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Radiation exposure at ground level by secondary cosmic radiation
Radiation Measurements 39 (2005) 95 – 104 www.elsevier.com/locate/radmeas
Radiation exposure at ground level by secondary cosmic radiation F. Wissmanna;∗ , V. Dangendorf a , U. Schreweb a Physikalisch-Technische b Fachhochschule
Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany Hannover, Ricklinger Stadtweg 120, D-30459 Hannover, Germany
Received 27 October 2003; accepted 1 March 2004
Abstract The contribution of the charged component of secondary cosmic radiation to the ambient dose equivalent H ∗ (10) at ground level is investigated using the muon detector MUDOS and a TEPC detector surrounded by the coincidence detector CACS to identify charged particles. The ambient dose equivalent rate H˙ ∗ (10)T as measured with the TEPC/CACS is used to calibrate the MUDOS count rate in terms of H˙ ∗ (10). First results from long-term measurements at the PTB reference site for ambient radiation dosimetry are reported. The air pressure corrected dose rate shows, as expected, a strong correlation with the neutron count rate as measured with the Kiel neutron monitor. The measured seasonal variations exhibit a negative correlation with the temperature changes in the upper layers of the atmosphere where the ground level muons are produced. c 2004 Elsevier Ltd. All rights reserved. PACS: 96.40.T; 87.53.R Keywords: Cosmic ray muons; Microdosimetry
1. Introduction Ionising radiation at ground level consists of two major components. One stems from the radioactive isotopes in the earth’s crust and therefore is named terrestrial radiation (TR). In addition to TR, there is the secondary cosmic radiation (SCR) which contributes approximately the same amount to the entire annual e?ective dose accumulated by an individual (UNSCEAR, 2000). The SCR has its origin in the primary cosmic radiation (or galactic cosmic radiation: GCR) consisting of almost 99% of protons and particles (Grieder, 2001). The GCR enters the solar system and is partially deDected by the interplanetary magnetic Eeld and, when approaching our planet, by the earth’s magnetic Eeld. When the GCR hits the upper layers of the atmosphere, nuclear reactions are induced. The production of secondary particles leads to an electromagnetic component of the SCR, which consists of -radiation, electrons and positrons, and a hadronic component. The latter consists ∗
Corresponding author. E-mail address: [email protected] (F. Wissmann).
c 2004 Elsevier Ltd. All rights reserved. 1350-4487/$ - see front matter doi:10.1016/j.radmeas.2004.03.025
mainly of protons, neutrons and even mesons (Grieder, 2001) among which the latter play an essential role. Immediately after production the neutral meson (0 meson) decays ( = 8:4 × 10−8 ns (Hagiwara et al., 2002)) into 2 photons which then may create electron–positron pairs. Via bremsstrahlung the electrons or positrons emit high-energy photons which are again a source for pair-production. This evolution of the electromagnetic component displays how the total energy of an initial particle, here the 0 meson, is distributed among all secondaries until the energy of a single particle is no longer suJcient to create another particle or until it is absorbed. The charged mesons (± mesons, = 26 ns (Hagiwara et al., 2002)) decay into muons (± ) and the corresponding muon neutrinos ( ; K ). The muon itself is unstable with a mean lifetime of = 2:2 s (Hagiwara et al., 2002), corresponding to a Dight path of c = 659 m which by far is not suJcient to reach ground level. But, the relativistic effect of time dilatation permits them to pass the entire atmosphere and to reach the earth’s surface. In contrast to the electromagnetic component which is largely absorbed after having traversed the atmosphere, the muons cross the
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F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
atmosphere without major interactions. Therefore, most of the muons reaching the surface have their origin high in the atmosphere. The energy distribution ranges from a few MeV up to hundreds of GeV with a mean kinetic energy of about 4 GeV (Grieder, 2001). The particles of the hadronic component also initiate nuclear reactions producing numerous secondaries. As for the electromagnetic component, the hadronic Dux decreases rapidly through the atmosphere leaving the neutrons as the main hadronic contribution at ground level (Grieder, 2001). Owing to the di?erent reaction mechanisms involved, the composition of the SCR in the atmosphere strongly depends on the altitude (Grieder, 2001). The charged particles of the SCR at ground level can be grouped in two components: the so-called “hard” component of highly penetrating muons, and a “soft” component of electrons and positrons which are easily absorbed in shielding material. According to Grieder (2001), the vertical particle radiance of charged particles is −2 −1 −1 ’soft s sr ; ; v = 31 m
(1)
−2 −1 −1 ’hard s sr : ; v = 82 m
(2)
The zenith angle dependence of the soft and hard component at ground level can be described by ’ (#) = ’ (0) cosn #;
(3)
with n = 2 for both, the soft and hard component, as a good choice at northern latitudes (Grieder, 2001). The evaluation of the vertical Duence rate traversing a horizontal area reads: ’1 = ’ (#) cos # d = ’ (#) cos # sin # d# d;
= 2’ (0)
The Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig has installed a reference site for ambient radiation dosimetry. The site is located at latitude 52◦ 17 N and longitude 10◦ 28 E (altitude approximately 80 m), which corresponds to a vertical cuto? rigidity of 2:8 GV (Smart and Shea, 1997). The Dux of the SCR at an altitude of 80 m is almost that at sea level. Ambient radiation is investigated with a set of ionisation chambers and proportional counters. These detectors measure both, the TR and the SCR and are calibrated in the reference radiation Eelds for -radiation at PTB. In addition, the Muon Dosimetry System (MUDOS) based on two proportional counters has been developed for the investigation of cosmic ray muons. The equipment is completed by standard neutron monitors for dosimetry of low energy neutrons and modiEed ones optimised for the dosimetry of high energy cosmic ray neutrons. Although the average kinetic energy of the muons at ground level is approximately 4 GeV, they can be treated as densely ionising particles. This enables us to build a system of two energy loss counters working in the coincidence mode. The MUDOS developed at PTB (Fig. 1) consists of two cylindrical multi-wire proportional chambers with a diameter of 200 mm and a height of approximately 30 mm. Each chamber is equipped with an anode plane with 50 tungsten–rhenium wires (?25 m) separated by 4 mm. Above and below the anode wires, stainless steel wire grids (?37 m, pitch 370 m, 81% optical transmission) are used as cathode. The chambers are Elled with CF4 counting gas at a pressure of 1100 hPa. The voltage applied between anode and cathode planes is 2700 V. Each chamber signal is fed into a discriminator module to create logic pulses. If a muon traverses the two chambers, the logic signals fulEl a coincidence condition. Between the two chambers a 25 mm thick Pb layer absorbs electrons or positrons with energies up to 435 MeV (Berger et al., 2003) and prevents
cosn+1 # sin # d# # −cosn+2 # max : n + 2 0
(4)
Owing to the exponent of the cosine function, the particle Duence rate is peaked into vertical directions. Therefore, any detector acceptance beyond #max ≈ 70◦ leads to corrections in the measured Duence rate of the order of 1% or less. The Duence rate of charged particles, i.e. the soft as well as the hard component, from a nearly vertical direction can be calculated with the simple formulas ’1 (soft) = 2
’soft ; v ≈ 50 m−2 s−1 ; n+2
(5)
’1 (hard) = 2
’hard ; v ≈ 130 m−2 s−1 : n+2
(6)
200 mm
25 mm
’1 = 2’ (0)
2. Muon detection system
50 Wire Anode
Pb Layer
Cathode Grids
Fig. 1. Schematic drawing of the MUDOS wire chambers. Each anode plane is covered above and below by the cathode grids. Between the two proportional chambers, a 25 mm thick lead layer prevents electrons or positrons from traversing the two chambers, which might create background coincidence events.
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
coincidence events, i.e. background events due to electrons or positrons. The minimum muon energy required to cross the entire Pb layer is approximately 59 MeV (Groom et al., 2001). Therefore, the coincident events can be deEned as muons. To prevent any e?ect from temperature changes, the chambers are operated in a temperature stabilised housing at 20◦ C. The single count rates of the two MUDOS chambers are about f1 = 7:2 s−1 and f2 = 6:9 s−1 , respectively, and the coincidence rate is about f = 2:7 s−1 . The coincidence rate f is proportional to the Duence rate of muons at ground level. From a simple Monte-Carlo calculation (Wissmann, 2003a) the geometrical eJciency of MUDOS was evaluated to be geo = 0:664 ± 0:008;
(7)
where the uncertainty given is the statistical 1 standard uncertainty of the Monte-Carlo calculation. Applied to f this leads to a muon Duence rate of 129:5 s−1 which is in perfect agreement with the value given in (6). 3. The TEPC reference instrument The conversion from the muon count rate f to ambient dose equivalent rate H˙ ∗ (10) requires a reference instrument such as a Tissue Equivalent Proportional Counter (TEPC). The device used here is a 2 -TEPC (nominal diameter: 5:69 cm) of Rossi type manufactured by Far West Technology (Fig. 2). The counting gas is propane-based TE gas with a reduced pressure inside the cavity which simulates 4 m of tissue with a density of 1 g=cm3 . The applied voltage is 850 V and the detector signal is fed into a
97
linear ampliEer having three di?erent gains with an approximate ratio of 1:10:100. This instrument alone does not have the ability to clearly identify muons. An additional charged particle counter, i.e. the 24 anode wire proportional counter Coincidence/Anti-Coincidence Shield (CACS), surrounds the TEPC (Fig. 2). The TEPC/CACS system has already been in operation as part of a mobile dosimetry system used at Dight altitudes. For more detailed information, the reader is referred to (Schrewe, 2000). The entire system Ets into a suitcase of cabin baggage size and can be taken aboard passenger aircrafts (Wissmann, 2003b). The TEPC pulse height analysis is performed in coincidence and anti-coincidence to the CACS. The Erst kind of events are the so-called charged events, the latter are the neutral events. CACS covers a geometrical solid angle of about 85% of 4. Taking the zenith angle distribution of muons and electrons or positrons from (3) into account, the coincidence eJciency for the charged component of the SCR can be estimated to be (Schrewe, 2000) = (0:9 ± 0:1):
(8)
The index represents the muons, electrons and positrons. The TEPC measures the lineal energy y, i.e. the energy deposition in the TEPC sphere normalised to a mean chord length (Rossi and Zaider, 1996) l =
2 d ; 3
(9)
with d = 4 m the simulated tissue diameter. The calibration in y is done using neutron sources. The neutrons interact with the cavity wall and gas producing protons of various energies. The minimum energy of the recoiling protons necessary to traverse tissue of 4 m with density 1:0 g=cm3 is Ep = 318:5 keV
(10)
calculated with SRIM 2003 (SRIM, 2003). Ep corresponds to the maximum deposited energy, and with (9) the so-called proton edge is evaluated to be yp = 119:4
keV : m
(11)
This edge is clearly visible in the event spectra of the lowest ampliEer gain. By relating the corresponding ADC channel to yp , the pulse height spectra are calibrated in lineal energy. The transition to a single event dose D(yi ) in a certain interval yi is given by the ratio of the energy RE deposited in the volume and the mass Rm inside this volume (Rossi and Zaider, 1996): Fig. 2. The TEPC/CACS system. The 2 TEPC is surrounded by the cylindrical 24 anode wire chamber CACS Elled with CF4 counting gas. The dose measured with the TEPC can be related to the charge of the primary particle entering the TEPC, if the events are analysed in coincidence and in anti-coincidence to the CACS.
