0.14 | 0.13 | 0.13 | 0.07 | 0.01 |  $-$0.10 | 0.97 | 1.00 |  |  |  |
| Hall C | 0.10 | 0.12 | 0.15 | 0.07 | 0.10 | 0.09 | 0.97 | 0.94 | 1.00 |  |  |
| Hall A | 0.73 | 0.69 | 0.69 |  $-$0.14 | 0.22 | 0.05 | 0.34 | 0.37 | 0.36 | 1.00 |  |
RHi | Hall B | 0.72 | 0.68 | 0.67 | 0.00 | 0.12 |  $-$0.12 | 0.35 | 0.41 | 0.33 | 0.96 | 1.00 |
| Hall C | 0.70 | 0.67 | 0.70 | 0.01 | 0.17 |  $-$0.07 | 0.36 | 0.41 | 0.38 | 0.96 | 0.98 | 1.00

The statistical significance of the $r$–value of $n$ pairs of two variables
can be easily calculated because the variable

$t=r\sqrt{\frac{n-2}{1-r^{2}}}$ (1)

follows the Student’s $t$ distribution with $n-2$ degrees of freedom for two
uncorrelated normal variables Kendall_1 . Even in the case of non–normal
variables or small size $n$, the Student’s $t$–distribution is a very good
approximation for the $t$ variable in Eq. (1) Kendall_2 . Therefore, the
decision threshold, $\left|r_{\alpha}\right|$, to reject the null hypothesis
(no correlation) is obtained from the corresponding two-tailed
$\left|t_{\alpha}\right|$.

We take a 99.92% CL for the decision threshold because if the variables of
Table 2 are uncorrelated, the probability to get some $r$–value $\ni$
$\left|r\right|>\left|r_{\alpha}\right|$ with 66 evaluated $r$–values is
$1-(0.9992)^{66}=0.05$, similar to a 95% CL if only one $r$–value were
evaluated. The monthly average 6-year data gives $n=72$, i.e., 70 degrees of
freedom for the Student’s $t$ and $\left|r_{\alpha=0.0008}\right|=0.39$.

The 222Rn concentration in halls A, B and C are highly correlated, $r=0.94$ to
0.98, and similar behaviour can be found for the pressure and the relative
humidity. The temperature behaviour is different: there is correlation between
the contiguous halls B and C, $r=0.86$; the halls A and B are slightly
correlated, $r=0.53$; meanwhile the halls A and C are uncorrelated, $r=0.32$.
This is a consequence of the liquefaction for several months Calvo_2017  of
the argon needed for the ArDM experiment, that increased the temperature of
the hall A (Figure 2) but not those of halls B and C (Figure 3). There is also
correlation between the relative humidity and the 222Rn concentration,
$r=0.7$, for the nine pairs of the three halls. There exists a hint of a minor
correlation between the relative humidity and the pressure, with $r$ close to
0.39. The other pairs are not significantly correlated.

Figure 2 plots the monthly averages of 222Rn concentration, relative humidity,
temperature and atmospheric pressure for the six years for the hall A. Halls B
and C have very similar plots, except for the temperature (Figure 3) because
both halls were not very affected by the argon liquefaction of the ArDM
experiment. The statistical uncertainty of the 222Rn monthly average is 0.24%
and those of the other three variables are unknown because of the lack of
information in the data sheet of the radon monitor, though likely they are
less than their calibration uncertainties. The relative humidity has a clear
seasonal periodicity and the 222Rn concentration points to a similar
behaviour, more evident in 2013, 2015 and 2018. Both seasonal periodicities
produce the here reported correlation between both parameters in the three
halls (Table 2 and Figure 4). The seasonal periodicity is not observed either
for the atmospheric pressure or the room temperature (Figure 2) because the
former is determined by the external atmospheric pressure (non seasonal, see
section 4) and the latter depends, mainly, on the internal air conditioning
system and, sometimes, on considerable local alterations.

