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A new generation γ-ray camera for planetary science applications: High pressure xenon time projection chamber
Advances in Space Research 37 (2006) 28–33 www.elsevier.com/locate/asr
A new generation c-ray camera for planetary science applications: High pressure xenon time projection chamber S. Kobayashi a,*, N. Hasebe a, T. Hosojima a, T. Igarashi a, M.-N. Kobayashi a, M. Mimura a, T. Miyachi a, M. Miyajima a, K.N. Pushkin a,b, H. Sakaba a, C. Tezuka a, T. Doke c, E. Shibamura d a
c
Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan b Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow 115409, Russia Kikuicho Branch, Advanced Research Institute for Science and Engineering, Waseda University, Kikuicho-17, Shinjuku, Tokyo 162-0044, Japan d Saitama Prefectural University, College of Health, Science, 820 Sannomiya, Koshigaya, Saitama 343-8540, Japan Received 1 November 2004; received in revised form 16 May 2005; accepted 29 May 2005
Abstract A new c-ray imaging camera based on High-pressure Xe Time-Projection-Chamber (HPXe-TPC) allows us to simultaneously determine arrival direction and its energy of individual incident c rays. HPXe-TPC is a promising c-ray detector for planetary science which provides means of global mapping of elemental composition in planetary surface as the remote sensing spectrometer. The simulation study by Geant4 and numerical calculation show that the angular resolution is mostly affected by multiple scattering of the recoil electron, and position resolution of electrodes of TPC. It is found that the angular resolution is 9° (50%) at 2 MeV for c rays. The feasibility of HPXe-TPC is discussed as a c-ray imaging camera for future planetary mission. Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: High-pressure xenon gas; Time-projection chamber; Planetary mission; c-ray camera
1. Introduction The main goal of planetary exploration is to understand the formation and evolution of planets. One of the approaches to answer basic questions regarding them is to measure the global elemental composition of the planet surfaces. Previous planetary and lunar missions so far have shown that a c-ray spectrometer is a powerful tool for the global mapping of the elemental composition (Laurence et al., 1998; Boynton et al., 2002). In the surface layer, the c rays are emitted from natural radioisotopes and nuclei which are excited by thermal or fast neutrons produced by the galactic cosmic-rays. By obtaining c-ray spectra in the energy range *
Corresponding author. Tel.:/fax: +81 3 5286 3897. E-mail address: [email protected] (S. Kobayashi).
of several MeV, we can derive elemental abundance of the surface layer, since the elements are identified by the characteristic c-ray energies. Planets and their satellites have many craters on their surface. It is important to investigate chemical composition inside and outside the craters with various radii, especially complex craters with the size greater than 15–20 km. Then, it is quite essential for nuclear c-ray spectroscopy to measure chemical composition in local regions together with the bulk composition of the planet. But in general, previous c-ray spectrometers carried on planetary missions so far are omnidirectional. Spatial resolution of a c-ray spectrometer is not so good as that of X-ray, visible, UV, or IR cameras because of the high penetrability of MeV c rays. It is obvious that the development of the c-ray spectrometer with the capability to resolve the arrival direction of incident c rays is very
0273-1177/$30 Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.05.106
S. Kobayashi et al. / Advances in Space Research 37 (2006) 28–33
essential. Here, we propose a new approach of remote sensing technology based on nuclear spectroscopy for planetary science. The c-ray imaging can be realized by the use of a high-pressure Xe time-projection-chamber (HPXe-TPC). The new generation imaging camera we propose allows us to simultaneously determine the arrival direction and energy of each c-ray emitted form the planetary surface. We have calculated the Monte Carlo simulation of electron tracks in HPXe-TPC for the design, construction and performance of HPXe-TPC. In this report, we discuss the angular resolution of HPXe-TPC for planetary c-ray observation.
2. Spatial resolution in planetary and lunar missions c-ray spectrometers boarded so far on previous planetary and lunar missions did not resolve the arrival direction of incident c-ray and they are omnidirectional. Because of the high penetrability of MeV c rays, the incident direction is not easily determined by using a collimator. Thus, its spatial resolution is determined primarily by geometrical conditions of the orbiter altitude and planet size. The spatial resolution is calculated as a function of observing altitude in lunar mission and are shown in Fig. 1. The spatial resolutions are about 150 km both of Lunar Prospector mission (Hubbard et al., 1998) and future SELENE mission (Sasaki et al., 2003; Kobayashi et al., 2002a; Hasebe, 1999) orbiting at the altitude of 100 km. Let us consider the spatial resolution of the c-ray camera that is able to measure the arrival direction of an incident c-ray. The spatial resolutions of a c-ray camera with angular resolutions (50%) from 5° to 20° is shown in Fig. 1. We see that the use of the c-ray camera improves the spatial resolution dramatically. The higher the spatial resolution is the longer observation time is requested to decrease the statistical error. Hence, the prac-
Spatial resolution, 50% (km)
10000
1000 Field of View
100
20˚
Omnidirectional 15˚
10˚
5˚
10
1 10
100 Altitude (km)
1000
Fig. 1. Spatial resolution as a function of the altitude in Lunar orbit.