D(yi ) =
REi yi lK = : Rm V
(12)
Here, lK is the mean chord length inside the TEPC cavity, is the gas density and V the gas volume. For a spherical shape of the volume the relation lK = (4V )=S is valid, with
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F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104 0.04 low-LET
high-LET
y d(y)
0.03
0.02
0.01
0 10-2
10-1
1 10 y / (keV/µm)
102
103
Fig. 3. The normalised dose distribution spectrum yd(y) as measured by the TEPC/CACS (neutral events only) with an AmBe neutron source. The sharp drop at around 120 keV=m corresponds to the proton edge used to calibrate the event spectra in terms of the lineal energy y.
the surface area S = d2 and d = 5:69 cm being the cavity diameter. Inserting this into (12) one obtains m yi 4 D(yi ) = = yi 6:3 × 10−5 Gy: (13) d2 keV The total dose obtained from the measured dose distribution is then D= n(yi )D(yi ); (14) i
and the ambient dose equivalent H ∗ (10)T can be evaluated (Rossi and Zaider, 1996; Gerdung et al., 1995) by H ∗ (10)T = n(yi )D(yi )q(yi ); (15) i
where n(yi ) is the number of events measured in the interval yi and q(yi ) is equal to the quality factor Q(L) deEned by ICRP (ICRP, 1991) with the approximation that L ≈ y. It is convenient to plot the event spectra in terms of normalised dose distribution spectra yi d(yi ) in logarithmic binning. Here, d(yi ) is obtained by normalising the event spectrum with the total event number. This kind of plot simpliEes the comparison of spectra due to di?erent types of radiation. For a more detailed description, the reader is referred to (Rossi and Zaider, 1996) and (Gerdung et al., 1995) and references therein. An example of the dose distribution spectrum from an AmBe neutron source is given in Fig. 3. Neutrons, i.e. the recoiling protons from np reactions in the cavity wall, particles and heavier nuclei lead to high-LET events above 10 keV=m. Compared to this, the spectrum of photons (Fig. 4) shows di?erent features. At y ¿ 10 keV=m, there are almost no events. Therefore, photons as well as electrons and positrons lead to low-LET events with y ¡ 10 keV=m in the dose distribution spectra. The charged component of the SCR, identiEed with the CACS running in coincidence to the TEPC (charged mode),
Fig. 4. The normalised dose distribution spectra yd(y) as measured in di?erent -radiation Eelds: Cs source with E =662 keV (hashed area); photons produced via the reaction 19 F(p; )16 O with E = 6 –7 MeV (BSuermann et al., 1999) (dashed line); ambient radiation measured with the TEPC/CACS in the coincidence mode (solid line), i.e. the charged component of the SCR.
leads only to low-LET events in the dose distribution spectra (solid line in Fig. 4). A comparable spectrum can be simulated with high-energy photons. Such a reference photon Eeld has been produced by the reaction 19 F(p; )16 O with photon energies between 6 MeV and 7 MeV (BSuermann et al., 1999) (ISO R-F quality; average photon energy is 6:6 MeV). The dose distribution spectrum obtained in this photon Eeld agrees quite well with that due to the charged component of the SCR, as shown by the dashed line in Fig. 4. Thus, this reference high-energy photon Eeld of 6:6 MeV photons has been used for a low-LET dose calibration. The low-LET calibration factor, deEned as the ratio of the reference value H˙ ∗ (10) and that measured with the TEPC alone, has been determined to be H˙ ∗ (10) = kT; low = 1:129 ± 0:099; H˙ ∗ (10)low
(16)
where the standard uncertainty includes the statistical 1 uncertainty of the measurement and the standard uncertainty of the reference value. Now, (15) reads as H ∗ (10)T; low = kT; low
n(yi )D(yi )q(yi ):
(17)
i
It has to be mentioned that the threshold of the TEPC system at around 0:3 keV=m has been lowered artiEcially by linear extrapolation of the event spectrum with the largest ampliEer gain down to very low ADC channels. The satisfactory agreement with measurements at a much lower detection threshold justiEes this approach. This procedure is taken into account when estimating the uncertainty of the equivalent dose rate measurements.
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
99
Table 1 The averaged count rate f of MUDOS, the corresponding ambient dose equivalent rate H˙ ∗ (10)T as measured with the TEPC/CACS system (charge mode) and corrected for the coincidence eJciency . The uncertainties include the uncertainty of the muon detection eJciency given in (8) and the uncertainty of the low-LET calibration factor given in (16). The last column gives the MUDOS calibration factor Date
RT (h)
f (s−1 )
H˙ ∗ (10)T ( nSv ) h
Calibration factor k f =
(DD/MM/YY) 06/05/02 07/05/02 08/05/02 09/05/02 10/05/02 11/05/02 12/05/02 13/05/02 14/05/02 15/05/02
12.0 23.0 23.5 23.0 22.5 23.0 22.5 22.0 22.0 14.0
2:713 ± 0:009 2:704 ± 0:005 2:720 ± 0:006 2:754 ± 0:007 2:774 ± 0:006 2:779 ± 0:007 2:780 ± 0:005 2:737 ± 0:007 2:741 ± 0:008 2:714 ± 0:008
33:92 ± 3:72 33:54 ± 3:67 35:68 ± 3:90 35:83 ± 3:91 34:06 ± 3:72 32:96 ± 3:60 31:68 ± 3:50 30:17 ± 3:30 31:04 ± 3:40 34:21 ± 4:86
H˙ ∗ (10)T nSv = h f
s
12:50 ± 1:37 12:40 ± 1:36 13:12 ± 1:43 13:01 ± 1:42 12:28 ± 1:34 11:86 ± 1:30 11:40 ± 1:26 11:02 ± 1:21 11:32 ± 1:24 12:61 ± 1:79
5. Pressure correction
The TEPC/CACS system was run near the MUDOS in the control hut of the PTB reference site. Due to the low count rate of the TEPC, the measurements had to be carried out on a 24 h basis. The measurements were performed from 6th May 2002 to 15th May 2002. For each day the average MUDOS count rate f and the averaged ambient dose equivalent rate H˙ ∗ (10)T of the TEPC/CACS due to charged events were determined. These events are due to electrons or positrons as well as to muons, and the measured dose rate was corrected with the coincidence eJciency given in (8). Assuming that at ground level the electron and positron Duence rate is strongly correlated with the muon Duence rate, the calibration of MUDOS yields the total ambient dose equivalent rate due to the charged component of the SCR, i.e. the soft and hard component, at ground level. The results are summarised in Table 1 from which the average calibration factor can be evaluated:
After the successful calibration of MUDOS, examples of long-term measurements are displayed in Figs. 5 and 6
nSv s: h
(18)
The given uncertainty includes the statistical 1 standard deviation of the values in the last column of Table 1, the uncertainty of the muon detection eJciency of (8) and the uncertainty of the low-LET calibration factor given in (16). The ambient dose equivalent rate due to the charged component of the SCR is then given by the equation: H˙ ∗ (10) = kf f :
(19)
One should clearly state that the ambient dose equivalent rate H˙ ∗ (10) obtained in this way is that due to the charged component of the SCR and not only due to muons. But the count rate f is due to muons only.
1100
MUDOS
35
1060
33
1040
32
1020
31
p / hPa
1080
34
1000
30 16 35
18
20
22
24
26
28
30
980 1 108
MUDOS pressure corrected
104
34 33
100
32
96
31 30 16
92
NM Kiel 18
20
NM Rate / s-1
kf = (12:2 ± 1:4)
(dH*(10)/dt)µ / (nSv/h)
4. In eld calibration
22 24 26 Date UTC
28
30
88 1
Fig. 5. As an example of the long-term measurements the results between 16th January and 31st January 2003 are shown in the top Egure as solid line. The time base is the Universal Time Coordinated (UTC). Plotted are the 1-h averages without uncertainties. The air pressure in that period (dashed line) increased from 21st to 24th by only about 5%. This caused H˙ ∗ (10) to decrease by almost 10%. After correction for the pressure changes (bottom Eg∗ ure), H˙ (10; p0 ) follows well the neutron count rate (NM rate) as measured with the Kiel neutron monitor (Kiel, 2003) (bottom Egure, lower line).