Figure 2: Monthly average of the hall A data: 222Rn concentration (upper
left), relative humidity (upper right), temperature (bottom left) and
atmospheric pressure (bottom right) from January 2013 to December 2018. The
fits of the 222Rn concentration and the relative humidity to Eq. 2 are also
shown. Corresponding plots for halls B and C are similar, except the
temperature (see Figure 3)

Figure 3: Monthly average of the temperature in the hall B (left) and hall C
(right) from January 2013 to December 2018. The sharp increase of the
temperature due to ArDM experiment (see text) is very attenuated in the hall B
and it is almost imperceptible in the hall C

Figure 4: Monthly averages of the 222Rn concentration versus the monthly
averages of the relative humidity at hall A from 2013 to 2018. Corresponding
plots for halls B and C are similar

###  3.2 Seasonal periodicity of the 222Rn concentration and of the relative
humidity inside the laboratory

The airborne radon depends on the radon concentration in soil gases and on its
release to the atmosphere. A long-term study on the effects of climate on soil
radon asher1992  found that wind speed, relative humidity, air and soil
temperatures, and the difference between those temperatures cause both day-to-
day and seasonal variations in soil radon, being seasonal variations of
greater magnitude than day-to-day fluctuations. Although meteorological
variables are not independent and it is difficult to estimate their relative
impact, the authors of reference asher1992  were able to conclude that
precipitation appears to be the most important meteorological variable
affecting the content and the seasonal variation of 222Rn in soil gases.
Differences between summer and winter 222Rn concentration have been reported
in large dwellings samples arvela1995rpd ; BOCHICCHIO2005rm . The general
trend is that indoor 222Rn is higher in winter than in summer (winter/summer
ratio, W/S>1); we have observed in LSC the opposite result. However, the
dispersion of the measurements in arvela1995rpd ; BOCHICCHIO2005rm  is
significant and there exist values of W/S<1\. Other observations of W/S<1 have
also been reported, see tanner1992  and references therein; on the other hand,
the result of hans_lyon1986  shows that W/S>1 for indoor 222Rn, whereas W/S<1
for outdoor 222Rn. A quantitative model Arvela2016  provides a sinusoidal
variation in the monthly average of the indoor 222Rn concentration with
W/S>1\. It is worth noting that this model has been applied with the typical
parameters (outdoor–indoor temperature gradient, wind speed and 222Rn
diffusion and convection rates) of Finnish climate and houses. But the model
also shows that if the building materials are the dominant radon source, then
the maximum 222Rn concentration occurs in summer.

The annual periodicity of the relative humidity and the concentration of 222Rn
at LSC can be analyzed fitting the values of their monthly average to an
equation of the type

$Y=A+B\cos\left(\frac{2\pi(t-t_{M})}{T}\right)$ (2)

where $A$ and $B$ are the annual average and the modulation amplitude,
respectively, $T$ is the period, $t_{M}$ is the time corresponding to the
first maximum amplitude and $t$ is the measurement time after 1st January 2013
at 00:00.

The parameters $A$, $B$, $T$ and $t_{M}$ are estimated by an unweighted least
squares fit because the standard deviations of the measurements of the
relative humidity are unknown and, although we know the statistical
uncertainty of the radon concentration, we do not know its standard deviation
due to its natural variability. Therefore, the square root of the minimum of
the sum of the squared residuals per degree of freedom is an estimate of the
standard deviation of a measurement, assuming that it is the same for each
measurement bevington . The results for the relative humidity are listed in
Table 3. The estimated standard deviations of the relative humidity monthly
averages are 3.6%, 4.2% and 4.3% for the halls A, B and C, respectively. The
three periods are compatible with 1 year and the three maxima $t_{M}$ are
equal (within uncertainties), their mean value is ${215\pm 3}$ d, around 3rd
August.

Table 3: Values of the fitted parameters of the relative humidity of the years 2013–2018 to Eq. (2). The maxima are in the first week of August Room | A (%) | B (%) | T (d) | tM (d)
---|---|---|---|---
Hall A | ${34.6\pm 0.4}$ | ${11.2\pm 0.6}$ | ${364\pm 2}$ | ${214\pm 5}$
Hall B | ${41.8\pm 0.5}$ | ${11.7\pm 0.7}$ | ${363\pm 2}$ | ${217\pm 6}$
Hall C | ${40.2\pm 0.5}$ | ${12.0\pm 0.7}$ | ${364\pm 2}$ | ${215\pm 6}$

The concentrations of 222Rn were also fitted to the Eq. (2). Table 4 shows the
values of the fitted parameters. The unweighted least squares fits show that
the estimated standard deviations of the measurements are 7.6, 7.6 and 8.0 Bq
m-3 for the halls A, B and C, respectively. These values imply a mean standard
deviation of 9% for the 222Rn concentration monthly averages, a value much
greater than their statistical uncertainty (0.24%, see section 3). Therefore,
the observed 222Rn monthly deviation from annual modulation is not linked to
the measurement precision, but to the natural variability of the 222Rn at the
mountain where the fresh air is taken.