29
tical value of the spatial resolution is 15 km for a next generation c-ray camera, since the size of a complex crater described above is larger than 15–20 km in radius.
3. High-pressure xenon time projection chamber Recently, a time projection chamber (TPC) has been studied in the field of particle physics to measure the energy and momentum of elementary particles at accelerators. While a Compton telescope is used in the astrophysical researches to detect MeV c rays. The principle of a HPXe-TPC is based on these two technologies. Though the HPXe-TPC measures the Compton scattering as the Compton telescope does, the HPXe-TPC additionally measures the 3D trajectory of the recoil electron by the method used in TPC. It is the outstanding characteristic of HPXe-TPC since the measurement of the 3D trajectory allows the complete reconstruction of the arrival direction of c rays, which is impossible for the classical Compton telescope. To measure the 3D trajectory, liquid or solid materials are not adequate as the detection medium, since the range of the recoil electron is too short in the materials in liquid or solid. HPXeTPC uses high-pressure xenon gas with an appropriate density for the measurement of the 3D trajectory. Furthermore, the high atomic number of xenon is useful to increase the detection efficiency to c rays. It is also known that a c-ray spectrometer using high-pressure xenon gas has a good energy resolution (2% (FWHM) for 662 keV Kobayashi et al., 2002b; Dmitrenko et al., 2001) better than that of a NaI(Tl) scintillator, a high stability for radiation damage (Ulin et al., 1997) and a wide operating temperature (100 °C) (Kobayashi et al., 2002b). The design of HPXe-TPC and the reconstruction method of the arrival direction of c-ray is described in the following sections. 3.1. Design of the HPXe-TPC The HPXe-TPC consists of a tracker and an absorber as shown in Fig. 2. The tracker detects a Compton vertex and measures the 3D trajectory and energy of the recoil electron. The absorber stops the scattered c-ray due to the photoelectric effect and measures its energy and the interaction point. Both the tracker and absorber consist of a cathode, a position sensitive electrode (PSE), and photodiodes or avalanche photodiodes (PDs). The PDs detects the scintillation of xenon around 175 nm (Saito et al., 2002) to detect the c-ray incidence. The tracker and the absorber are filled with xenon gas. The pressure in the absorber (5 MPa) is larger than that in the tracker (1–3 MPa) to increase the efficiency of photoelectric absorption. When a c-ray arrives in the tracker, it is scattered by a xenon atom and generates a recoil electron. The recoil
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S. Kobayashi et al. / Advances in Space Research 37 (2006) 28–33
Fig. 3. Compton scattering and definition of angular resolution.
m 0 c2 m 0 c2 ; ð1Þ E 1 þ E2 E2 E1 m 0 c2 E 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; cos u ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ E21 þ 2m0 c2 E1 ðE1 þ E2 Þ E21 þ 2m0 c2 E1
cos h ¼ 1 þ
Fig. 2. Schematic drawing of a high-pressure xenon time projection chamber. The upper chamber is a tracker and the lower one is an absorber.
electron ionizes xenon gas along its trajectory. At the same time, scintillation light is generated and is detected with PDs. The signal from PDs is used to determine an arrival time t0 of the c-ray. The liberated electrons are swept by the electric field applied between the cathode and PSE toward the PSE keeping the shape of trajectory. The PSE measures a 2D trajectory of the recoil electron in the x–y plane. Furthermore, when the liberated electrons are collected by PSE at time t1, the time difference between t0 and t1 multiplied by the electron drift velocity in xenon gives the third coordinate, z. As a result, the 3D trajectory of the recoil electron is obtained. The position of the Compton interaction P1 is obtained from the 3D trajectory and the energy of the recoil electron E1 is measured with the signals of PSE. In the absorber, the scattered c-ray is detected and the energy E2 and position P2, where the interaction occurs, is obtained by the same method used in the tracker. Hence, the energies of recoil electron E1, scattered c ray E2, the initial direction of the recoil electron ~ e after the scattering and the scattered c-ray ! ~ g ¼ P1 P2 are obtained. 3.2. Reconstruction of the arrival direction of an incident c-ray The question is how to reconstruct the arrival direction of an incident c-ray by using the values of E1, E2, ~ e and ~ g in HPXe-TPC. Let us begin with the Compton kinematics. The recoil electron and scattered c-ray are produced in the direction ~ e and ~ g, with energies of E1 and E2, respectively, as shown in Fig. 3. Using the momentum and energy conservation laws, the scattering angles of the c-ray h and the recoil electron u are given by
ð2Þ where m0 is electron rest mass and c is the light velocity. In Eqs. (1) and (2), the recoil electron is presumed to be at rest before the scattering. From the h and ~ g, we can limit the arrival direction to the generatrices of the cone Sh whose axis is corresponding to the ~ g as shown in Fig. 3. Note that the Compton scattering occurs on the plane S0 formed by the vectors of ~ e and ~ g. Hence, the intersections of Sh and S0 are two candidates of the incident direction, but we can uniquely determine the direction due to the relation between u and ~ e. As the classical Compton telescope does not measure ~ e, it is only able to confine the arrival direction to the generatrices. Reconstructing at least three events of c-ray from the same direction, the classical Compton telescope makes the image of the static source. On the other hand, the HPXe-TPC can uniquely determine the arrival direction by measuring~ e and reconstructing an event of c-ray interaction.
