- Email: [email protected]
Large vessel imaging using cosmic-ray muons
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
Large vessel imaging using cosmic-ray muons P.M. Jenneson* School of Physical Sciences and Electronics, University of Surrey, Guildford, Surrey GU2 7XH, UK
Abstract Cosmic-ray muons are assessed for their practical use in the tomographic imaging of the internal composition of large vessels over 2 m in diameter. The technique is based on the attenuation and scattering of cosmic-ray muons passing through a vessel and has advantages over photon-based methods of tomography that it is extendable to object containing high-density materials over many tens of metres. The main disadvantage is the length of time required to produce images of sufficient resolution and hence cosmic ray muon tomography will be most suited to the imaging of large structures whose internal composition is effectively static for the duration of the imaging period. Simulation and theoretical results are presented here which demonstrate the feasibility of cosmic ray muon tomography. r 2004 Elsevier B.V. All rights reserved. PACS: 13.85.Tp; 81.70.Tx; 95.55.Vj Keywords: Cosmic rays; Muons; Large vessels; Tomography
1. Introduction Imaging the contents of large vessels ðdiameter > 2 mÞ is of significant interest to many industries where storage or long-term structural integrity is an important consideration. The internal structure of large vessels may contain unknown materials or be inaccessible and therefore non-destructive evaluation prior to manual inspection may be an important issue.
2. Photon imaging It is well known that energetic photons can produce excellent images for diagnostic purposes [1,2]. However, it may be shown that this is *Fax: +44-1483-686781. E-mail address: [email protected] (P.M. Jenneson).
generally only possible for vessels of up to a maximum of 2 m in diameter [3]. This is due to several considerations. The noise propagated in a tomographic reconstructed image, due to the finite photon count, n per ray-sum, using the Nyquist angular sampling criterion for filtered back projection is Dm ¼ k
2p nDt
1=2 ð1Þ
where t is the spacing between ray-sums, D is the diameter of reconstruction, and k a weighting factor dependent on the Fourier reconstruction filtered used (k ¼ 0:289 for a Bracewell filter). The total run-time, T for a complete tomographic acquisition T ¼ 8pnN 4
0168-9002/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2004.03.093
sinhðmDÞ mDA
ð2Þ
ARTICLE IN PRESS P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
Dm D sinhðmDÞ 1=2 ¼ 4pkN 2 : m tTAðmDÞ3
ð3Þ
1.E+01 1.E+00 1.E-01
Distance (m)
where A is the source activity, and N N is the number of pixels used for reconstruction. By combining Eqs. (1) and (2) an additional relationship emerges,
347
1.E-02 1.E-03
water glass lead
1.E-04 1.E-05 1.E-06
If all the geometrical factors, the total run-time and the source intensity are fixed, the accuracy depends on the ‘‘sensitivity factor’’ ½sinhðmDÞ=ðmDÞ3 1=2 : Fig. 1 shows the plot of ‘‘sensitivity factor’’ versus the diameter of the object expressed in mean free paths. This shows the optimum energy for imaging is between one and six radiation mean free path lengths, optimized at three mean free paths [2]. Using the interaction cross-section data of Berger and Hubbell [4] for three different materials, water, glass, and lead we can plot the distance for three mean free paths in each of these for energies up to 100 GeV; see Fig. 2. This shows that, even for low Z materials, photons can only be used to image objects up to 2 m in diameter. This is due to an increase in the pair-production cross-section as the photon energy is increased, which limits its range.
[sinh(D)/(D)3]1/2
10
1
1.E-07 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05
Energy (MeV)
Fig. 2. Plot of three mean free paths lengths for a range of photon energies for water, glass and lead.