Table 4: Values of the fitted parameters of the 222Rn concentration of the years 2013–2018 to Eq. (2). The maxima are in mid-July Room | A (Bq m-3) | B (Bq m-3) | T (d) | tM (d)
---|---|---|---|---
Hall A | ${82.8\pm 0.9}$ | ${10.6\pm 1.3}$ | ${366\pm 4}$ | ${194\pm 12}$
Hall B | ${85.2\pm 0.9}$ | ${10.0\pm 1.3}$ | ${368\pm 4}$ | ${193\pm 13}$
Hall C | ${84.8\pm 0.9}$ | ${~{}~{}9.8\pm 1.3}$ | ${367\pm 5}$ | ${189\pm 14}$

The differences between the observed and the fitted values do not show any
particular trend (Figure 5). Most of the differences are less than 10 Bq m-3
and their maximum is 20 Bq m-3. Therefore, the sinusoidal function is a
reasonable model. As in the case of the humidity, the three maxima, $t_{M}$,
are compatible within their uncertainties, giving a mean value of ${192\pm 8}$
d, around 11th July. This means that the 222Rn maxima (minima) occur ${23\pm
8}$ days before the humidity maxima (minima).

Figure 5: Differences between the experimental and the fitted values of 222Rn
concentration of hall A to Eq. (2). Corresponding plots for halls B and C are
similar

The origin of the winter-summer 222Rn level difference can be attributed to
the different conditions of the airflow and weather patterns. There exist
different features of the 222Rn concentration in different laboratories. For
instance, the annual periodicity has not been observed in the Laboratori
Nazionali del Gran Sasso (LNGS) BASSIGNANIrm1997 , which is connected to a
road tunnel in Italy, under the Gran Sasso mountain. On the contrary, the
periodicity has been observed in the Soudan Underground Laboratory (SUL)
Goodmancrc1999 , located in an old iron mine in Minnesota, with the maximum in
summer and the minimum in winter, as we report in LSC. However, as the
relative humidity in SUL is constant, it is not correlated to the 222Rn
concentration inside the laboratory PhysRevC.96.044609 .

It was suggested in Goodmancrc1999  that the radon periodicity in the SUL is
due to the pressure gradients created by the relative temperature differences
between the air in the laboratory and that on the surface. This qualitative
model can also be applied to LSC: in winter, when the outside temperature is
lower than the inside one, the ventilation rate is enhanced and the purge of
the inside radon is more efficient than in summer, when the temperature
gradient is reversed. Then, the 222Rn concentration has a positive correlation
with the outside temperature and the winter-summer ratio, W/S, inside the
laboratory is less than one. The observed positive correlation between the
radon level and the relative humidity inside the LSC can be explained because
in winter the rock of the tunnel contains less water than in summer, when the
snow had melted mostly well before and the rock is plenty of water. In these
conditions, the relative humidity inside the laboratory is greater in summer
than in winter. Therefore, the high (low) humidity inside LSC is a consequence
of the high (low) outside temperature.

##  4 Meteorological data

A quantitative estimate of the positive correlation between the 222Rn
concentration and the temperature outside the laboratory can be obtained from
the data provided by the Spanish Meteorological Agency (Agencia Española de
Meteorología, AEMET).

The nearest AEMET observation point to the LSC is the Canfranc station, 3 km
away from the underground laboratory. It records the temperature (To) and
relative humidity (RHo) every 10 minutes. The Aragüés del Puerto station, 13
km away, records the atmospheric pressure (Po) four times per day: midnight,
7:00, 12:00 and 18:00 hours. Table 5 lists the altitudes and coordinates of
LSC and both AEMET stations.