4. The angular resolution of the HPXe-TPC The angular resolution of the HPXe-TPC is determined by the ambiguity due to (1) Energy resolution of HPXe-TPC for E1 and E2; DE1 and DE2. (2) Doppler broadening (DB); the validity of Eqs. (1) and (2). (3) Position resolution of PSE for ~ g; D~ gpos . (4) Multiple scattering of the recoil electron in xenon for ~ e; D~ emul . (5) Position resolution of PSE for ~ e; D~ epos . Next, each ambiguity is estimated.
S. Kobayashi et al. / Advances in Space Research 37 (2006) 28–33
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4.1. Energy resolution DE1 and DE2
emul and D~ epos 4.4. D~ etotal ; D~
We measure E1 and E2 to determine the arrival direction h using Eq. (1). The energy resolution of HPXeTPC affects the angular resolution. The angular resolution due to the energy resolution effect is calculated and shown in Fig. 4. In this calculation, the energy resolution of HPXe-TPC is assumed to be 2% in FWHM for 662 keV including the electric noise of the amplifier. The c-ray is supposed to be scattered with the mean angle which is derived from the differential cross section of Klein–Nishina formula, for instance, h = 55° and u = 33° at 1 MeV. The ambiguity by the effect of energy resolution is much smaller than that by DB described below.
We estimate the angular resolution attributed from the ambiguity of D~ e. First, assuming that the Compton scattering plane S0 is simply determined as ~ e ~ g, the angular resolution depends on the measurement error of ~ e, i.e. D~ e because D~ g is negligibly small. A HPXe-TPC recognizes that the incident single c-ray comes from the arc shown in Fig. 3. Let us define the angle of xmax. It is half of the angle between two end points of the arc. If the direction in which the recoil electron is scattered is determined with an angular accuracy of Dg shown in Fig. 3, the angular resolution Dxobs is expressed as tanðDgÞ Dxobs 6 Dxmax ¼ sin1 sin hsin tan1 . sinðh þ uÞ ð3Þ
4.2. Doppler broadening Eqs. (1) and (2) are derived in the classic Compton scattering that the recoil electron is initially at rest at the scattering. Thus, the reconstructed direction of a c-ray is deteriorated by the effect of Doppler Broadening (DB) (Zoglauer and Kanbach, 2003). The angular resolution of h only due to DB in xenon is calculated by Geant4.6.2 (Agostinelli et al., 2003) and the result is shown in Fig. 4. The effect of DB decreases with the c-ray energy, since the initial momentum of the electron relative to that of c-ray becomes smaller and less significant. The ambiguity by DB is 1.1° at 1 MeV. 4.3. D~ gpos
Doppler Broadening Energy resolution
1.5
Vacuum
Xe (0.06 g/cm3)
1 1 mm
Angular resolution 50%, (deg.)
The ambiguity D~ g is obviously small compared with the D~ e, because the mean free path of the scattered cray is generally a few tens cm and the position resolution of PSE is typically 1 mm.
The recoil electron is scattered through the multiple scattering process after its production and information of the initial direction is gradually lost. The electron trajectory in xenon at 0.06 g/cm3 is simulated by Geant4.6.2 to estimate the magnitude of the electron multiple scattering and is shown in Fig. 5. In this figure, 50 electrons with 1 MeV enter the xenon gas. We define a circular cone with an apex angle of 2Dgmul, where its axis corresponds to the initial direction of the electron and whose summit is placed at the incident point. In addition, we evaluate Dgmul from the radius of the base circle which contains 50% of incident electrons at the distance l from the incident point. The result is shown in Fig. 6. It shows that the incident direction for 1 MeV electron is determined with an error of Dgmul = 7°, at 1 mm from the initial point. The position resolution of the PSE also affects D~ e since the trajectory is measured using PSE for x, y axes. For simplicity, we assume that the position resolution rpos ispthe ffiffiffiffiffi same for the x, y and z directions. rpos is equal to d= 12 (Grupen, 1996), where d is the distance between strip electrodes of the PSE. When a line segment ~ l with a length of l is measured with a spatial resolution of rpos, the angle between the true ~ l and the observed line segment ~ lobs is
0.5
0
0
1
2 3 Gamma-ray energy (MeV)
4
5
Fig. 4. The ambiguity due to the Doppler broadening and energy resolution as a function of c-ray energy.