3. Charged particle imaging Charged particles such as electrons, protons and ions are not limited by the same physical restrictions as photons as they lose energy continuously in matter through a number of discrete interactions. This implies that increasing their initial energy will increase their range in matter. 3.1. Electrons Electrons are also limited in range and are unable to penetrate very far into matter. This is due to the high-momentum transfers that occur as the incoming electrons interact with the atomic electrons. Even with electron energies as high as 1 GeV; the range in water is 1 m; but for lead is still only a few centimetres [5], see Fig. 3. Betatrons are the most portable source of high-energy electrons but are currently only available with energies of up to 10 MeV: 3.2. Ions
0.1 0
1
2
3
4
5 D
6
7
8
9
10
Fig. 1. Plot of the ‘‘sensitivity factor’’ ½sinhðmDÞ=ðmDÞ3 1=2 ; mD is the object diameter expressed in mean free paths.
Protons and heavier ions undergo many collisions as they traverse matter. Conservation of energy and momentum for a head on collision of an ion of mass mi and kinetic energy T with an electron mass me results in the following change of
ARTICLE IN PRESS P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
348
kinetic energy of the ion: 4me DT ¼ T mi
ð4Þ
which results in a proton of 1 GeV losing 2:18 MeV per collision, thus the minimum number of collisions a proton undergoes before coming to rest is about 500. The range of protons in water, glass and lead is shown in Fig. 4 for a range of energies up to 10 GeV and demonstrates the imaging potential of protons as the range increases with energy even through several metres of lead [7]. Protons could be used for radiographically or tomographically imaging large vessels and imaging has been performed at the Los Alamos Nuclear 1.E+01
Distance (m)
1.E+00 1.E-01
1.E-02 water glass lead
1.E-03 1.E-04 1.E-05 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Energy (MeV)
Fig. 3. The range of electrons in water, glass and lead as predicted by the continuously slowing down approximation, data generated by ESTAR [6].
Science Center using a 800 MeV proton beam [9]. The generation of high-energy protons requires large, expensive and immovable facilities, thus they are only practicable for portable objects. If the object of interest is immovable a more convenient source of radiation must be found.
4. Cosmic-ray radiation Primary cosmic rays consist of particles such as protons, alpha particles and occasionally heavier particles that are accelerated through space to energies in excess of many TeV. Each primary cosmic-ray particle results in the formation of a shower of thousands of secondary cosmic rays. At sea level, this shower is around 1 km in diameter and 1 m thick. The primary components of the secondary cosmic radiation shower at sea level are muons, electrons, neutrons and gamma rays [10]. Pions are unstable particles with a short lifetime of 26 ns; and are not observed very frequently at sea level. Muons, however, have a longer lifetime of 2:2 ms: Consequently, due to relativistic time dilation, the muon flux at sea level is approximately 40 particles/s=m2 : A muon is essentially a ‘‘heavy electron’’ with a mass of 207me ; where me is the rest mass of the electron. The muon also carries a single negative charge. Secondary cosmicray muons exist over a wide range of energies at sea level [11], as shown in Fig. 5. 1.E-03
Muon Intensity (cm-2 sec str GeV)
1.E+02 1.E+01
Distance (m)
1.E+00 1.E-01 1.E-02 1.E-03
water glass lead
1.E-04 1.E-05 1.E-06 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
Energy (MeV)
Fig. 4. The range of protons in water, glass and lead as predicted by the continuously slowing down approximation, data generated by PSTAR [8].
1.E-04 1.E-05
0°
10°
20°
30°
40°
50°
60°
70°
80°
1.E-06 increasing zenith angle 1.E-07 1.E-08 1.E-09 1.E-10 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Energy (GeV)
Fig. 5. Cosmic-ray muon energy spectra for different zenith angles.
ARTICLE IN PRESS P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
At high zenith angles the muon flux is hardened by the atmosphere, but falls by a factor of a thousand in intensity. At these high zenith angles, the cos2 ðyÞ muon flux intensity commonly attributed to the intensity variation with zenith angle, is offset by a measurable flux of muons arriving at the azimuthal angle.