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
38
1100
MUDOS
1080 1060
33
1040
32
1020
31
37 (dH*(10)/dt)µ / (nSv/h)
34
p / hPa
35
1000
30
980 1
5
9
13
17
21 25
1 108
35 MUDOS pressure corrected
104
34 33
100
32
96
31
1
5
9
13 17 21 25 Date UTC
1
(20)
was adjusted to the H˙ ∗ (10) versus p distribution as shown in Fig. 7. A minimum '2 procedure 1 leads to nSv ; h
pK = (639:4 ± 3:9) hPa:
(21) (22)
2 The quoted uncertainties were obtained from the 'min +1 boundary and denote the 1 standard uncertainties of the parameters. This allows the measured muon dose rate to be corrected to a rate at a Exed pressure. Here, the pressure changes are taken into account by correcting H˙ ∗ (10) to the value at normal pressure p0 = 1013:25 hPa by ∗ H˙ (10; p0 ) = H˙ ∗ (10; p) · e−(p0 −p)=pK :
980
990 1000 p / hPa
1010
Fig. 7. For the period from 3rd January to 10th January 2003, the decrease in H˙ ∗ (10) corresponds to an increase in air pressure. The uncertainties shown are the statistical ones only. The solid line is the result of the Etting procedure explained in the text.
88
(top Egures, solid line) together with the air pressure p (top Egures, dashed line) measured at the PTB reference site. The expected anti-correlation between air pressure p and muon count rate or, equivalently, the ambient dose equivalent rate H˙ ∗ (10) is clearly visible. In periods of drastic changes in p, an exponential function
H0 = (164:9 ± 1:6)
34
970
Fig. 6. Same as Fig. 5 but for the period between 1st February and 28th February 2003 (top Egure). After correction for the pressure changes (bottom Egure), H˙ ∗ (10; p0 ) follows well the neutron count rate as measured with the Kiel neutron monitor (Kiel, 2003) (bottom Egure, lower line).
H˙ ∗ (10; p) = H˙ ∗0 (10) · e−p=pK
35
32
92
NM Kiel
30
36
33 NM Rate / s-1
(dH*(10)/dt)µ / (nSv/h)
100
(23)
1 For the Etting procedures, the program package MINUIT from CERNlib was used throughout this work (CERN, 2003).
For small pressure variations, i.e. p = p0 + Rp, the exponential can be expanded and the relative deviation reads ∗ H˙ ∗ (10; p) − H˙ (10; p0 ) RH˙ ∗ (10; p) = ∗ = −p Rp: ∗ H˙ (10; p0 ) H˙ (10; p0 )
(24) With p =1= pK the same expression as used in Grieder (2001) (Section 6.3.2) is obtained. The value quoted in Grieder (2001), p =2:15×10−3 (mm Hg)−1 =1:613×10−3 hPa−1 , is in remarkable agreement with our Ending in (22) from which p = (1:564 ± 0:010) × 10−3 hPa−1
(25)
follows.
6. Contribution of the charged component to H˙ ∗ (10) The pressure corrected ambient dose equivalent rate H˙ ∗ (10; p0 ) as plotted in Figs. 5 and 6 (bottom Egure, upper line) agrees well with the shape of the pressure corrected neutron monitor count rate (bottom Egure, lower line) measured with the Kiel neutron monitor (NM rate) (Kiel, 2003). This is a clear proof that MUDOS detects cosmic ray particles. Of the pressure corrected data the monthly averages H˙ ∗ (10; p0 );mon are displayed in upper left plot of Fig. 8 (•). The Erst year of continuous measurements shows a clear seasonal variation. In summer H˙ ∗ (10; p0 );mon is about 4:6% lower than in winter (lower left part of Fig. 8) with
100
32
96
31 92
30
36
108
MUDOS corrected for NM Kiel NM
35
104
34 33
100
32
96
31 92
30
88
88 4 2 0 -2
4 2 0 -2 -4
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb
-4
(a)
101
NM Rate / s-1
33
NM Rate / s
104
34
-1
108
MUDOS Kiel NM
35
(dH*(10)/dt)µ / (nSv/h)
36
rel. Deviation / %
rel. Deviation / %
(dH*(10)/dt)µ / (nSv/h)
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
2002
2003
(b)
2002
2003
Fig. 8. For the period from March 2002 to February 2003, the monthly averages of H˙ ∗ (10; p0 ); mon (•) compared to the monthly averages of the Kiel neutron monitor rate ( ) are displayed. The uncertainties of H˙ ∗ (10; p0 ); mon are the 1 variations within one month. Left Egure: the uncorrected MUDOS data are shown. Right Egure: the MUDOS date were corrected according to the relative deviations of the Kiel Neutron Monitor (NM). The relative deviations from the yearly average are shown at the bottom of each Egure. The solid line in the right bottom Egure is Eq. (33) with the parameters as given in (35).
the minimum in August. A comparison with the Kiel neutron monitor data ( ) is not very satisfactory although the minimum in August is also visible. The relative deviations displayed in the lower part of Fig. 8 are based on the 1-year average between March 2002 and February 2003 which is nSv H˙ ∗ (10; p0 ); yr = (32:7 ± 3:7) : (26) h The standard uncertainty is obtained from the 1 standard deviation of the data plotted in Fig. 8 (left upper Egure), the standard uncertainty of the TEPC calibration factor of (16) and the uncertainty of the TEPC/CACS coincidence eJciency given in (8). This result of (26) may be compared with the outdoor muon energy dose rate as measured with a Ge detector (Clouvas et al., 2003). Clouvas et al. (2003) have identiEed muons by their energy deposition in the Ge detector. From the measured energy deposition the dose rate in the ICRU sphere (ICRU, 1994) was determined with the aid of MonteCarlo simulations. The quoted result of D˙ Ge = 25 nGy=h can easily be transferred to equivalent dose rate because the radiation weighting factor for muons, i.e. for low-LET radiation, is equal to 1. Therefore, the result to compare with is H˙ Ge = 25 nSv=h. The measurements were made in Thessaloniki, in the northern part of Greece (40◦ 31 N, 22◦ 58 E) for which a cuto? rigidity of approximately 7:1 GV is valid. During the measurements no air pressure was recorded. Thus, no pressure correction was applied. According to (5) and (6) a Duence rate corresponding to about 38% of the muon rate must be attributed to the soft component. From this an estimate of the total dose equivalent rate due to the
charged component of the SCR gives 34:5 nSv=h for the results of Clouvas et al. (2003). This is in reasonable agreement with the MUDOS value of (26), although the di?erent values of the vertical cuto? rigidity were not taken into account. One would expect a smaller value at latitudes closer to the equator. 7. Seasonal variation The seasonal variation of the muon Dux has already been described in great detail in the early 50’s by Barrett (Barrett et al., 1952). There the variation of muons detected deep underground was investigated. These muons are very energetic with energies above 1 TeV. It was clearly demonstrated in Barrett et al. (1952) and with the most recent experimental proofs in Ambrosio et al. (1997, 2002) that a positive correlation with the temperature changes in the upper layers of the atmosphere exists. The net e?ect on the muon count rate is dominated by the interplay between meson absorption and decay (Barrett et al., 1952). At sea level, this e?ect is negligible and the muon decay dominates the variations of the muon rate as explained by Blackett (1938). An increase in the atmospheric temperature leads to a rise of the atmospheric layer in which muon production takes place. This in turn means an increase in Dight path down to ground level. More muons can therefore decay before they reach ground level. This behaviour is expressed by the survival probability, which describes the probability P(h0 ) of a particle traversing a certain distance h0 before it decays, P(h0 ) = e−h0 m0 = P c ;
(27)
102
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
where m0 =105:66 MeV is the muon rest mass, =2:20 s the muon mean lifetime and P the muon momentum in GeV=c. On the assumption that the altitude variation Rh is small compared to the entire Dight path, the exponential in (27) can be expanded and the relative di?erence of the survival probabilities can be written as P(h0 + Rh) − P(h0 ) m0 Rh =− : P(h0 ) P c
(28)
For a static isothermal atmosphere, the particle density n(h) = n(h0 ) · e−h=hs
(29)
depends on the altitude h and the scale height hs = kT=Mg, where k is the Boltzmann constant, T the temperature, M the molar mass of the atmosphere and g the gravitational acceleration at sea level. An increase in the temperature in a certain layer will cause a rise in altitude. On the assumption that the density remains constant, it follows from (29) that Rh = h0
RT : T0
(30)
Inserting this into (28) leads to P(h0 + Rh) − P(h0 ) m0 h0 RTi RI =− ; = P(h0 ) Iyr P c Tyr
(31)
where RI denotes the change in the muon Duence rate, Iyr the annual average muon Duence rate, Tyr the annual average of the layer temperature Ti and RTi its deviation. It was also assumed that the ratio of the survival probabilities is directly reDected in the ratio of the muon Duence rates. Thus, Eq. (31) gives an explicit relation between the muon Duence rate and the temperature changes in the atmospheric layer where the muons are created. Since the variations are rather small, the inDuence of the primary cosmic radiation has also to be included. This can be done via the neutron count rate at ground level. As mentioned above, the count rate of the Kiel neutron monitor (NM) does not exactly agree with the behaviour of the MUDOS rate since the NM rate directly reDects the changes in the Dux of the primary spectrum. Therefore, the muon Duence rate at ground level will also be a?ected. Using the NM rate, the MUDOS data can be corrected according to kNM =
1 ; 1 + -NM
(32)
with -NM being the relative deviations as plotted in Fig. 8 ( ). After applying this NM correction, the monthly averages of MUDOS and their relative deviations lead to the data shown in the right plot of Fig. 8. The behaviour of the relative deviations of the NM corrected monthly averages from the 1-year average can be parameterised as (Ambrosio et al., 1997, 2002) ˙∗
RH (10; p0 )mon = Ayr cos(2(tm − m )); H˙ ∗ (10); yr
(33)
where RH˙ ∗ (10; p0 )mon = H˙ ∗ (10; p0 ); mon − H˙ ∗ (10; p0 ); yr ; (34) Ayr is the variation amplitude, tm the time in months divided by 12 since January 1st, 2002, and the phase shift m also given in the same units, respectively. The solid line in Fig. 8 (right side, bottom plot) is the function given in (33) adjusted to measured data. The values as obtained from a minimum '2 procedure are Ayr = (1:55 ± 0:61)%;
m = (0:096 ± 0:061):
(35)
2 The standard uncertainties were obtained from the 'min +1 boundary and denote the 1 standard uncertainties of the parameters.