1 mm Fig. 5. Multiple scatterings of 1 MeV electrons in Xe at 0.06 g/cm3.
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S. Kobayashi et al. / Advances in Space Research 37 (2006) 28–33
increasing c-ray energy, since the recoil electron tends to penetrate straightly when the energy of the primary cray is large. Thus, it results in a small ambiguity of the direction of the recoil electron. We consider that d = 1 mm is reasonable, from the viewpoint of the fabrication and stability of the PSE. The angular resolution Dxobs is within 9° for a 2 MeV c-ray with 50% probability.
20 500 keV
∆η with 50% probability (deg.)
1 MeV 15 1.5 MeV 10
2 MeV
5. Discussion
3 MeV 5
5 MeV 7 MeV 10 MeV
0 0
1
2
3 4 Distance, l (mm)
5
6
Fig. 6. gmul with 50% probability as a function of l at 0.06 g/cm3.
Dgpos ðlÞ ¼
pffiffiffi d 2rpos ¼ pffiffiffi . l 6l
ð4Þ
The ambiguity Dgtotal of the 3D trajectory, including the effects of multiple scattering and position resolution, is given by 2
2
Dg2total ðlÞ ¼ Dgmul ðlÞ þ Dgpos ðlÞ .
ð5Þ
The error of Dgtotal is a function of l and this function has a local minimum, Dgmin. It means that there is an optimum value of l which minimizes the error when we measure the 3D trajectory. So, we adopt Dgmin as the ambiguity of Dgtotal. Assume that the c-ray with energy E is scattered with the most probable scattering angle as the same method in Section 4.1. Then, the values of E1, E2, h and u are determined. The effect of multiple scattering is calculated using the E1, and then Dgmin(E) is obtained from Eqs. (4) and (5). As a result, the ambiguity of Dxmax is calculated as shown in Fig. 7. The angular resolution decreases with
0.5mm 1.0mm 1.5mm
Angular resolution, 50% (deg.)
20
10
0 0
2
4 6 Gamma-ray energy (MeV)
8
10
Fig. 7. The angular resolution Dxmax as a function of c-ray energy.
From the Section 4, we can see that the effect of the ambiguity of ~ e is the most significant. So it is thought that the angular resolution of HPXe-TPC is mostly dominated by the multiple scattering and position resolution and is corresponding to the Dxmax. We obtained 9° for 2 MeV as the angular resolution. This values is equivalent to a spatial resolution of 16 km for Lunar observations from 100-km altitude. Therefore, spatial resolution of a HPXe-TPC will be improved by a factor of 10 for 2-MeV c rays in comparison to c-ray spectrometers used in previous missions. There are some difficulties to realize the HPXe-TPC as a tool for a planetary mission. One of the technical problems is the method of measuring the 3D trajectory of the recoil electrons. The number of liberated electrons due to the recoil electron is very few to measure the trajectory. Hence, electron multiplication is necessary in the high-pressure xenon gas. Nowadays, some researchers concentrate on this kind of problem for their purpose and succeeds in measuring the 3D trajectory of the recoil electron in Ar + C2H6 gas (Miuchi et al., 2004). The second problem is the method of measuring the scintillation light of xenon gas. We have measured the scintillation yield in Xe and Xe with some dopants to resolve the problem (Kobayashi et al., 2004). The third issue is the detection efficiency of HPXeTPC for c-ray. The density of xenon gas is approximately 10 times smaller than a solid state c-ray spectrometer. However, the sensitivity of HPXe-TPC may be higher than the omnidirectional c-ray spectrometer because it is possible for HPXe-TPC to discriminate cray background from the composite material of the orbiter. This high sensitivity and the high atomic number of xenon somewhat compensate the disadvantage in the detection efficiency. Further experimental research and simulation study on the sensitivity are necessary. We would like to emphasize that the HPXe-TPC is the only tool which has the potential to determine the arrival direction of incident c-ray.