The energy loss of the muon caused by the ionization of matter can be expressed by the Bethe–Bloche equation [12] dE Z 1 1 2me c2 b2 g2 Tmax d 2 ¼ Kz2 ln b dx A b2 2 2 I2 ð5Þ 2me c2 b2 g2 1 þ 2gme =M þ ðme =MÞ2
where p is the momentum of the muon, x is the distance travelled through the absorber and X0 is the radiation length. The root mean square lateral displacement, r0 is approximated by the following: x r0 ¼ pffiffiffi y0 : 3
ð8Þ
Both ionization and scattering of muons can be used to form a radiographic image of the absorber.
4.1. Muon ionization interactions
Tmax ¼
349
ð6Þ
where Z=A is the ratio of charge number over mass number of the absorber, z is the charge of the ionizing particle, M is the mass of the ionizing particle, me c2 is the mass energy of the electron, I is the mean excitation energy of the absorber, g is E=me c2 ; b2 is 1 ð1=g2 Þ; d is the density effect function and K=A is a constant ð0:3 MeV=g cm2 Þ: The ionization can be considered as a continuous energy loss process. Using the Bethe–Bloche equation we can calculate the ionization caused in a Na(Tl) scintillator in a single interaction by a 10 GeV muon as being, dE=dx ¼ 6:8 MeV=g cm2 ; which is an easily detectable signal. 4.2. Muon scattering interactions At each interaction point, as well as losing energy, the incoming muon is scattered. This is mostly from interactions with the atomic electrons, but the muons occasionally interact with the atomic nucleus and either undergo large angle scattering or are captured. The root mean square scattering angle can be described by the Moliere multiple scattering formula [12] rffiffiffiffiffiffi 13:6 MeV x x z y0 ¼ 1 þ 0:0038 ln ð7Þ bcp X0 X0
5. Cosmic-ray muon imaging Cosmic-ray muons have been previously used to radiographically image a number of large-scale objects. The earliest work was reported by George [13] in 1955, who imaged the overburden of a tunnel using vertical muon attenuation. He imaged the over lying topology of the tunnel and produced the first muon radiograph. The most notable work in the field was conducted by Alvarez [14] in 1970. Alvarez imaged Cephren’s pyramid at Giza with the aim of locating a hidden Queen’s chamber. It is often reported that the work was a failure. Quite the opposite is true and Alvarez conclusively proved that there was no Queen’s chamber, a result which has subsequently been proven. This work used a spark chamber and detected perturbations in the near azimuthal cosmic-ray flux. Nagamine used cosmic rays to investigate volcanoes with the aim of predicting eruptions [11]. This work has shown that cosmic-ray muon tomography is viable for imaging very large structures, up to 20 km in size. Given the enormous size of such a structure the typical imaging time was reported as being 800 h: Here large pieces of plastic scintillator were used each with four photomulitplier tubes to act as a largescale position sensitive detector. Recently Borozdin et al. at Los Almos [15] showed the feasibility of using muon scattering radiography to detect uranium/plutonium contraband in trucks. The work here differed from previous work as they measured the scattering of muons rather than the simple attenuation of muon flux, as had been previously used.
ARTICLE IN PRESS 350
P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
All of the techniques above describe simple radiography of the large structures of interest. It is a relatively simple task to take multiple radiographs at different projection angles and extend these radiographic techniques into a full tomographic system, if desired.
6. Cosmic-ray muon tomography Cosmic-ray muon tomography is inherently a slow process as the intensity variation with zenith angle is cos2 ðyÞ dependent. It is proposed therefore to use near azimuthal angles ð60280 from the zenith) to obtain sufficient muon flux to allow reasonable imaging times and ensure the local topology does not affect the results. The primary issue with using muons as a radiographic source is the determination of their incoming direction. It is proposed that two pixellated detectors be used to determine the presence of a muon with a vector than traverses the object. Two subsequent pixellated detectors are used to detect whether the muon has passed through the object or has been attenuated [16], see Fig. 6. The four detectors are run in a timing coincidence modality to ensure that muons which do not pass through the object are rejected. Each radiograph will have to be collected over a large period of time to ensure that the cosmic-ray muon
spectra is sufficiently sampled for each ray sum in the projection. The system can be further adapted to include energy measurement at each pixel further increasing the useful information collected. If the detector system is able to resolve the energy loss of the muon as it passes through the imaging object this energy loss can then be used for reconstructing the internal structure of the object. The final proposed tomographic system is based on the scattering of muons as they pass through the imaging object. If the momentum vector of the muon can be determined before and after it passes through the object then scattering information can be inferred relating to the atomic number of the internal structure of the object.