Table 5: Altitude and coordinates of the LSC and of the AEMET stations used in this work. The stations data were provided by AEMET; those of LSC are our estimates on the application iberpix iberpix  of the Spanish National Geographic Institute (Instituto Geográfico Nacional) Site | Altitude (m) | Latitude | Longitude
---|---|---|---
LSC | $1120$ |  $42^{\circ}$ $46^{\prime}$ $30^{\prime\prime}$ N |  $0^{\circ}$ $31^{\prime}$ $42^{\prime\prime}$ W
Canfranc | $1170$ |  $42^{\circ}$ $44^{\prime}$ $58^{\prime\prime}$ N |  $0^{\circ}$ $30^{\prime}$ $58^{\prime\prime}$ W
Aragüés del Puerto | $1040$ |  $42^{\circ}$ $42^{\prime}$ $32^{\prime\prime}$ N |  $0^{\circ}$ $40^{\prime}$ $23^{\prime\prime}$ W

We use data from 2015 to 2018 because the meteorological Canfranc data are
available since the end of October, 2014. The correlation coefficients between
the inside (four) and outside (three) studied variables from 2015 to 2018 for
the three halls of the LSC are listed in Table 6. In this case with 36
evaluated $r$–values, we use 99.86% CL for the decision threshold because
$1-(0.9986)^{36}=0.05$, see section 3.1. The monthly average 4-year data gives
$n=48$ in Eq. (1), i.e., 46 degrees of freedom for the Student’s $t$ and
$\left|r_{\alpha=0.0014}\right|=0.46$.

Table 6: Correlation coefficients (2015-18) between the four inside variables, recorded underground by our radon monitors, for the halls A, B and C of LSC and the outside variables recorded by the AEMET stations of Canfranc (temperature and relative humidity) and Aragüés del Puerto (pressure) Room | Outside variables
---|---
Hall A | To | Po | RHo
Rni | 0.71 | 0.10 |  $-$0.10
Ti | 0.14 |  $-$0.01 |  $-$0.20
Pi | 0.38 | 0.99 |  $-$0.40
RHi | 0.95 | 0.25 |  $-$0.25
Hall B | To | Po | RHo
Rni | 0.68 | 0.09 |  $-$0.08
Ti | 0.28 |  $-$0.14 | 0.32
Pi | 0.32 | 0.97 |  $-$0.36
RHi | 0.94 | 0.29 |  $-$0.34
Hall C | To | Po | RHo
Rni | 0.64 | 0.09 |  $-$0.16
Ti | 0.10 |  $-$0.15 | 0.31
Pi | 0.39 | 0.99 |  $-$0.40
RHi | 0.94 | 0.28 |  $-$0.36

Independently of the hall, we observe three main features regarding the
correlations inside-outside. First, the atmospheric pressures inside and
outside are the variables with the highest correlation, $r\approx 1$, because
two close points (13 km away and 80 m altitude difference) have the same
pressure gradient. Second, the inside relative humidity and the outside
temperature are highly correlated, $r=0.94$, most likely linked to the thaw
season because the outside temperature follows a sinusoidal curve of one-year
period (Figure 7) driving the inside relative humidity (Figure 2). Note also
that the outside relative humidity (Figure 7) is not a sinusoidal curve
similar to the inside relative humidity. Third, the inside 222Rn concentration
is correlated with the outside temperature (Figure 6), $r=0.64$ to $r=0.71$, a
similar amount to the correlation between the inside 222Rn concentration and
the inside relative humidity, $r=0.67$ to $r=0.73$ (Table 2). Latter
correlation occurs in the same hall and also for different halls.

Figure 6: Monthly averages of the 222Rn concentration at hall A versus the
monthly averages of the outside temperature from 2015 to 2018. Corresponding
plots for halls B and C are similar

Figure 7: Monthly averages of AEMET meteorological data: temperature (upper
left), pressure (upper right) and relative humidity (bottom left). The bottom
right panel shows the high correlation between the atmospheric pressures in
hall A (Pi) and Aragüés del Puerto (Po); halls B and C have similar
correlation with Po