6. Concluding remarks The c-ray spectrometers carried on the previous planetary missions could not measure the arrival direction of
S. Kobayashi et al. / Advances in Space Research 37 (2006) 28–33
an incident c-ray. The spatial resolution, however, is improved by a HPXe-TPC which measures the recoil electron and the scattered c-ray of a Compton scattering and reconstructs the arrival direction. The simulation results show that the angular resolution of the HPXe-TPC is mostly affected by the multiple scattering of a recoil electron and the position resolution of the electrode. The HPXe-TPC in lunar mission has a spatial resolution of 16 km for 2-MeV c-ray at 100-km altitude. It is concluded that a new generation MeV c-ray imaging camera clearly distinguish the arrival direction of the incident c-ray to improve the spatial resolution. The imaging camera based on HPXe-TPC will provide means of precise global mapping of various chemical composition as a remote sensing spectrometer in future missions. Acknowledgements This work is financially supported in part by Institute of Space and Astronautical Science (ISAS) in the Japan Aerospace Exploration Agency (JAXA), the Tokyo Electric Power Company, and Scientific Research Grant-in-Aid from JSPS. This work is partly supported by a Grant-in-Aid for The 21st Century COE Program at Waseda University from the MEXT. References Agostinelli, S. et al. GEANT4 – a simulation toolkit. Nucl. Instrum. Meth. A506, 250–303, 2003. Boynton, W.V.24 colleagues Distribution of hydrogen in the near surface of Mars: evidence for subsurface ice deposits. Science 297, 81–85, 2002. Dmitrenko, V.V., Hasebe, N., Chernyshova, I.V., Batkov, O.B., Grachev, V.M., Kobayashi, S., Miyachi, T., Shibamura, E.,
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Sokolov, D.V., Ulin, S.E., Uteshev, Z.M., Vlasik, K.F. High Pressure Xenon Detector for Measurement of Planetary c Rays. IEEE NSS, San Diego, pp. 3980–3983, November 4–10, 2001. Grupen, C. Particle Detectors. Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology. Cambridge University Press, London, 1996, p. 47. Hasebe, N. et al. c-ray spectrometer for Japanese lunar polar orbiter. Adv. Space Res. 23 (11), 1837–1840, 1999. Hubbard, G.S., Binder, A.B., Feldman, W. The lunar prospector discovery mission: mission and measurement description. IEEE Trans. Nucl. Sci. 45 (3), 880–887, 1998. Kobayashi, M.-N. et al. High-purity germanium c-ray spectrometer with stirling cycle cryocooler. Adv. Space. Res. 30 (8), 1927–1931, 2002a. Kobayashi, S., Doke, T., Hasebe, N., Igarashi, T., Miyachi, T., Okada, H., Takenouchi, M., Shibamura, E., Dmitrenko, V.V., Grachev, V.M., Ulin, S.E., Vlasik, K.F. Planetary science application of high pressure Xe c-ray spectrometer, in: Proceedings of the 23rd International symposium on Space Technology and Science, Shimane Prefectural Assembly Hall (Kenmin-kaikan) and Kunibiki Messe, Matsue, Japan, pp. 1934–1938, May 26–June 2, 2002. Kobayashi, S., Hasebe, N., Igarashi, T., Kobayashi, M.-N., Miyachi, T., Miyajima, M., Okada, H., Okudaira, O., Tezuka, C., Yokoyama, E., Doke, T., Shibamura, E., Dmitrenko, V.V., Ulin, S.E., Vlasik, K.F. Scintillation luminescence for high-pressure xenon gas. Nucl. Instrum. Meth. A531, 327–332, 2004. Laurence, D.J., Feldman, W.C., Barraclough, B.L., Binder, A.B., Elphic, R.C., Maurice, S., Thomsen, D.R. Global elemental maps of the Moon: the lunar prospector c-ray spectrometer. Science 281, 1484–1489, 1998. Miuchi, K. et al. Performance and applications of a l-TPC. Nucl. Instrum. Meth. A535, 236, 2004. Saito, K., Tawara, H., Sanami, T., Shibamura, E., Sasaki, S. Absolute number of scintillation photons emitted by alpha particles in rare gases. IEEE Trans. Nucl. Sci. 49 (4), 1674–1680, 2002. Sasaki, S. et al. The selene mission: goal and status. Adv. Space. Res. 31 (11), 2335–2340, 2003. Ulin, S.E. et al. Proc. SPIE 3114, 499, 1997. Zoglauer, A., Kanbach, G. Doppler broadening as a lower limit to the angular resolution of next generation Compton telescope. Proc. SPIE 4851, 1302–1309, 2003.
A new generation c-ray camera for planetary science applications: High pressure xenon time projection chamber S. Kobayashi a,*, N. Hasebe a, T. Hosojima a, T. Igarashi a, M.-N. Kobayashi a, M. Mimura a, T. Miyachi a, M. Miyajima a, K.N. Pushkin a,b, H. Sakaba a, C. Tezuka a, T. Doke c, E. Shibamura d a
c
Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan b Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow 115409, Russia Kikuicho Branch, Advanced Research Institute for Science and Engineering, Waseda University, Kikuicho-17, Shinjuku, Tokyo 162-0044, Japan d Saitama Prefectural University, College of Health, Science, 820 Sannomiya, Koshigaya, Saitama 343-8540, Japan Received 1 November 2004; received in revised form 16 May 2005; accepted 29 May 2005
Abstract A new c-ray imaging camera based on High-pressure Xe Time-Projection-Chamber (HPXe-TPC) allows us to simultaneously determine arrival direction and its energy of individual incident c rays. HPXe-TPC is a promising c-ray detector for planetary science which provides means of global mapping of elemental composition in planetary surface as the remote sensing spectrometer. The simulation study by Geant4 and numerical calculation show that the angular resolution is mostly affected by multiple scattering of the recoil electron, and position resolution of electrodes of TPC. It is found that the angular resolution is 9° (50%) at 2 MeV for c rays. The feasibility of HPXe-TPC is discussed as a c-ray imaging camera for future planetary mission. Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: High-pressure xenon gas; Time-projection chamber; Planetary mission; c-ray camera
1. Introduction The main goal of planetary exploration is to understand the formation and evolution of planets. One of the approaches to answer basic questions regarding them is to measure the global elemental composition of the planet surfaces. Previous planetary and lunar missions so far have shown that a c-ray spectrometer is a powerful tool for the global mapping of the elemental composition (Laurence et al., 1998; Boynton et al., 2002). In the surface layer, the c rays are emitted from natural radioisotopes and nuclei which are excited by thermal or fast neutrons produced by the galactic cosmic-rays. By obtaining c-ray spectra in the energy range *
Corresponding author. Tel.:/fax: +81 3 5286 3897. E-mail address: [email protected] (S. Kobayashi).