7. Conclusions It is proposed to use cosmic-ray muon tomography to image large vessels or other large engineering structures which are too large to be imaged by photons or other methods (i.e. between 5 m and 20 km in diameter). The technique is both non-invasive, quantitative and uses naturally occurring radiation. The technique is slow at near azimuthal angles and not suitable for imaging structures whose internal structure is changing within these long imaging times. Muon radiography can be used in two modes, ionization attenuation radiography and scattering radiography, both of these methods can be extended into a fully tomographic imaging system.
References
Fig. 6. A muon attenuation CT system.
[1] R.D. Luggar, E.J. Morton, P.M. Jenneson, M.J. Key, Radiat. Phys. Chem. 61 (2001) 785. [2] W.B. Gilboy, Nucl. Instr. and Meth. 221 (1984) 193. [3] P. Burstein, P.J. Bjorkholm, R.C. Chase, F.H. Seguin, Nucl. Instr. and Meth. 221 (1984) 207. [4] M.J. Berger, J.H. Hubbell, XCOM: photon cross section on a personal computer, NBSIR 87-3597, 1987. http:// physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html. [5] ICRU, International Commission on Radiation Units and Measurements. ICRU Report 37, Stopping Powers for Electrons and Positrons, 1984.
ARTICLE IN PRESS P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351 [6] M.J. Berger, J.S. Coursey, M.A. Zucker, ESTAR: Stopping Powers and Ranges for Electrons, 1998. http:// physics.nist.gov/PhysRefData/Star/Text/ESTAR.html. [7] ICRU, International Commission on Radiation Units and Measurements. ICRU Report 49, Stopping Powers and Ranges for Protons and Alpha Particles, 1993. [8] M.J. Berger, J.S. Coursey, M.A. Zucker, PSTAR: Stopping Powers and Ranges for Protons, 1998. http:// physics.nist.gov/PhysRefData/Star/Text/PSTAR.html. [9] N.S.P. King, et al., Nucl. Instr. and Meth. A 424 (1999) 84.
351
[10] T. Gaisser, Cosmic Rays and Particle Physics, Cambridge University Press, Cambridge, 1990, p. 71. [11] K. Nagamine, M. Iwasaki, K. Shimomura, K. Ishida, Nucl. Instr. and Meth. A 356 (1995) 585. [12] K. Haiwara, et al., Particle Data Group, Review of Particle Physics, Phys. Rev. D 66 (2002) 010001. [13] E.P. George, Commonw. Eng. (July 1955) 455. [14] L.W. Alvarez, et al., Science 167 (1970) 832. [15] K. Borozdin, et al., Nature 422 (2003) 277. [16] M. Key, M.Sc. Thesis, University of Surrey, 1994.
Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
Large vessel imaging using cosmic-ray muons P.M. Jenneson* School of Physical Sciences and Electronics, University of Surrey, Guildford, Surrey GU2 7XH, UK
Abstract Cosmic-ray muons are assessed for their practical use in the tomographic imaging of the internal composition of large vessels over 2 m in diameter. The technique is based on the attenuation and scattering of cosmic-ray muons passing through a vessel and has advantages over photon-based methods of tomography that it is extendable to object containing high-density materials over many tens of metres. The main disadvantage is the length of time required to produce images of sufficient resolution and hence cosmic ray muon tomography will be most suited to the imaging of large structures whose internal composition is effectively static for the duration of the imaging period. Simulation and theoretical results are presented here which demonstrate the feasibility of cosmic ray muon tomography. r 2004 Elsevier B.V. All rights reserved. PACS: 13.85.Tp; 81.70.Tx; 95.55.Vj Keywords: Cosmic rays; Muons; Large vessels; Tomography
1. Introduction Imaging the contents of large vessels ðdiameter > 2 mÞ is of significant interest to many industries where storage or long-term structural integrity is an important consideration. The internal structure of large vessels may contain unknown materials or be inaccessible and therefore non-destructive evaluation prior to manual inspection may be an important issue.