The Table 7 collects the results of fitting To, RHi, and Rni to Eq. (2) within
the same interval of available data for To (2015 to 2018). To has a period
compatible with 1 year and the maximum is ${204\pm 3}$ d, around 23rd July.
The period of the internal relative humidity, RHi, is also compatible with one
year and the maxima $t_{M}$ in every hall are equal within uncertainties,
their mean value is ${213\pm 3}$ d, around 1st August, ${9\pm 5}$ days after
the maximum of To. Though this delay has a low statistical significance, it
could be a rough estimate of the time interval between the maximum thaw on the
Tobazo Mountain and the maximum rock humidity at 800 m rock depth. The mean
values and modulation amplitudes of the internal relative humidity are similar
to those of the 2013-2018 series (Table 3). The 222Rn results of the 2015-2018
series show three periods compatible with one year and three maxima ${10\pm
14}$ days after the maximum of To. Compared to the 2013-2018 series (Table 4),
the subset 2015-2018 exhibits differences in the estimated parameters (the
most remarkable are $\sim 10$ days in the period values and $\sim 3$ weeks in
the tM values). In this subset the 222Rn maxima (minima) occur at the same
time the humidity maxima (minima), whereas in the total set 2013-2018 they
occur ${23\pm 8}$ days before (see section 3.2). This behaviour appears
because the seasonal periodicity of the 222Rn concentration has more
fluctuations than the one of the relative humidity, see the fits of the Figure
2, because it is more sensitive to variations in the environmental conditions;
for instance, the outside rainfall changes the radon content of the fresh air
cleaning the laboratory, but it does not change the relative humidity inside
the laboratory, 800 meters down in the rock.

Table 7: Values of the fitted parameters (2015-18) according Eq. (2) of the
variables showing seasonal periodicity: outside temperature (maximum on 23rd
July), inside relative humidity and inside radon concentration (maxima on
beginning August) Outside temperature
---
| A (∘C) | B (∘C) | T (d) | tM (d)
Canfranc | ${9.1\pm 0.2}$ | ${8.1\pm 0.3}$ | ${366\pm 2}$ | ${204\pm 3}$
Inside relative humidity
| A (%) | B (%) | T (d) | tM (d)
Hall A | ${33.9\pm 0.4}$ | ${11.1\pm 0.5}$ | ${361\pm 2}$ | ${218\pm 4}$
Hall B | ${40.5\pm 0.5}$ | ${11.9\pm 0.7}$ | ${365\pm 3}$ | ${210\pm 6}$
Hall C | ${39.3\pm 0.5}$ | ${12.2\pm 0.7}$ | ${367\pm 3}$ | ${208\pm 6}$
Inside 222Rn concentration
| A (Bq m-3) | B (Bq m-3) | T (d) | tM (d)
Hall A | ${82.0\pm 1.1}$ | ${11.2\pm 1.5}$ | ${357\pm 7}$ | ${214\pm 13}$
Hall B | ${84.9\pm 1.1}$ | ${10.4\pm 1.5}$ | ${358\pm 7}$ | ${215\pm 14}$
Hall C | ${84.4\pm 1.1}$ | ${10.3\pm 1.5}$ | ${358\pm 8}$ | ${214\pm 14}$

##  5 222Rn control in the ANAIS–112 experiment

The 222Rn annual periodicity in the Hall B of LSC was also reported by the
ANAIS collaboration maolivan2016 , an experiment looking for the dark matter
annual modulation with NaI(Tl) scintillators at LSC Amare2021prd ;
Amare2019prl ; Amare:2018sxx ; Amare2019epjc  to test the DAMA-LIBRA result
dama2020ijmpa  using the same target and experimental approach. To keep low
the concentration of 222Rn, the air inside the ANAIS–112 shielding has been
kept continuously flushed with radon-free nitrogen gas. During most of the
ANAIS–112 operation this radon-free nitrogen gas has been produced by
evaporating liquid nitrogen, but also pure nitrogen from compressed gas
bottles has been used. Although there was no direct measurement of the 222Rn
content of this nitrogen, from the absence of lines coming from 214Bi and
214Pb in the current NaI(Tl) detectors Amare2016epjc  as well as in the
ANAIS–0 prototype CEBRIAN2012app , the ANAIS collaboration estimated an upper
limit of 0.6 Bq m-3 of 222Rn in the air filling the shielding.