of several MeV, we can derive elemental abundance of the surface layer, since the elements are identified by the characteristic c-ray energies. Planets and their satellites have many craters on their surface. It is important to investigate chemical composition inside and outside the craters with various radii, especially complex craters with the size greater than 15–20 km. Then, it is quite essential for nuclear c-ray spectroscopy to measure chemical composition in local regions together with the bulk composition of the planet. But in general, previous c-ray spectrometers carried on planetary missions so far are omnidirectional. Spatial resolution of a c-ray spectrometer is not so good as that of X-ray, visible, UV, or IR cameras because of the high penetrability of MeV c rays. It is obvious that the development of the c-ray spectrometer with the capability to resolve the arrival direction of incident c rays is very
0273-1177/$30 Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.05.106
S. Kobayashi et al. / Advances in Space Research 37 (2006) 28–33
essential. Here, we propose a new approach of remote sensing technology based on nuclear spectroscopy for planetary science. The c-ray imaging can be realized by the use of a high-pressure Xe time-projection-chamber (HPXe-TPC). The new generation imaging camera we propose allows us to simultaneously determine the arrival direction and energy of each c-ray emitted form the planetary surface. We have calculated the Monte Carlo simulation of electron tracks in HPXe-TPC for the design, construction and performance of HPXe-TPC. In this report, we discuss the angular resolution of HPXe-TPC for planetary c-ray observation.
2. Spatial resolution in planetary and lunar missions c-ray spectrometers boarded so far on previous planetary and lunar missions did not resolve the arrival direction of incident c-ray and they are omnidirectional. Because of the high penetrability of MeV c rays, the incident direction is not easily determined by using a collimator. Thus, its spatial resolution is determined primarily by geometrical conditions of the orbiter altitude and planet size. The spatial resolution is calculated as a function of observing altitude in lunar mission and are shown in Fig. 1. The spatial resolutions are about 150 km both of Lunar Prospector mission (Hubbard et al., 1998) and future SELENE mission (Sasaki et al., 2003; Kobayashi et al., 2002a; Hasebe, 1999) orbiting at the altitude of 100 km. Let us consider the spatial resolution of the c-ray camera that is able to measure the arrival direction of an incident c-ray. The spatial resolutions of a c-ray camera with angular resolutions (50%) from 5° to 20° is shown in Fig. 1. We see that the use of the c-ray camera improves the spatial resolution dramatically. The higher the spatial resolution is the longer observation time is requested to decrease the statistical error. Hence, the prac-
Spatial resolution, 50% (km)
10000
1000 Field of View
100
20˚
Omnidirectional 15˚
10˚
5˚
10
1 10
100 Altitude (km)
1000
Fig. 1. Spatial resolution as a function of the altitude in Lunar orbit.
29
tical value of the spatial resolution is 15 km for a next generation c-ray camera, since the size of a complex crater described above is larger than 15–20 km in radius.