8. Temperature dependence The atmospheric temperature proEles have been supplied by the World Data Center for Remote Sensing of the Atmosphere (WDC, 2003) and processed in order to obtain the atmospheric temperature distributions above Braunschweig for each day of the period under consideration (Schroedter, 2003; Li et al., 2000). According to Ambrosio et al. (1997), the e?ective temperature was evaluated as T (Xi )[e−Xi =1 − e−Xi =1N ]=Xi Te? = i −X =1 ; (36) i − e−Xi =1N ]=Xi i [e where 1 = 160 g=cm2 and 1N = 120 g=cm2 are the atmospheric attenuation lengths for pions and nucleons, respectively, and Xi the atmospheric depth (in the units g=cm2 ) of the ith layer. Data from atmospheric layers at equal pressure, i.e. at 1000, 850, 700, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30 and 10 hPa, have been used (Fig. 9). In Table 2 the monthly averages of Te? from March 2002 to February 2003 are tabulated and their relative deviations plotted in Fig. 10 in comparison with the relative deviations measured with MUDOS as shown in Fig. 8 (right Egure, bottom plot). There is remarkable agreement in the behaviour of the MUDOS data and the e?ective temperature. In accordance with (31), i.e. RI RT = − ; Iyr Tyr
(37)
the relative deviations of MUDOS are plotted vs. the relative deviations of Te? in Fig. 11. The solid line is the result of a '2 minimisation procedure leading to = 0:51 ± 0:21
(38)
from which the temperature coeJcient is evaluated at T =
10−3 = (2:3 ± 1:0) : Tyr K
(39)
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
Teff July 2002 January 2003 Mar02-Feb03 Avg.
30000
Altitude / m
25000 20000
4 MUDOS corr. rel. Deviation / %
35000
103
2 0 -2
15000 -4 10000 6 5000
2 300
0 -2
Fig. 9. Shown are the atmospheric temperature distributions along the altitude for July 2002 (dashed line) and January 2003 (dotted line) and the 1-year average of the entire period (solid line). The pressure levels have been converted into altitude. The corresponding e?ective temperatures Te? are indicated by the vertical lines.
Month
Te? (Xi )
Rel. deviation/%
March 02 April 02 May 02 June 02 July 02 August 02 September 02 October 02 November 02 December 02 January 03 February 03
217:76 ± 0:63 220:09 ± 0:73 221:42 ± 0:67 224:34 ± 0:69 225:67 ± 0:53 224:11 ± 0:67 220:80 ± 0:70 217:91 ± 0:88 213:99 ± 1:62 209:42 ± 3:39 214:94 ± 3:95 213:69 ± 2:24
−0:42 ± 0:29 0:65 ± 0:33 1:26 ± 0:31 2:59 ± 0:31 3:20 ± 0:24 2:49 ± 0:31 0:97 ± 0:32 −0:35 ± 0:40 −2:15 ± 0:74 −4:23 ± 1:55 −1:71 ± 1:81 −2:28 ± 1:02
The absolute temperatures at di?erent atmospheric depths were obtained from WDC (2003), Schroedter (2003), Li et al. (2000) for each day. The last column shows the relative deviations of the monthly averages from the annual average Tyr = (218:7 ± 4:8) K.
In Fig. 10 (bottom part), the dashed line represents the function given in (33) adjusted to the MUDOS data (see (35) for the parameters) and divided by (−) according to (37) and (38). There is excellent agreement between the relative deviations of the e?ective temperature and the muon rate at ground level, and the assumption that this e?ect is due to the muon decay has been proven. Using (30) and (37), the rise in altitude of the muon production layer can be estimated. The approximated altitude of maximum muon production is h0 = 12 km (Grieder, 2001;
2002
Feb
Jan
Dec
Oct
Nov
Sep
Jul
Mar
-6
2003
Fig. 10. For the period from March 2002 to February 2003, the relative deviations from the yearly average of the NM corrected MUDOS results (top Egure, •) compared to the relative deviations from the yearly average of the e?ective temperature (bottom Egure, ). The solid line in the upper part corresponds to (33) with the parameters given in (35). The dashed line in the bottom part is the same function but divided by (−) according to (37) and (38).
4
(∆Hµ / Hyr) / %
Table 2 The monthly averages of the e?ective temperature Te? of the atmosphere as deEned in (36)
Teff
-4
Aug
280
Jun
240 260 Temperature / K
Apr
220
May
0 200
4
2
0
-2
-4 -6
-4
-2 0 2 (∆Teff / Tyr) / %
4
6
Fig. 11. The measured relative deviations from MUDOS versus the relative deviations of the e?ective temperatures Te? . The solid line is the result of a linear function adjusted to the data.
104
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
Poirier et al., 2002) which leads to a rise of the corresponding layer between winter and summer of Rhmax ≈ 750 m:
(40)
9. Summary After the Erst year of monitoring the SCR at the PTB reference site, the ambient dose equivalent rate H˙ ∗ (10) of the charged component of the SCR was determined. This result is of importance since the traceability of the TEPC system used is given by its calibration in the PTB reference Eeld for high energy -radiation. The detailed investigation of the SCR with MUDOS demonstrates the inDuence of air pressure, the solar activity and the e?ective temperature of the entire atmosphere. It could be shown that variations of up to 15% are possible. The seasonal variations also prove that MUDOS detects cosmic ray muons since this e?ect is caused by the temperature variations of the atmosphere leading to altitude changes for the muon production layer. Acknowledgements The authors appreciate the intense work of J. Kretzer, F. Langner and J. Roth (all PTB), who are responsible for the development of detector systems, data acquisition software and optimisation of the infrastructure. Especially their continuous e?ort to keep the measurements running was the basis for such long term measurements as presented in this work. Many thanks to R. Behrens (PTB) who maintains the 6:6 MeV -reference Eeld and the sta? of the PTB Department 6.4 for preparing excellent proton beams. The development of the mobile TEPC/CACS system is supported by the European Commission contract FIGM-CT-2000-00068 Dosimetry of Aircrew Exposure to Radiation During Solar Maximum (DOSMAX). Our gratitude also belongs to M. Schroedter (German Aerospace Center, DLR) who furnished the atmospheric temperature distributions above Braunschweig. References Ambrosio, M., et al., 1997. Seasonal variations in the underground muon intensity as seen by MACRO. Astropart. Phys. 7, 109. Ambrosio, M., et al., 2002. The MACRO detector at Gran Sasso. Nucl. Instrum. Methods A 486, 663. Barrett, P.H., et al., 1952. Interpretation of cosmic-ray measurements far underground. Rev. Mod. Phys. 24, 133. Berger, M.J., Coursey, J.S., Zucker, M.A., 2003. ESTAR, PSTAR and ASTAR: Computer Programs for Calculating Stopping-Power and Range Tables for Electrons, Protons, and Helium Ions. National Institute of Standards and Technology,
Gaithersburg, MD, USA. Available via http://physics. nist.gov/Star; Blackett, P.M.S., 1938. On the instability of the barytron and the temperature e?ect of cosmic rays. Phys. Rev. 54, 973. BSuermann, L., Guldbakke, S., Kramer, H.-M., 1999. Calibration of personal and area dosimeters in high-energy photon Eelds. PTB-Bericht PTB-Dos-32, 1999, Braunschweig. CERN, 2003. The program package CERNlib is accessible via http://www.cern.ch. Clouvas, A., Xanthos, S., Antonopoulos-Domis, M., Silva, J., 2003. Measurements with a Ge detector and Monte Carlo computations of dose rate yields due to cosmic muons. Health Phys. 84, 212. Gerdung, S., Pihet, P., Grindborg, J.E., Roos, H., Schrewe, U.J., Schuhmacher, H., 1995. Operation and application of tissue-equivalent proportional counters. Radiat. Prot. Dosim. 61, 381. Grieder, P.K.F., 2001. Cosmic Rays at Earth. Elsevier Science, Amsterdam. Groom, D.E., Mokhov, N.V., Striganov, S.I., 2001. At. Data Nucl. Data Tables 78, 183. Available via http://pdg.lbl.gov/ AtomicNuclearProperties. Hagiwara, K., et al., 2002. Phys. Rev. D 66, 010001. Review of Particle Physics, Particle Data Group, http://www-pdg. lbl.gov. ICRP, 1991. International Commission on Radiological Protection, 1991. Recommendations of the International Commission on Radiological Protection. ICRP Publication 60, Pergamon Press, Oxford. ICRU, 1994. International Commission on Radiation Units and Measurements. -Ray Spectrometry in the Environment. ICRU Report 53. Kiel, 2003. The Kiel neutron monitor data can be accessed via http://134.245.132.179/Kiel/main.htm. Li, J., et al., 2000. Global soundings of the atmosphere from ATOVS measurements: the algorithm and validation. J. Appl. Meteor. 39, 1248. Poirier, J., Roesler, S., Fasso, A., 2002. Distribution of secondary muons at sea level from cosmic gamma rays below 10 TeV. Astropart. Phys. 17, 441. Rossi, H.H., Zaider, M., 1996. Microdosimetry and its Applications. Springer, Berlin, Heidelberg. Schrewe, U., 2000. Global measurements of the radiation exposure of civil air crew from 1997 to 1999. Radiat. Prot. Dosim. 91, 347. Schroedter, M., 2003. German Aerospace Center (DLR), D-82234 Wessling, Germany. Private communication. Smart, D.F., Shea, M.A., 1997. Proceedings of the 25th International Cosmic Ray Conference, Contributed Papers 2, 401. SRIM, 2003. The program SRIM 2003 can be obtained via http://www.srim.org. UNSCEAR, 2000. United Nations ScientiEc Committee on the E?ects of Atomic Radiation, Sources and E?ects of Ionizing Radiation. UNSCEAR 2000. Report to the General Assembly, Vol. I: Sources. Accessible via http://www.unscear.org. WDC, 2003. ICSU World Data Center for Remote Sensing of the Atmosphere. http://wdc.dlr.de. Wissmann, F., 2003a. To be published. Wissmann, F., 2003b. To be published.