2. Photon imaging It is well known that energetic photons can produce excellent images for diagnostic purposes [1,2]. However, it may be shown that this is *Fax: +44-1483-686781. E-mail address: [email protected] (P.M. Jenneson).
generally only possible for vessels of up to a maximum of 2 m in diameter [3]. This is due to several considerations. The noise propagated in a tomographic reconstructed image, due to the finite photon count, n per ray-sum, using the Nyquist angular sampling criterion for filtered back projection is Dm ¼ k
2p nDt
1=2 ð1Þ
where t is the spacing between ray-sums, D is the diameter of reconstruction, and k a weighting factor dependent on the Fourier reconstruction filtered used (k ¼ 0:289 for a Bracewell filter). The total run-time, T for a complete tomographic acquisition T ¼ 8pnN 4
0168-9002/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2004.03.093
sinhðmDÞ mDA
ð2Þ
ARTICLE IN PRESS P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
Dm D sinhðmDÞ 1=2 ¼ 4pkN 2 : m tTAðmDÞ3
ð3Þ
1.E+01 1.E+00 1.E-01
Distance (m)
where A is the source activity, and N N is the number of pixels used for reconstruction. By combining Eqs. (1) and (2) an additional relationship emerges,
347
1.E-02 1.E-03
water glass lead
1.E-04 1.E-05 1.E-06
If all the geometrical factors, the total run-time and the source intensity are fixed, the accuracy depends on the ‘‘sensitivity factor’’ ½sinhðmDÞ=ðmDÞ3 1=2 : Fig. 1 shows the plot of ‘‘sensitivity factor’’ versus the diameter of the object expressed in mean free paths. This shows the optimum energy for imaging is between one and six radiation mean free path lengths, optimized at three mean free paths [2]. Using the interaction cross-section data of Berger and Hubbell [4] for three different materials, water, glass, and lead we can plot the distance for three mean free paths in each of these for energies up to 100 GeV; see Fig. 2. This shows that, even for low Z materials, photons can only be used to image objects up to 2 m in diameter. This is due to an increase in the pair-production cross-section as the photon energy is increased, which limits its range.
[sinh(D)/(D)3]1/2
10
1
1.E-07 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05
Energy (MeV)
Fig. 2. Plot of three mean free paths lengths for a range of photon energies for water, glass and lead.
3. Charged particle imaging Charged particles such as electrons, protons and ions are not limited by the same physical restrictions as photons as they lose energy continuously in matter through a number of discrete interactions. This implies that increasing their initial energy will increase their range in matter. 3.1. Electrons Electrons are also limited in range and are unable to penetrate very far into matter. This is due to the high-momentum transfers that occur as the incoming electrons interact with the atomic electrons. Even with electron energies as high as 1 GeV; the range in water is 1 m; but for lead is still only a few centimetres [5], see Fig. 3. Betatrons are the most portable source of high-energy electrons but are currently only available with energies of up to 10 MeV: 3.2. Ions
0.1 0
1
2
3
4
5 D
6
7
8
9
10
Fig. 1. Plot of the ‘‘sensitivity factor’’ ½sinhðmDÞ=ðmDÞ3 1=2 ; mD is the object diameter expressed in mean free paths.