3. High-pressure xenon time projection chamber Recently, a time projection chamber (TPC) has been studied in the field of particle physics to measure the energy and momentum of elementary particles at accelerators. While a Compton telescope is used in the astrophysical researches to detect MeV c rays. The principle of a HPXe-TPC is based on these two technologies. Though the HPXe-TPC measures the Compton scattering as the Compton telescope does, the HPXe-TPC additionally measures the 3D trajectory of the recoil electron by the method used in TPC. It is the outstanding characteristic of HPXe-TPC since the measurement of the 3D trajectory allows the complete reconstruction of the arrival direction of c rays, which is impossible for the classical Compton telescope. To measure the 3D trajectory, liquid or solid materials are not adequate as the detection medium, since the range of the recoil electron is too short in the materials in liquid or solid. HPXeTPC uses high-pressure xenon gas with an appropriate density for the measurement of the 3D trajectory. Furthermore, the high atomic number of xenon is useful to increase the detection efficiency to c rays. It is also known that a c-ray spectrometer using high-pressure xenon gas has a good energy resolution (2% (FWHM) for 662 keV Kobayashi et al., 2002b; Dmitrenko et al., 2001) better than that of a NaI(Tl) scintillator, a high stability for radiation damage (Ulin et al., 1997) and a wide operating temperature (100 °C) (Kobayashi et al., 2002b). The design of HPXe-TPC and the reconstruction method of the arrival direction of c-ray is described in the following sections. 3.1. Design of the HPXe-TPC The HPXe-TPC consists of a tracker and an absorber as shown in Fig. 2. The tracker detects a Compton vertex and measures the 3D trajectory and energy of the recoil electron. The absorber stops the scattered c-ray due to the photoelectric effect and measures its energy and the interaction point. Both the tracker and absorber consist of a cathode, a position sensitive electrode (PSE), and photodiodes or avalanche photodiodes (PDs). The PDs detects the scintillation of xenon around 175 nm (Saito et al., 2002) to detect the c-ray incidence. The tracker and the absorber are filled with xenon gas. The pressure in the absorber (5 MPa) is larger than that in the tracker (1–3 MPa) to increase the efficiency of photoelectric absorption. When a c-ray arrives in the tracker, it is scattered by a xenon atom and generates a recoil electron. The recoil
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Fig. 3. Compton scattering and definition of angular resolution.
m 0 c2 m 0 c2 ; ð1Þ E 1 þ E2 E2 E1 m 0 c2 E 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; cos u ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ E21 þ 2m0 c2 E1 ðE1 þ E2 Þ E21 þ 2m0 c2 E1
cos h ¼ 1 þ
Fig. 2. Schematic drawing of a high-pressure xenon time projection chamber. The upper chamber is a tracker and the lower one is an absorber.
electron ionizes xenon gas along its trajectory. At the same time, scintillation light is generated and is detected with PDs. The signal from PDs is used to determine an arrival time t0 of the c-ray. The liberated electrons are swept by the electric field applied between the cathode and PSE toward the PSE keeping the shape of trajectory. The PSE measures a 2D trajectory of the recoil electron in the x–y plane. Furthermore, when the liberated electrons are collected by PSE at time t1, the time difference between t0 and t1 multiplied by the electron drift velocity in xenon gives the third coordinate, z. As a result, the 3D trajectory of the recoil electron is obtained. The position of the Compton interaction P1 is obtained from the 3D trajectory and the energy of the recoil electron E1 is measured with the signals of PSE. In the absorber, the scattered c-ray is detected and the energy E2 and position P2, where the interaction occurs, is obtained by the same method used in the tracker. Hence, the energies of recoil electron E1, scattered c ray E2, the initial direction of the recoil electron ~ e after the scattering and the scattered c-ray ! ~ g ¼ P1 P2 are obtained. 3.2. Reconstruction of the arrival direction of an incident c-ray The question is how to reconstruct the arrival direction of an incident c-ray by using the values of E1, E2, ~ e and ~ g in HPXe-TPC. Let us begin with the Compton kinematics. The recoil electron and scattered c-ray are produced in the direction ~ e and ~ g, with energies of E1 and E2, respectively, as shown in Fig. 3. Using the momentum and energy conservation laws, the scattering angles of the c-ray h and the recoil electron u are given by
ð2Þ where m0 is electron rest mass and c is the light velocity. In Eqs. (1) and (2), the recoil electron is presumed to be at rest before the scattering. From the h and ~ g, we can limit the arrival direction to the generatrices of the cone Sh whose axis is corresponding to the ~ g as shown in Fig. 3. Note that the Compton scattering occurs on the plane S0 formed by the vectors of ~ e and ~ g. Hence, the intersections of Sh and S0 are two candidates of the incident direction, but we can uniquely determine the direction due to the relation between u and ~ e. As the classical Compton telescope does not measure ~ e, it is only able to confine the arrival direction to the generatrices. Reconstructing at least three events of c-ray from the same direction, the classical Compton telescope makes the image of the static source. On the other hand, the HPXe-TPC can uniquely determine the arrival direction by measuring~ e and reconstructing an event of c-ray interaction.
4. The angular resolution of the HPXe-TPC The angular resolution of the HPXe-TPC is determined by the ambiguity due to (1) Energy resolution of HPXe-TPC for E1 and E2; DE1 and DE2. (2) Doppler broadening (DB); the validity of Eqs. (1) and (2). (3) Position resolution of PSE for ~ g; D~ gpos . (4) Multiple scattering of the recoil electron in xenon for ~ e; D~ emul . (5) Position resolution of PSE for ~ e; D~ epos . Next, each ambiguity is estimated.
S. Kobayashi et al. / Advances in Space Research 37 (2006) 28–33
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4.1. Energy resolution DE1 and DE2
emul and D~ epos 4.4. D~ etotal ; D~
We measure E1 and E2 to determine the arrival direction h using Eq. (1). The energy resolution of HPXeTPC affects the angular resolution. The angular resolution due to the energy resolution effect is calculated and shown in Fig. 4. In this calculation, the energy resolution of HPXe-TPC is assumed to be 2% in FWHM for 662 keV including the electric noise of the amplifier. The c-ray is supposed to be scattered with the mean angle which is derived from the differential cross section of Klein–Nishina formula, for instance, h = 55° and u = 33° at 1 MeV. The ambiguity by the effect of energy resolution is much smaller than that by DB described below.