Radiation exposure at ground level by secondary cosmic radiation F. Wissmanna;∗ , V. Dangendorf a , U. Schreweb a Physikalisch-Technische b Fachhochschule
Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany Hannover, Ricklinger Stadtweg 120, D-30459 Hannover, Germany
Received 27 October 2003; accepted 1 March 2004
Abstract The contribution of the charged component of secondary cosmic radiation to the ambient dose equivalent H ∗ (10) at ground level is investigated using the muon detector MUDOS and a TEPC detector surrounded by the coincidence detector CACS to identify charged particles. The ambient dose equivalent rate H˙ ∗ (10)T as measured with the TEPC/CACS is used to calibrate the MUDOS count rate in terms of H˙ ∗ (10). First results from long-term measurements at the PTB reference site for ambient radiation dosimetry are reported. The air pressure corrected dose rate shows, as expected, a strong correlation with the neutron count rate as measured with the Kiel neutron monitor. The measured seasonal variations exhibit a negative correlation with the temperature changes in the upper layers of the atmosphere where the ground level muons are produced. c 2004 Elsevier Ltd. All rights reserved. PACS: 96.40.T; 87.53.R Keywords: Cosmic ray muons; Microdosimetry
1. Introduction Ionising radiation at ground level consists of two major components. One stems from the radioactive isotopes in the earth’s crust and therefore is named terrestrial radiation (TR). In addition to TR, there is the secondary cosmic radiation (SCR) which contributes approximately the same amount to the entire annual e?ective dose accumulated by an individual (UNSCEAR, 2000). The SCR has its origin in the primary cosmic radiation (or galactic cosmic radiation: GCR) consisting of almost 99% of protons and particles (Grieder, 2001). The GCR enters the solar system and is partially deDected by the interplanetary magnetic Eeld and, when approaching our planet, by the earth’s magnetic Eeld. When the GCR hits the upper layers of the atmosphere, nuclear reactions are induced. The production of secondary particles leads to an electromagnetic component of the SCR, which consists of -radiation, electrons and positrons, and a hadronic component. The latter consists ∗
Corresponding author. E-mail address: [email protected] (F. Wissmann).
c 2004 Elsevier Ltd. All rights reserved. 1350-4487/$ - see front matter doi:10.1016/j.radmeas.2004.03.025
mainly of protons, neutrons and even mesons (Grieder, 2001) among which the latter play an essential role. Immediately after production the neutral meson (0 meson) decays ( = 8:4 × 10−8 ns (Hagiwara et al., 2002)) into 2 photons which then may create electron–positron pairs. Via bremsstrahlung the electrons or positrons emit high-energy photons which are again a source for pair-production. This evolution of the electromagnetic component displays how the total energy of an initial particle, here the 0 meson, is distributed among all secondaries until the energy of a single particle is no longer suJcient to create another particle or until it is absorbed. The charged mesons (± mesons, = 26 ns (Hagiwara et al., 2002)) decay into muons (± ) and the corresponding muon neutrinos ( ; K ). The muon itself is unstable with a mean lifetime of = 2:2 s (Hagiwara et al., 2002), corresponding to a Dight path of c = 659 m which by far is not suJcient to reach ground level. But, the relativistic effect of time dilatation permits them to pass the entire atmosphere and to reach the earth’s surface. In contrast to the electromagnetic component which is largely absorbed after having traversed the atmosphere, the muons cross the
96
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
atmosphere without major interactions. Therefore, most of the muons reaching the surface have their origin high in the atmosphere. The energy distribution ranges from a few MeV up to hundreds of GeV with a mean kinetic energy of about 4 GeV (Grieder, 2001). The particles of the hadronic component also initiate nuclear reactions producing numerous secondaries. As for the electromagnetic component, the hadronic Dux decreases rapidly through the atmosphere leaving the neutrons as the main hadronic contribution at ground level (Grieder, 2001). Owing to the di?erent reaction mechanisms involved, the composition of the SCR in the atmosphere strongly depends on the altitude (Grieder, 2001). The charged particles of the SCR at ground level can be grouped in two components: the so-called “hard” component of highly penetrating muons, and a “soft” component of electrons and positrons which are easily absorbed in shielding material. According to Grieder (2001), the vertical particle radiance of charged particles is −2 −1 −1 ’soft s sr ; ; v = 31 m
(1)
−2 −1 −1 ’hard s sr : ; v = 82 m
(2)
The zenith angle dependence of the soft and hard component at ground level can be described by ’ (#) = ’ (0) cosn #;
(3)
with n = 2 for both, the soft and hard component, as a good choice at northern latitudes (Grieder, 2001). The evaluation of the vertical Duence rate traversing a horizontal area reads: ’1 = ’ (#) cos # d = ’ (#) cos # sin # d# d;
= 2’ (0)
The Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig has installed a reference site for ambient radiation dosimetry. The site is located at latitude 52◦ 17 N and longitude 10◦ 28 E (altitude approximately 80 m), which corresponds to a vertical cuto? rigidity of 2:8 GV (Smart and Shea, 1997). The Dux of the SCR at an altitude of 80 m is almost that at sea level. Ambient radiation is investigated with a set of ionisation chambers and proportional counters. These detectors measure both, the TR and the SCR and are calibrated in the reference radiation Eelds for -radiation at PTB. In addition, the Muon Dosimetry System (MUDOS) based on two proportional counters has been developed for the investigation of cosmic ray muons. The equipment is completed by standard neutron monitors for dosimetry of low energy neutrons and modiEed ones optimised for the dosimetry of high energy cosmic ray neutrons. Although the average kinetic energy of the muons at ground level is approximately 4 GeV, they can be treated as densely ionising particles. This enables us to build a system of two energy loss counters working in the coincidence mode. The MUDOS developed at PTB (Fig. 1) consists of two cylindrical multi-wire proportional chambers with a diameter of 200 mm and a height of approximately 30 mm. Each chamber is equipped with an anode plane with 50 tungsten–rhenium wires (?25 m) separated by 4 mm. Above and below the anode wires, stainless steel wire grids (?37 m, pitch 370 m, 81% optical transmission) are used as cathode. The chambers are Elled with CF4 counting gas at a pressure of 1100 hPa. The voltage applied between anode and cathode planes is 2700 V. Each chamber signal is fed into a discriminator module to create logic pulses. If a muon traverses the two chambers, the logic signals fulEl a coincidence condition. Between the two chambers a 25 mm thick Pb layer absorbs electrons or positrons with energies up to 435 MeV (Berger et al., 2003) and prevents
cosn+1 # sin # d# # −cosn+2 # max : n + 2 0
(4)
Owing to the exponent of the cosine function, the particle Duence rate is peaked into vertical directions. Therefore, any detector acceptance beyond #max ≈ 70◦ leads to corrections in the measured Duence rate of the order of 1% or less. The Duence rate of charged particles, i.e. the soft as well as the hard component, from a nearly vertical direction can be calculated with the simple formulas ’1 (soft) = 2
’soft ; v ≈ 50 m−2 s−1 ; n+2
(5)
’1 (hard) = 2
’hard ; v ≈ 130 m−2 s−1 : n+2
(6)
200 mm
25 mm
’1 = 2’ (0)
2. Muon detection system
50 Wire Anode
Pb Layer
Cathode Grids
Fig. 1. Schematic drawing of the MUDOS wire chambers. Each anode plane is covered above and below by the cathode grids. Between the two proportional chambers, a 25 mm thick lead layer prevents electrons or positrons from traversing the two chambers, which might create background coincidence events.
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
coincidence events, i.e. background events due to electrons or positrons. The minimum muon energy required to cross the entire Pb layer is approximately 59 MeV (Groom et al., 2001). Therefore, the coincident events can be deEned as muons. To prevent any e?ect from temperature changes, the chambers are operated in a temperature stabilised housing at 20◦ C. The single count rates of the two MUDOS chambers are about f1 = 7:2 s−1 and f2 = 6:9 s−1 , respectively, and the coincidence rate is about f = 2:7 s−1 . The coincidence rate f is proportional to the Duence rate of muons at ground level. From a simple Monte-Carlo calculation (Wissmann, 2003a) the geometrical eJciency of MUDOS was evaluated to be geo = 0:664 ± 0:008;
(7)
where the uncertainty given is the statistical 1 standard uncertainty of the Monte-Carlo calculation. Applied to f this leads to a muon Duence rate of 129:5 s−1 which is in perfect agreement with the value given in (6). 3. The TEPC reference instrument The conversion from the muon count rate f to ambient dose equivalent rate H˙ ∗ (10) requires a reference instrument such as a Tissue Equivalent Proportional Counter (TEPC). The device used here is a 2 -TEPC (nominal diameter: 5:69 cm) of Rossi type manufactured by Far West Technology (Fig. 2). The counting gas is propane-based TE gas with a reduced pressure inside the cavity which simulates 4 m of tissue with a density of 1 g=cm3 . The applied voltage is 850 V and the detector signal is fed into a
97
linear ampliEer having three di?erent gains with an approximate ratio of 1:10:100. This instrument alone does not have the ability to clearly identify muons. An additional charged particle counter, i.e. the 24 anode wire proportional counter Coincidence/Anti-Coincidence Shield (CACS), surrounds the TEPC (Fig. 2). The TEPC/CACS system has already been in operation as part of a mobile dosimetry system used at Dight altitudes. For more detailed information, the reader is referred to (Schrewe, 2000). The entire system Ets into a suitcase of cabin baggage size and can be taken aboard passenger aircrafts (Wissmann, 2003b). The TEPC pulse height analysis is performed in coincidence and anti-coincidence to the CACS. The Erst kind of events are the so-called charged events, the latter are the neutral events. CACS covers a geometrical solid angle of about 85% of 4. Taking the zenith angle distribution of muons and electrons or positrons from (3) into account, the coincidence eJciency for the charged component of the SCR can be estimated to be (Schrewe, 2000) = (0:9 ± 0:1):
(8)
The index represents the muons, electrons and positrons. The TEPC measures the lineal energy y, i.e. the energy deposition in the TEPC sphere normalised to a mean chord length (Rossi and Zaider, 1996) l =
2 d ; 3
(9)
with d = 4 m the simulated tissue diameter. The calibration in y is done using neutron sources. The neutrons interact with the cavity wall and gas producing protons of various energies. The minimum energy of the recoiling protons necessary to traverse tissue of 4 m with density 1:0 g=cm3 is Ep = 318:5 keV
(10)
calculated with SRIM 2003 (SRIM, 2003). Ep corresponds to the maximum deposited energy, and with (9) the so-called proton edge is evaluated to be yp = 119:4
keV : m
(11)
This edge is clearly visible in the event spectra of the lowest ampliEer gain. By relating the corresponding ADC channel to yp , the pulse height spectra are calibrated in lineal energy. The transition to a single event dose D(yi ) in a certain interval yi is given by the ratio of the energy RE deposited in the volume and the mass Rm inside this volume (Rossi and Zaider, 1996): Fig. 2. The TEPC/CACS system. The 2 TEPC is surrounded by the cylindrical 24 anode wire chamber CACS Elled with CF4 counting gas. The dose measured with the TEPC can be related to the charge of the primary particle entering the TEPC, if the events are analysed in coincidence and in anti-coincidence to the CACS.