Protons and heavier ions undergo many collisions as they traverse matter. Conservation of energy and momentum for a head on collision of an ion of mass mi and kinetic energy T with an electron mass me results in the following change of
ARTICLE IN PRESS P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
348
kinetic energy of the ion: 4me DT ¼ T mi
ð4Þ
which results in a proton of 1 GeV losing 2:18 MeV per collision, thus the minimum number of collisions a proton undergoes before coming to rest is about 500. The range of protons in water, glass and lead is shown in Fig. 4 for a range of energies up to 10 GeV and demonstrates the imaging potential of protons as the range increases with energy even through several metres of lead [7]. Protons could be used for radiographically or tomographically imaging large vessels and imaging has been performed at the Los Alamos Nuclear 1.E+01
Distance (m)
1.E+00 1.E-01
1.E-02 water glass lead
1.E-03 1.E-04 1.E-05 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Energy (MeV)
Fig. 3. The range of electrons in water, glass and lead as predicted by the continuously slowing down approximation, data generated by ESTAR [6].
Science Center using a 800 MeV proton beam [9]. The generation of high-energy protons requires large, expensive and immovable facilities, thus they are only practicable for portable objects. If the object of interest is immovable a more convenient source of radiation must be found.
4. Cosmic-ray radiation Primary cosmic rays consist of particles such as protons, alpha particles and occasionally heavier particles that are accelerated through space to energies in excess of many TeV. Each primary cosmic-ray particle results in the formation of a shower of thousands of secondary cosmic rays. At sea level, this shower is around 1 km in diameter and 1 m thick. The primary components of the secondary cosmic radiation shower at sea level are muons, electrons, neutrons and gamma rays [10]. Pions are unstable particles with a short lifetime of 26 ns; and are not observed very frequently at sea level. Muons, however, have a longer lifetime of 2:2 ms: Consequently, due to relativistic time dilation, the muon flux at sea level is approximately 40 particles/s=m2 : A muon is essentially a ‘‘heavy electron’’ with a mass of 207me ; where me is the rest mass of the electron. The muon also carries a single negative charge. Secondary cosmicray muons exist over a wide range of energies at sea level [11], as shown in Fig. 5. 1.E-03
Muon Intensity (cm-2 sec str GeV)
1.E+02 1.E+01
Distance (m)
1.E+00 1.E-01 1.E-02 1.E-03
water glass lead
1.E-04 1.E-05 1.E-06 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
Energy (MeV)
Fig. 4. The range of protons in water, glass and lead as predicted by the continuously slowing down approximation, data generated by PSTAR [8].
1.E-04 1.E-05
0°
10°
20°
30°
40°
50°
60°
70°
80°
1.E-06 increasing zenith angle 1.E-07 1.E-08 1.E-09 1.E-10 1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Energy (GeV)
Fig. 5. Cosmic-ray muon energy spectra for different zenith angles.
ARTICLE IN PRESS P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
At high zenith angles the muon flux is hardened by the atmosphere, but falls by a factor of a thousand in intensity. At these high zenith angles, the cos2 ðyÞ muon flux intensity commonly attributed to the intensity variation with zenith angle, is offset by a measurable flux of muons arriving at the azimuthal angle.
The energy loss of the muon caused by the ionization of matter can be expressed by the Bethe–Bloche equation [12] dE Z 1 1 2me c2 b2 g2 Tmax d 2 ¼ Kz2 ln b dx A b2 2 2 I2 ð5Þ 2me c2 b2 g2 1 þ 2gme =M þ ðme =MÞ2
where p is the momentum of the muon, x is the distance travelled through the absorber and X0 is the radiation length. The root mean square lateral displacement, r0 is approximated by the following: x r0 ¼ pffiffiffi y0 : 3
ð8Þ
Both ionization and scattering of muons can be used to form a radiographic image of the absorber.