This upper limit can be improved through HPGe gamma spectrometry. We purged
for two years (2017-2018) the inner volume ($20\times 20\times 30$ cm3) of the
shielding Coarasa2016jpcs  of a HPGe detector ($\sim$1 kg and 41% relative
efficiency with respect to a 3 in$\times$3 in NaI(Tl) detector) with the same
gas purging the ANAIS–112 shielding. The gain shifts were controlled weekly
with a 22Na source. The total live time of the measurement was 670 days; the
lost acquisition days were due to maintenance works in LSC, power outages and,
in a minor amount, to the periodic calibrations and the refilling of the HPGe
dewar with liquid nitrogen. The total spectrum is plotted in Figure 8, where
the annihilation peak at 511 keV and the peaks at 1460.8 keV (40K) and at
2614.6 keV (208Tl) are clearly distinguishable.

Figure 8: Total HPGe spectrum for 2017-2018 (670 days live time)

###  5.1 HPGe photopeak efficiency of an extended 222Rn source

We have a precise knowledge of the efficiency of the HPGe used in this work
because it is one of our ultra low background HPGe detectors located in the
LSC, that is routinely used for the screening of material radiopurity. For
this reason, its efficiency has been measured for samples facing the HPGe
window and also for Marinelli beakers. The nitrogen source is quite different
from the habitual samples because it fills all the internal cavity of the
shielding and, therefore, the efficiency measurement cannot be completed for
the total volume because the access to the rear of the HPGe is not possible
once the shielding has been built.

Figure 9: Efficiency of our HPGe detector to a 222Rn source filling the inner
volume of its shielding. The squares were estimated profiting a 222Rn
efficiency relative measurement and the circles using Geant4 with an
approximate geometry. In both cases the estimated values were normalized to
the measured efficiency at 1460.8 keV

The efficiency to the 222Rn source was estimated in two steps. First, we
measured the efficiency at 1460.8 keV, $\epsilon(1460.8$ keV), using a
homemade source of 260 g of KCl (40K isotopic abundance of 0.0117% Browne1986
) and chemical purity >95%, located at several positions in the accessible
volume around the HPGe, and a smaller one of 20.6 g to measure the HPGe
efficiency at several distances from the HPGe window. The self-attenuation of
the 1460.8 keV gamma ray is 10% for the 260 g source and 2% for the 20.6 g
source. Second, we used the airborne 222Rn filling the inner volume of the
shielding due to an accidental cut of the purging system. Because of the
activity of 222Rn was unknown, we were able to obtain only the relative
efficiency, $\epsilon_{R}(E)$, of the HPGe to a source identical to the one we
intended to measure.

A linear interpolation, in a double logarithmic scale, between
$\epsilon_{R}(1120.3$ keV) and $\epsilon_{R}(1764.5$ keV) was used to
calculate the relative efficiency $\epsilon_{R}(1460.8$ keV). We take into
account in this interpolation the true coincidence summing of 1120.3 and 609.3
keV through a correction factor $c_{TS}\sim 1.1$ for $\epsilon_{R}(1120.3$
keV), that we estimated by Monte Carlo for the extended 222Rn source. The
matching factor $f_{m}=\epsilon(1460.8$ keV)$/\epsilon_{R}(1460.8$ keV) gives
the efficiencies for the 222Rn gamma lines (Figure 9).

The matching factor $f_{m}$ has a main uncertainty linked to the lack of
measurements for sources located at the rear of the HPGe, where we know
neither the materials nor the sizes of the detector components (cooling rod,
electronics, supports, etc.). Initially we assumed that the HPGe efficiencies
to rear and frontal sources were identical, but if the detector components
attenuated all the photons coming from the rear volume, then $f_{m}$ would
decrease a 20%. Hence, we have assumed that the rear contribution is one half
of the frontal one, we have diminished $f_{m}$ by a 10% and we have added a
10% systematic uncertainty to all the values of the Figure 9.

As a crosschecking, we did a Monte Carlo simulation with Geant4 geant4nim2003
according to the known dimensions and materials of the germanium crystal and
its end cup. The results of the simulation were multiplied by a factor 0.94 to
match the experimental and calculated efficiencies at 1460.8 keV for the 20.6
g source located in frontal positions. Subsequently, the same factor was
applied to the calculated efficiencies of the more intense gamma lines of the
222Rn daughters (Figure 9) coming from the inner volume of the HPGe shielding.
This estimate agrees with the former around the normalization energy (1460.8
keV), as expected, and shows some differences at lower energies because a more
precise knowledge of the detector geometry is needed to match by Monte Carlo
the efficiencies at 295.2 and 351.9 keV.