D(yi ) =
REi yi lK = : Rm V
(12)
Here, lK is the mean chord length inside the TEPC cavity, is the gas density and V the gas volume. For a spherical shape of the volume the relation lK = (4V )=S is valid, with
98
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104 0.04 low-LET
high-LET
y d(y)
0.03
0.02
0.01
0 10-2
10-1
1 10 y / (keV/µm)
102
103
Fig. 3. The normalised dose distribution spectrum yd(y) as measured by the TEPC/CACS (neutral events only) with an AmBe neutron source. The sharp drop at around 120 keV=m corresponds to the proton edge used to calibrate the event spectra in terms of the lineal energy y.
the surface area S = d2 and d = 5:69 cm being the cavity diameter. Inserting this into (12) one obtains m yi 4 D(yi ) = = yi 6:3 × 10−5 Gy: (13) d2 keV The total dose obtained from the measured dose distribution is then D= n(yi )D(yi ); (14) i
and the ambient dose equivalent H ∗ (10)T can be evaluated (Rossi and Zaider, 1996; Gerdung et al., 1995) by H ∗ (10)T = n(yi )D(yi )q(yi ); (15) i
where n(yi ) is the number of events measured in the interval yi and q(yi ) is equal to the quality factor Q(L) deEned by ICRP (ICRP, 1991) with the approximation that L ≈ y. It is convenient to plot the event spectra in terms of normalised dose distribution spectra yi d(yi ) in logarithmic binning. Here, d(yi ) is obtained by normalising the event spectrum with the total event number. This kind of plot simpliEes the comparison of spectra due to di?erent types of radiation. For a more detailed description, the reader is referred to (Rossi and Zaider, 1996) and (Gerdung et al., 1995) and references therein. An example of the dose distribution spectrum from an AmBe neutron source is given in Fig. 3. Neutrons, i.e. the recoiling protons from np reactions in the cavity wall, particles and heavier nuclei lead to high-LET events above 10 keV=m. Compared to this, the spectrum of photons (Fig. 4) shows di?erent features. At y ¿ 10 keV=m, there are almost no events. Therefore, photons as well as electrons and positrons lead to low-LET events with y ¡ 10 keV=m in the dose distribution spectra. The charged component of the SCR, identiEed with the CACS running in coincidence to the TEPC (charged mode),
Fig. 4. The normalised dose distribution spectra yd(y) as measured in di?erent -radiation Eelds: Cs source with E =662 keV (hashed area); photons produced via the reaction 19 F(p; )16 O with E = 6 –7 MeV (BSuermann et al., 1999) (dashed line); ambient radiation measured with the TEPC/CACS in the coincidence mode (solid line), i.e. the charged component of the SCR.
leads only to low-LET events in the dose distribution spectra (solid line in Fig. 4). A comparable spectrum can be simulated with high-energy photons. Such a reference photon Eeld has been produced by the reaction 19 F(p; )16 O with photon energies between 6 MeV and 7 MeV (BSuermann et al., 1999) (ISO R-F quality; average photon energy is 6:6 MeV). The dose distribution spectrum obtained in this photon Eeld agrees quite well with that due to the charged component of the SCR, as shown by the dashed line in Fig. 4. Thus, this reference high-energy photon Eeld of 6:6 MeV photons has been used for a low-LET dose calibration. The low-LET calibration factor, deEned as the ratio of the reference value H˙ ∗ (10) and that measured with the TEPC alone, has been determined to be H˙ ∗ (10) = kT; low = 1:129 ± 0:099; H˙ ∗ (10)low
(16)
where the standard uncertainty includes the statistical 1 uncertainty of the measurement and the standard uncertainty of the reference value. Now, (15) reads as H ∗ (10)T; low = kT; low
n(yi )D(yi )q(yi ):
(17)
i
It has to be mentioned that the threshold of the TEPC system at around 0:3 keV=m has been lowered artiEcially by linear extrapolation of the event spectrum with the largest ampliEer gain down to very low ADC channels. The satisfactory agreement with measurements at a much lower detection threshold justiEes this approach. This procedure is taken into account when estimating the uncertainty of the equivalent dose rate measurements.
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
99
Table 1 The averaged count rate f of MUDOS, the corresponding ambient dose equivalent rate H˙ ∗ (10)T as measured with the TEPC/CACS system (charge mode) and corrected for the coincidence eJciency . The uncertainties include the uncertainty of the muon detection eJciency given in (8) and the uncertainty of the low-LET calibration factor given in (16). The last column gives the MUDOS calibration factor Date
RT (h)
f (s−1 )
H˙ ∗ (10)T ( nSv ) h
Calibration factor k f =
(DD/MM/YY) 06/05/02 07/05/02 08/05/02 09/05/02 10/05/02 11/05/02 12/05/02 13/05/02 14/05/02 15/05/02
12.0 23.0 23.5 23.0 22.5 23.0 22.5 22.0 22.0 14.0
2:713 ± 0:009 2:704 ± 0:005 2:720 ± 0:006 2:754 ± 0:007 2:774 ± 0:006 2:779 ± 0:007 2:780 ± 0:005 2:737 ± 0:007 2:741 ± 0:008 2:714 ± 0:008
33:92 ± 3:72 33:54 ± 3:67 35:68 ± 3:90 35:83 ± 3:91 34:06 ± 3:72 32:96 ± 3:60 31:68 ± 3:50 30:17 ± 3:30 31:04 ± 3:40 34:21 ± 4:86
H˙ ∗ (10)T nSv = h f
s
12:50 ± 1:37 12:40 ± 1:36 13:12 ± 1:43 13:01 ± 1:42 12:28 ± 1:34 11:86 ± 1:30 11:40 ± 1:26 11:02 ± 1:21 11:32 ± 1:24 12:61 ± 1:79
5. Pressure correction
The TEPC/CACS system was run near the MUDOS in the control hut of the PTB reference site. Due to the low count rate of the TEPC, the measurements had to be carried out on a 24 h basis. The measurements were performed from 6th May 2002 to 15th May 2002. For each day the average MUDOS count rate f and the averaged ambient dose equivalent rate H˙ ∗ (10)T of the TEPC/CACS due to charged events were determined. These events are due to electrons or positrons as well as to muons, and the measured dose rate was corrected with the coincidence eJciency given in (8). Assuming that at ground level the electron and positron Duence rate is strongly correlated with the muon Duence rate, the calibration of MUDOS yields the total ambient dose equivalent rate due to the charged component of the SCR, i.e. the soft and hard component, at ground level. The results are summarised in Table 1 from which the average calibration factor can be evaluated:
After the successful calibration of MUDOS, examples of long-term measurements are displayed in Figs. 5 and 6
nSv s: h
(18)
The given uncertainty includes the statistical 1 standard deviation of the values in the last column of Table 1, the uncertainty of the muon detection eJciency of (8) and the uncertainty of the low-LET calibration factor given in (16). The ambient dose equivalent rate due to the charged component of the SCR is then given by the equation: H˙ ∗ (10) = kf f :
(19)
One should clearly state that the ambient dose equivalent rate H˙ ∗ (10) obtained in this way is that due to the charged component of the SCR and not only due to muons. But the count rate f is due to muons only.
1100
MUDOS
35
1060
33
1040
32
1020
31
p / hPa
1080
34
1000
30 16 35
18
20
22
24
26
28
30
980 1 108
MUDOS pressure corrected
104
34 33
100
32
96
31 30 16
92
NM Kiel 18
20
NM Rate / s-1
kf = (12:2 ± 1:4)
(dH*(10)/dt)µ / (nSv/h)
4. In eld calibration
22 24 26 Date UTC
28
30
88 1
Fig. 5. As an example of the long-term measurements the results between 16th January and 31st January 2003 are shown in the top Egure as solid line. The time base is the Universal Time Coordinated (UTC). Plotted are the 1-h averages without uncertainties. The air pressure in that period (dashed line) increased from 21st to 24th by only about 5%. This caused H˙ ∗ (10) to decrease by almost 10%. After correction for the pressure changes (bottom Eg∗ ure), H˙ (10; p0 ) follows well the neutron count rate (NM rate) as measured with the Kiel neutron monitor (Kiel, 2003) (bottom Egure, lower line).