4.1. Muon ionization interactions
Tmax ¼
349
ð6Þ
where Z=A is the ratio of charge number over mass number of the absorber, z is the charge of the ionizing particle, M is the mass of the ionizing particle, me c2 is the mass energy of the electron, I is the mean excitation energy of the absorber, g is E=me c2 ; b2 is 1 ð1=g2 Þ; d is the density effect function and K=A is a constant ð0:3 MeV=g cm2 Þ: The ionization can be considered as a continuous energy loss process. Using the Bethe–Bloche equation we can calculate the ionization caused in a Na(Tl) scintillator in a single interaction by a 10 GeV muon as being, dE=dx ¼ 6:8 MeV=g cm2 ; which is an easily detectable signal. 4.2. Muon scattering interactions At each interaction point, as well as losing energy, the incoming muon is scattered. This is mostly from interactions with the atomic electrons, but the muons occasionally interact with the atomic nucleus and either undergo large angle scattering or are captured. The root mean square scattering angle can be described by the Moliere multiple scattering formula [12] rffiffiffiffiffiffi 13:6 MeV x x z y0 ¼ 1 þ 0:0038 ln ð7Þ bcp X0 X0
5. Cosmic-ray muon imaging Cosmic-ray muons have been previously used to radiographically image a number of large-scale objects. The earliest work was reported by George [13] in 1955, who imaged the overburden of a tunnel using vertical muon attenuation. He imaged the over lying topology of the tunnel and produced the first muon radiograph. The most notable work in the field was conducted by Alvarez [14] in 1970. Alvarez imaged Cephren’s pyramid at Giza with the aim of locating a hidden Queen’s chamber. It is often reported that the work was a failure. Quite the opposite is true and Alvarez conclusively proved that there was no Queen’s chamber, a result which has subsequently been proven. This work used a spark chamber and detected perturbations in the near azimuthal cosmic-ray flux. Nagamine used cosmic rays to investigate volcanoes with the aim of predicting eruptions [11]. This work has shown that cosmic-ray muon tomography is viable for imaging very large structures, up to 20 km in size. Given the enormous size of such a structure the typical imaging time was reported as being 800 h: Here large pieces of plastic scintillator were used each with four photomulitplier tubes to act as a largescale position sensitive detector. Recently Borozdin et al. at Los Almos [15] showed the feasibility of using muon scattering radiography to detect uranium/plutonium contraband in trucks. The work here differed from previous work as they measured the scattering of muons rather than the simple attenuation of muon flux, as had been previously used.
ARTICLE IN PRESS 350
P.M. Jenneson / Nuclear Instruments and Methods in Physics Research A 525 (2004) 346–351
All of the techniques above describe simple radiography of the large structures of interest. It is a relatively simple task to take multiple radiographs at different projection angles and extend these radiographic techniques into a full tomographic system, if desired.
6. Cosmic-ray muon tomography Cosmic-ray muon tomography is inherently a slow process as the intensity variation with zenith angle is cos2 ðyÞ dependent. It is proposed therefore to use near azimuthal angles ð60280 from the zenith) to obtain sufficient muon flux to allow reasonable imaging times and ensure the local topology does not affect the results. The primary issue with using muons as a radiographic source is the determination of their incoming direction. It is proposed that two pixellated detectors be used to determine the presence of a muon with a vector than traverses the object. Two subsequent pixellated detectors are used to detect whether the muon has passed through the object or has been attenuated [16], see Fig. 6. The four detectors are run in a timing coincidence modality to ensure that muons which do not pass through the object are rejected. Each radiograph will have to be collected over a large period of time to ensure that the cosmic-ray muon
spectra is sufficiently sampled for each ray sum in the projection. The system can be further adapted to include energy measurement at each pixel further increasing the useful information collected. If the detector system is able to resolve the energy loss of the muon as it passes through the imaging object this energy loss can then be used for reconstructing the internal structure of the object. The final proposed tomographic system is based on the scattering of muons as they pass through the imaging object. If the momentum vector of the muon can be determined before and after it passes through the object then scattering information can be inferred relating to the atomic number of the internal structure of the object.
7. Conclusions It is proposed to use cosmic-ray muon tomography to image large vessels or other large engineering structures which are too large to be imaged by photons or other methods (i.e. between 5 m and 20 km in diameter). The technique is both non-invasive, quantitative and uses naturally occurring radiation. The technique is slow at near azimuthal angles and not suitable for imaging structures whose internal structure is changing within these long imaging times. Muon radiography can be used in two modes, ionization attenuation radiography and scattering radiography, both of these methods can be extended into a fully tomographic imaging system.
References
Fig. 6. A muon attenuation CT system.
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