###  5.2 Upper limit to 222Rn concentration

The observed peaks of the 222Rn progeny can also be produced by 226Ra and 238U
contamination in the shielding or in the HPGe itself, but our current data
cannot separate the three contributions. Then, we only can estimate an upper
limit to the residual 222Rn in air. The best upper limit, 0.06 Bq m-3 (95%
C.L.), is obtained with the 351.9 keV gamma line. This value is one order of
magnitude better than our previous estimate based on the NaI(Tl) spectrometry
data and it is not affected by the systematic uncertainty of $f_{m}$ because
the dominant one is statistical. According to the ANAIS–112 background model
Amare2016epjc , this upper limit means that the contribution of the 222Rn to
the total rate is $<4\times 10^{-4}$ counts keV-1kg-1d-1 in the region of
interest, [1–6] keV, amounting to less than 0.01% of the background
Amare2021prd .

The possible contribution of some modulation of some tiny 222Rn activity to
the expected signal in ANAIS–112 is negligible because if we would take the
above upper limit of 0.06 Bq m-3 as a true 222Rn concentration with a
modulation amplitude $\sim 10\%$, similar to the one observed in the Hall B
(Table 4), its contribution to the ANAIS–112 modulation signal would be
$4\times 10^{-5}$ counts keV-1kg-1d-1 in the region [1–6] keV, much below the
modulation observed by the DAMA/LIBRA collaboration dama2020ijmpa  and the
sensitivity of ANAIS–112 experiment Coarasa2019epjc .

##  6 Upper limit to 222Rn concentration of the radon-free air provided by the
LSC

The laboratory has installed a radon abatement system (RAS), built by the
company Apparatuses Technologies Construction (ATEKO a. s.) from Czech
Republic, that can provide 220 m3h-1 with $\sim$1 mBq m-3 of 222Rn for the
experiments hosted by the LSC perezperez2021radon . Though this 222Rn
concentration is very low to be detected by our HPGe detector, we have tested
the 222Rn content from the RAS as we did for the nitrogen purging ANAIS–112
(see section 5). We have collected data for 25 months from January, 2019 to
June, 2021; adding up to 728 days live time. There are two gaps in the data
taking, from September to December, 2019 and April, 2021, that were devoted to
other measurements. The remaining lost days are due to the weekly maintenance
of the HPGe detector.

The Table 8 shows the total rate and the rates of the more intense lines of
222Rn daughters for both measurements. We have not observed significant
differences between this measurement and the one done with evaporated nitrogen
(section 5). The total spectrum is equal, within statistical uncertainties, to
the one obtained purging with nitrogen (Figure 8).

Table 8: Total rate from 50 keV to 5.6 MeV and rates of the more intense lines of 222Rn daughters for the two radon purging systems keV | Evaporated N2 (d-1) | RAS (d-1)
---|---|---
[50, 5600] | ${128.93\pm 0.44}$ | ${129.63\pm 0.42}$
295.2 | ${0.119\pm 0.035}$ | ${0.116\pm 0.032}$
351.9 | ${0.189\pm 0.036}$ | ${0.216\pm 0.033}$
609.3 | ${0.181\pm 0.032}$ | ${0.223\pm 0.029}$
1120.3 | ${0.051\pm 0.023}$ | ${0.062\pm 0.017}$
1764.5 | ${0.117\pm 0.017}$ | ${0.079\pm 0.015}$
2204.2 | ${0.052\pm 0.012}$ | ${0.064\pm 0.012}$

The 351.9 keV line gives the best upper limit to the 222Rn around our HPGe
detector, 0.06 Bq m-3 (95% C.L.), the same value obtained when purging with
evaporated nitrogen.