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
38
1100
MUDOS
1080 1060
33
1040
32
1020
31
37 (dH*(10)/dt)µ / (nSv/h)
34
p / hPa
35
1000
30
980 1
5
9
13
17
21 25
1 108
35 MUDOS pressure corrected
104
34 33
100
32
96
31
1
5
9
13 17 21 25 Date UTC
1
(20)
was adjusted to the H˙ ∗ (10) versus p distribution as shown in Fig. 7. A minimum '2 procedure 1 leads to nSv ; h
pK = (639:4 ± 3:9) hPa:
(21) (22)
2 The quoted uncertainties were obtained from the 'min +1 boundary and denote the 1 standard uncertainties of the parameters. This allows the measured muon dose rate to be corrected to a rate at a Exed pressure. Here, the pressure changes are taken into account by correcting H˙ ∗ (10) to the value at normal pressure p0 = 1013:25 hPa by ∗ H˙ (10; p0 ) = H˙ ∗ (10; p) · e−(p0 −p)=pK :
980
990 1000 p / hPa
1010
Fig. 7. For the period from 3rd January to 10th January 2003, the decrease in H˙ ∗ (10) corresponds to an increase in air pressure. The uncertainties shown are the statistical ones only. The solid line is the result of the Etting procedure explained in the text.
88
(top Egures, solid line) together with the air pressure p (top Egures, dashed line) measured at the PTB reference site. The expected anti-correlation between air pressure p and muon count rate or, equivalently, the ambient dose equivalent rate H˙ ∗ (10) is clearly visible. In periods of drastic changes in p, an exponential function
H0 = (164:9 ± 1:6)
34
970
Fig. 6. Same as Fig. 5 but for the period between 1st February and 28th February 2003 (top Egure). After correction for the pressure changes (bottom Egure), H˙ ∗ (10; p0 ) follows well the neutron count rate as measured with the Kiel neutron monitor (Kiel, 2003) (bottom Egure, lower line).
H˙ ∗ (10; p) = H˙ ∗0 (10) · e−p=pK
35
32
92
NM Kiel
30
36
33 NM Rate / s-1
(dH*(10)/dt)µ / (nSv/h)
100
(23)
1 For the Etting procedures, the program package MINUIT from CERNlib was used throughout this work (CERN, 2003).
For small pressure variations, i.e. p = p0 + Rp, the exponential can be expanded and the relative deviation reads ∗ H˙ ∗ (10; p) − H˙ (10; p0 ) RH˙ ∗ (10; p) = ∗ = −p Rp: ∗ H˙ (10; p0 ) H˙ (10; p0 )
(24) With p =1= pK the same expression as used in Grieder (2001) (Section 6.3.2) is obtained. The value quoted in Grieder (2001), p =2:15×10−3 (mm Hg)−1 =1:613×10−3 hPa−1 , is in remarkable agreement with our Ending in (22) from which p = (1:564 ± 0:010) × 10−3 hPa−1
(25)
follows.
6. Contribution of the charged component to H˙ ∗ (10) The pressure corrected ambient dose equivalent rate H˙ ∗ (10; p0 ) as plotted in Figs. 5 and 6 (bottom Egure, upper line) agrees well with the shape of the pressure corrected neutron monitor count rate (bottom Egure, lower line) measured with the Kiel neutron monitor (NM rate) (Kiel, 2003). This is a clear proof that MUDOS detects cosmic ray particles. Of the pressure corrected data the monthly averages H˙ ∗ (10; p0 );mon are displayed in upper left plot of Fig. 8 (•). The Erst year of continuous measurements shows a clear seasonal variation. In summer H˙ ∗ (10; p0 );mon is about 4:6% lower than in winter (lower left part of Fig. 8) with
100
32
96
31 92
30
36
108
MUDOS corrected for NM Kiel NM
35
104
34 33
100
32
96
31 92
30
88
88 4 2 0 -2
4 2 0 -2 -4
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb
-4
(a)
101
NM Rate / s-1
33
NM Rate / s
104
34
-1
108
MUDOS Kiel NM
35
(dH*(10)/dt)µ / (nSv/h)
36
rel. Deviation / %
rel. Deviation / %
(dH*(10)/dt)µ / (nSv/h)
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
2002
2003
(b)
2002
2003
Fig. 8. For the period from March 2002 to February 2003, the monthly averages of H˙ ∗ (10; p0 ); mon (•) compared to the monthly averages of the Kiel neutron monitor rate ( ) are displayed. The uncertainties of H˙ ∗ (10; p0 ); mon are the 1 variations within one month. Left Egure: the uncorrected MUDOS data are shown. Right Egure: the MUDOS date were corrected according to the relative deviations of the Kiel Neutron Monitor (NM). The relative deviations from the yearly average are shown at the bottom of each Egure. The solid line in the right bottom Egure is Eq. (33) with the parameters as given in (35).
the minimum in August. A comparison with the Kiel neutron monitor data ( ) is not very satisfactory although the minimum in August is also visible. The relative deviations displayed in the lower part of Fig. 8 are based on the 1-year average between March 2002 and February 2003 which is nSv H˙ ∗ (10; p0 ); yr = (32:7 ± 3:7) : (26) h The standard uncertainty is obtained from the 1 standard deviation of the data plotted in Fig. 8 (left upper Egure), the standard uncertainty of the TEPC calibration factor of (16) and the uncertainty of the TEPC/CACS coincidence eJciency given in (8). This result of (26) may be compared with the outdoor muon energy dose rate as measured with a Ge detector (Clouvas et al., 2003). Clouvas et al. (2003) have identiEed muons by their energy deposition in the Ge detector. From the measured energy deposition the dose rate in the ICRU sphere (ICRU, 1994) was determined with the aid of MonteCarlo simulations. The quoted result of D˙ Ge = 25 nGy=h can easily be transferred to equivalent dose rate because the radiation weighting factor for muons, i.e. for low-LET radiation, is equal to 1. Therefore, the result to compare with is H˙ Ge = 25 nSv=h. The measurements were made in Thessaloniki, in the northern part of Greece (40◦ 31 N, 22◦ 58 E) for which a cuto? rigidity of approximately 7:1 GV is valid. During the measurements no air pressure was recorded. Thus, no pressure correction was applied. According to (5) and (6) a Duence rate corresponding to about 38% of the muon rate must be attributed to the soft component. From this an estimate of the total dose equivalent rate due to the
charged component of the SCR gives 34:5 nSv=h for the results of Clouvas et al. (2003). This is in reasonable agreement with the MUDOS value of (26), although the di?erent values of the vertical cuto? rigidity were not taken into account. One would expect a smaller value at latitudes closer to the equator. 7. Seasonal variation The seasonal variation of the muon Dux has already been described in great detail in the early 50’s by Barrett (Barrett et al., 1952). There the variation of muons detected deep underground was investigated. These muons are very energetic with energies above 1 TeV. It was clearly demonstrated in Barrett et al. (1952) and with the most recent experimental proofs in Ambrosio et al. (1997, 2002) that a positive correlation with the temperature changes in the upper layers of the atmosphere exists. The net e?ect on the muon count rate is dominated by the interplay between meson absorption and decay (Barrett et al., 1952). At sea level, this e?ect is negligible and the muon decay dominates the variations of the muon rate as explained by Blackett (1938). An increase in the atmospheric temperature leads to a rise of the atmospheric layer in which muon production takes place. This in turn means an increase in Dight path down to ground level. More muons can therefore decay before they reach ground level. This behaviour is expressed by the survival probability, which describes the probability P(h0 ) of a particle traversing a certain distance h0 before it decays, P(h0 ) = e−h0 m0 = P c ;
(27)
102
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
where m0 =105:66 MeV is the muon rest mass, =2:20 s the muon mean lifetime and P the muon momentum in GeV=c. On the assumption that the altitude variation Rh is small compared to the entire Dight path, the exponential in (27) can be expanded and the relative di?erence of the survival probabilities can be written as P(h0 + Rh) − P(h0 ) m0 Rh =− : P(h0 ) P c
(28)
For a static isothermal atmosphere, the particle density n(h) = n(h0 ) · e−h=hs
(29)
depends on the altitude h and the scale height hs = kT=Mg, where k is the Boltzmann constant, T the temperature, M the molar mass of the atmosphere and g the gravitational acceleration at sea level. An increase in the temperature in a certain layer will cause a rise in altitude. On the assumption that the density remains constant, it follows from (29) that Rh = h0
RT : T0
(30)
Inserting this into (28) leads to P(h0 + Rh) − P(h0 ) m0 h0 RTi RI =− ; = P(h0 ) Iyr P c Tyr
(31)
where RI denotes the change in the muon Duence rate, Iyr the annual average muon Duence rate, Tyr the annual average of the layer temperature Ti and RTi its deviation. It was also assumed that the ratio of the survival probabilities is directly reDected in the ratio of the muon Duence rates. Thus, Eq. (31) gives an explicit relation between the muon Duence rate and the temperature changes in the atmospheric layer where the muons are created. Since the variations are rather small, the inDuence of the primary cosmic radiation has also to be included. This can be done via the neutron count rate at ground level. As mentioned above, the count rate of the Kiel neutron monitor (NM) does not exactly agree with the behaviour of the MUDOS rate since the NM rate directly reDects the changes in the Dux of the primary spectrum. Therefore, the muon Duence rate at ground level will also be a?ected. Using the NM rate, the MUDOS data can be corrected according to kNM =
1 ; 1 + -NM
(32)
with -NM being the relative deviations as plotted in Fig. 8 ( ). After applying this NM correction, the monthly averages of MUDOS and their relative deviations lead to the data shown in the right plot of Fig. 8. The behaviour of the relative deviations of the NM corrected monthly averages from the 1-year average can be parameterised as (Ambrosio et al., 1997, 2002) ˙∗
RH (10; p0 )mon = Ayr cos(2(tm − m )); H˙ ∗ (10); yr
(33)
where RH˙ ∗ (10; p0 )mon = H˙ ∗ (10; p0 ); mon − H˙ ∗ (10; p0 ); yr ; (34) Ayr is the variation amplitude, tm the time in months divided by 12 since January 1st, 2002, and the phase shift m also given in the same units, respectively. The solid line in Fig. 8 (right side, bottom plot) is the function given in (33) adjusted to measured data. The values as obtained from a minimum '2 procedure are Ayr = (1:55 ± 0:61)%;
m = (0:096 ± 0:061):
(35)
2 The standard uncertainties were obtained from the 'min +1 boundary and denote the 1 standard uncertainties of the parameters.
8. Temperature dependence The atmospheric temperature proEles have been supplied by the World Data Center for Remote Sensing of the Atmosphere (WDC, 2003) and processed in order to obtain the atmospheric temperature distributions above Braunschweig for each day of the period under consideration (Schroedter, 2003; Li et al., 2000). According to Ambrosio et al. (1997), the e?ective temperature was evaluated as T (Xi )[e−Xi =1 − e−Xi =1N ]=Xi Te? = i −X =1 ; (36) i − e−Xi =1N ]=Xi i [e where 1 = 160 g=cm2 and 1N = 120 g=cm2 are the atmospheric attenuation lengths for pions and nucleons, respectively, and Xi the atmospheric depth (in the units g=cm2 ) of the ith layer. Data from atmospheric layers at equal pressure, i.e. at 1000, 850, 700, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30 and 10 hPa, have been used (Fig. 9). In Table 2 the monthly averages of Te? from March 2002 to February 2003 are tabulated and their relative deviations plotted in Fig. 10 in comparison with the relative deviations measured with MUDOS as shown in Fig. 8 (right Egure, bottom plot). There is remarkable agreement in the behaviour of the MUDOS data and the e?ective temperature. In accordance with (31), i.e. RI RT = − ; Iyr Tyr
(37)
the relative deviations of MUDOS are plotted vs. the relative deviations of Te? in Fig. 11. The solid line is the result of a '2 minimisation procedure leading to = 0:51 ± 0:21
(38)
from which the temperature coeJcient is evaluated at T =
10−3 = (2:3 ± 1:0) : Tyr K
(39)
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
Teff July 2002 January 2003 Mar02-Feb03 Avg.
30000
Altitude / m
25000 20000
4 MUDOS corr. rel. Deviation / %
35000
103
2 0 -2
15000 -4 10000 6 5000
2 300
0 -2
Fig. 9. Shown are the atmospheric temperature distributions along the altitude for July 2002 (dashed line) and January 2003 (dotted line) and the 1-year average of the entire period (solid line). The pressure levels have been converted into altitude. The corresponding e?ective temperatures Te? are indicated by the vertical lines.
Month
Te? (Xi )
Rel. deviation/%
March 02 April 02 May 02 June 02 July 02 August 02 September 02 October 02 November 02 December 02 January 03 February 03
217:76 ± 0:63 220:09 ± 0:73 221:42 ± 0:67 224:34 ± 0:69 225:67 ± 0:53 224:11 ± 0:67 220:80 ± 0:70 217:91 ± 0:88 213:99 ± 1:62 209:42 ± 3:39 214:94 ± 3:95 213:69 ± 2:24
−0:42 ± 0:29 0:65 ± 0:33 1:26 ± 0:31 2:59 ± 0:31 3:20 ± 0:24 2:49 ± 0:31 0:97 ± 0:32 −0:35 ± 0:40 −2:15 ± 0:74 −4:23 ± 1:55 −1:71 ± 1:81 −2:28 ± 1:02
The absolute temperatures at di?erent atmospheric depths were obtained from WDC (2003), Schroedter (2003), Li et al. (2000) for each day. The last column shows the relative deviations of the monthly averages from the annual average Tyr = (218:7 ± 4:8) K.
In Fig. 10 (bottom part), the dashed line represents the function given in (33) adjusted to the MUDOS data (see (35) for the parameters) and divided by (−) according to (37) and (38). There is excellent agreement between the relative deviations of the e?ective temperature and the muon rate at ground level, and the assumption that this e?ect is due to the muon decay has been proven. Using (30) and (37), the rise in altitude of the muon production layer can be estimated. The approximated altitude of maximum muon production is h0 = 12 km (Grieder, 2001;
2002
Feb
Jan
Dec
Oct
Nov
Sep
Jul
Mar
-6
2003
Fig. 10. For the period from March 2002 to February 2003, the relative deviations from the yearly average of the NM corrected MUDOS results (top Egure, •) compared to the relative deviations from the yearly average of the e?ective temperature (bottom Egure, ). The solid line in the upper part corresponds to (33) with the parameters given in (35). The dashed line in the bottom part is the same function but divided by (−) according to (37) and (38).
4
(∆Hµ / Hyr) / %
Table 2 The monthly averages of the e?ective temperature Te? of the atmosphere as deEned in (36)
Teff
-4
Aug
280
Jun
240 260 Temperature / K
Apr
220
May
0 200
4
2
0
-2
-4 -6
-4
-2 0 2 (∆Teff / Tyr) / %
4
6
Fig. 11. The measured relative deviations from MUDOS versus the relative deviations of the e?ective temperatures Te? . The solid line is the result of a linear function adjusted to the data.
104
F. Wissmann et al. / Radiation Measurements 39 (2005) 95 – 104
Poirier et al., 2002) which leads to a rise of the corresponding layer between winter and summer of Rhmax ≈ 750 m:
(40)
9. Summary After the Erst year of monitoring the SCR at the PTB reference site, the ambient dose equivalent rate H˙ ∗ (10) of the charged component of the SCR was determined. This result is of importance since the traceability of the TEPC system used is given by its calibration in the PTB reference Eeld for high energy -radiation. The detailed investigation of the SCR with MUDOS demonstrates the inDuence of air pressure, the solar activity and the e?ective temperature of the entire atmosphere. It could be shown that variations of up to 15% are possible. The seasonal variations also prove that MUDOS detects cosmic ray muons since this e?ect is caused by the temperature variations of the atmosphere leading to altitude changes for the muon production layer. Acknowledgements The authors appreciate the intense work of J. Kretzer, F. Langner and J. Roth (all PTB), who are responsible for the development of detector systems, data acquisition software and optimisation of the infrastructure. Especially their continuous e?ort to keep the measurements running was the basis for such long term measurements as presented in this work. Many thanks to R. Behrens (PTB) who maintains the 6:6 MeV -reference Eeld and the sta? of the PTB Department 6.4 for preparing excellent proton beams. The development of the mobile TEPC/CACS system is supported by the European Commission contract FIGM-CT-2000-00068 Dosimetry of Aircrew Exposure to Radiation During Solar Maximum (DOSMAX). Our gratitude also belongs to M. Schroedter (German Aerospace Center, DLR) who furnished the atmospheric temperature distributions above Braunschweig. References Ambrosio, M., et al., 1997. Seasonal variations in the underground muon intensity as seen by MACRO. Astropart. Phys. 7, 109. Ambrosio, M., et al., 2002. The MACRO detector at Gran Sasso. Nucl. Instrum. Methods A 486, 663. Barrett, P.H., et al., 1952. Interpretation of cosmic-ray measurements far underground. Rev. Mod. Phys. 24, 133. Berger, M.J., Coursey, J.S., Zucker, M.A., 2003. ESTAR, PSTAR and ASTAR: Computer Programs for Calculating Stopping-Power and Range Tables for Electrons, Protons, and Helium Ions. National Institute of Standards and Technology,
Gaithersburg, MD, USA. Available via http://physics. nist.gov/Star; Blackett, P.M.S., 1938. On the instability of the barytron and the temperature e?ect of cosmic rays. Phys. Rev. 54, 973. BSuermann, L., Guldbakke, S., Kramer, H.-M., 1999. Calibration of personal and area dosimeters in high-energy photon Eelds. PTB-Bericht PTB-Dos-32, 1999, Braunschweig. CERN, 2003. The program package CERNlib is accessible via http://www.cern.ch. Clouvas, A., Xanthos, S., Antonopoulos-Domis, M., Silva, J., 2003. Measurements with a Ge detector and Monte Carlo computations of dose rate yields due to cosmic muons. Health Phys. 84, 212. Gerdung, S., Pihet, P., Grindborg, J.E., Roos, H., Schrewe, U.J., Schuhmacher, H., 1995. Operation and application of tissue-equivalent proportional counters. Radiat. Prot. Dosim. 61, 381. Grieder, P.K.F., 2001. Cosmic Rays at Earth. Elsevier Science, Amsterdam. Groom, D.E., Mokhov, N.V., Striganov, S.I., 2001. At. Data Nucl. Data Tables 78, 183. Available via http://pdg.lbl.gov/ AtomicNuclearProperties. Hagiwara, K., et al., 2002. Phys. Rev. D 66, 010001. Review of Particle Physics, Particle Data Group, http://www-pdg. lbl.gov. ICRP, 1991. International Commission on Radiological Protection, 1991. Recommendations of the International Commission on Radiological Protection. ICRP Publication 60, Pergamon Press, Oxford. ICRU, 1994. International Commission on Radiation Units and Measurements. -Ray Spectrometry in the Environment. ICRU Report 53. Kiel, 2003. The Kiel neutron monitor data can be accessed via http://134.245.132.179/Kiel/main.htm. Li, J., et al., 2000. Global soundings of the atmosphere from ATOVS measurements: the algorithm and validation. J. Appl. Meteor. 39, 1248. Poirier, J., Roesler, S., Fasso, A., 2002. Distribution of secondary muons at sea level from cosmic gamma rays below 10 TeV. Astropart. Phys. 17, 441. Rossi, H.H., Zaider, M., 1996. Microdosimetry and its Applications. Springer, Berlin, Heidelberg. Schrewe, U., 2000. Global measurements of the radiation exposure of civil air crew from 1997 to 1999. Radiat. Prot. Dosim. 91, 347. Schroedter, M., 2003. German Aerospace Center (DLR), D-82234 Wessling, Germany. Private communication. Smart, D.F., Shea, M.A., 1997. Proceedings of the 25th International Cosmic Ray Conference, Contributed Papers 2, 401. SRIM, 2003. The program SRIM 2003 can be obtained via http://www.srim.org. UNSCEAR, 2000. United Nations ScientiEc Committee on the E?ects of Atomic Radiation, Sources and E?ects of Ionizing Radiation. UNSCEAR 2000. Report to the General Assembly, Vol. I: Sources. Accessible via http://www.unscear.org. WDC, 2003. ICSU World Data Center for Remote Sensing of the Atmosphere. http://wdc.dlr.de. Wissmann, F., 2003a. To be published. Wissmann, F., 2003b. To be published.