##  7 Conclusions

The measurements performed at the LSC over six years (2013-2018) have shown
that the monthly average 222Rn concentration in air is lower than the maximum
allowed for working places, 600 Bq m-3, according to the Spanish legislation
csn11-04  and the international recommendations icrp103 . It is essentially
similar in the three experimentation halls at LAB2400 (see Table 1),
indicating that the heating and the forced ventilation of the air reaching the
LSC halls work properly.

There is a correlation between the 222Rn concentration and the relative
humidity in the three halls. An annual and sinusoidal periodicity of the
values of the relative humidity and the 222Rn concentration was observed in
the three halls. The data from 2013 to 2018 show that the maximal humidity
inside LSC occurs at beginning August and the maximal 222Rn concentration
occurs 3 weeks before, at mid-July. The partial data from 2015 to 2018 show
that the time of maximal humidity remains stable whereas the time of maximal
222Rn concentration is less stable, in fact, for this series it occurs at
beginning August. The relative amplitude of the 222Rn concentration with
respect to the annual average is about 10% for the three halls. According to
the AEMET data used in this work, the 222Rn concentration is correlated with
the temperature of the fresh air intake on the mountain covering the LSC. The
correlation with the relative humidity inside LSC is indirect, because of the
likely correlation between the external temperature and the internal humidity
via the snow melting.

The low 222Rn content (if any) of the nitrogen purging the ANAIS–112 shielding
does not affect to the achieved low background and it guarantees the
sensitivity of the experiment Coarasa2019epjc .

We have also tested the radon abatement system of the laboratory in the same
way we tested the ANAIS–112 purging system with evaporated nitrogen. We have
obtained the same upper limit to the 222Rn concentration in both cases, 0.06
Bq m-3 (95% C.L.), concluding that both systems are equivalent at this level
of 222Rn sensitivity.

###### Acknowledgements.

This research was funded by MCIN/AEI/10.13039/501100011033 under grant
PID2019-104374GB-I00; by MINECO-FEDER under grants FPA2017-83133-P, and
FPA2014-55986-P; by MICINN-FEDER under grants FPA2011-23749; by CONSOLIDER-
Ingenio 2010 Programme under grants MultiDark CSD2009-00064 and CPAN
CSD2007-00042; by the University of Zaragoza under grant UZ2017-CIE-09; by the
Spanish Meteorological Agency (AEMET), the Gobierno de Aragón (Group in
Nuclear and Astroparticle Physics, ARAID Foundation and I. Coarasa predoctoral
grant), the European Social Fund and by the LSC consortium. The authors would
like to acknowledge the use of Servicio General de Apoyo a la Investigación-
SAI, Universidad de Zaragoza. The authors also thank Carlos Peña–Garay,
Director of the LSC, Aldo Ianni and Alessandro Bettini (former LSC Directors)
and José Ángel Villar (former LSC Associate Director) for their support and
encouragement.

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# Shape oscillation of bubbles in the acoustic field

Keishi Matsumoto1, Ichiro Ueno2

1Graduate School, Tokyo University of Science,
2641 Yamazaki, Noda, Chiba 278-8510, JAPAN
2Tokyo University of Science, Noda, JAPAN

###### Abstract

The authors introduce dynamics of multiple air bubbles exposed to ultrasonic
wave while ascending in water in the present fluid dynamics video. The authors
pay attention to the shape oscillation and the transition from the volume to
the shape oscillations of the bubble. Correlation between the bubble size and
the mechanism of the excitation of the shape oscillation is introduced.

##  1 Introduction

The video is Video1.

To understand a behavior of the bubbles, their shape and volume oscillations,
under periodic external force is of one of great importance in order to
control heat/mass transfer in multiphase flows. A large number of researches
have been carried out on the volume oscillation by theoretical and
experimental approaches (reviewed by Plesset & Prosperetti (1) and Feng & Leal
(2)). On the shape oscillation, however, there exist few experimental works
although there have been accumulated theoretical predictions. In the present
study, The authors introduce the effect of the preceding bubble in the
acoustic field on the shape oscillation arisen on the following bubble.

REFERENCES
(1) Pleset, M. S. Prosperetti,A., Bubble Dynamics and Cavitaion,Ann. Rev.
Fluid Mech.,29(1977),145-185
(2) Feng, Z. C. & Leal, L. G., Nonlinear Bubble Dynamics, Ann. Rev. Fluid
Mech., 29(1997), 201-243