We estimate the angular resolution attributed from the ambiguity of D~ e. First, assuming that the Compton scattering plane S0 is simply determined as ~ e ~ g, the angular resolution depends on the measurement error of ~ e, i.e. D~ e because D~ g is negligibly small. A HPXe-TPC recognizes that the incident single c-ray comes from the arc shown in Fig. 3. Let us define the angle of xmax. It is half of the angle between two end points of the arc. If the direction in which the recoil electron is scattered is determined with an angular accuracy of Dg shown in Fig. 3, the angular resolution Dxobs is expressed as tanðDgÞ Dxobs 6 Dxmax ¼ sin1 sin hsin tan1 . sinðh þ uÞ ð3Þ
4.2. Doppler broadening Eqs. (1) and (2) are derived in the classic Compton scattering that the recoil electron is initially at rest at the scattering. Thus, the reconstructed direction of a c-ray is deteriorated by the effect of Doppler Broadening (DB) (Zoglauer and Kanbach, 2003). The angular resolution of h only due to DB in xenon is calculated by Geant4.6.2 (Agostinelli et al., 2003) and the result is shown in Fig. 4. The effect of DB decreases with the c-ray energy, since the initial momentum of the electron relative to that of c-ray becomes smaller and less significant. The ambiguity by DB is 1.1° at 1 MeV. 4.3. D~ gpos
Doppler Broadening Energy resolution
1.5
Vacuum
Xe (0.06 g/cm3)
1 1 mm
Angular resolution 50%, (deg.)
The ambiguity D~ g is obviously small compared with the D~ e, because the mean free path of the scattered cray is generally a few tens cm and the position resolution of PSE is typically 1 mm.
The recoil electron is scattered through the multiple scattering process after its production and information of the initial direction is gradually lost. The electron trajectory in xenon at 0.06 g/cm3 is simulated by Geant4.6.2 to estimate the magnitude of the electron multiple scattering and is shown in Fig. 5. In this figure, 50 electrons with 1 MeV enter the xenon gas. We define a circular cone with an apex angle of 2Dgmul, where its axis corresponds to the initial direction of the electron and whose summit is placed at the incident point. In addition, we evaluate Dgmul from the radius of the base circle which contains 50% of incident electrons at the distance l from the incident point. The result is shown in Fig. 6. It shows that the incident direction for 1 MeV electron is determined with an error of Dgmul = 7°, at 1 mm from the initial point. The position resolution of the PSE also affects D~ e since the trajectory is measured using PSE for x, y axes. For simplicity, we assume that the position resolution rpos ispthe ffiffiffiffiffi same for the x, y and z directions. rpos is equal to d= 12 (Grupen, 1996), where d is the distance between strip electrodes of the PSE. When a line segment ~ l with a length of l is measured with a spatial resolution of rpos, the angle between the true ~ l and the observed line segment ~ lobs is
0.5
0
0
1
2 3 Gamma-ray energy (MeV)
4
5
Fig. 4. The ambiguity due to the Doppler broadening and energy resolution as a function of c-ray energy.
1 mm Fig. 5. Multiple scatterings of 1 MeV electrons in Xe at 0.06 g/cm3.
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increasing c-ray energy, since the recoil electron tends to penetrate straightly when the energy of the primary cray is large. Thus, it results in a small ambiguity of the direction of the recoil electron. We consider that d = 1 mm is reasonable, from the viewpoint of the fabrication and stability of the PSE. The angular resolution Dxobs is within 9° for a 2 MeV c-ray with 50% probability.
20 500 keV
∆η with 50% probability (deg.)
1 MeV 15 1.5 MeV 10
2 MeV
5. Discussion
3 MeV 5
5 MeV 7 MeV 10 MeV
0 0
1
2
3 4 Distance, l (mm)
5
6
Fig. 6. gmul with 50% probability as a function of l at 0.06 g/cm3.
Dgpos ðlÞ ¼
pffiffiffi d 2rpos ¼ pffiffiffi . l 6l
ð4Þ
The ambiguity Dgtotal of the 3D trajectory, including the effects of multiple scattering and position resolution, is given by 2
2
Dg2total ðlÞ ¼ Dgmul ðlÞ þ Dgpos ðlÞ .
ð5Þ
The error of Dgtotal is a function of l and this function has a local minimum, Dgmin. It means that there is an optimum value of l which minimizes the error when we measure the 3D trajectory. So, we adopt Dgmin as the ambiguity of Dgtotal. Assume that the c-ray with energy E is scattered with the most probable scattering angle as the same method in Section 4.1. Then, the values of E1, E2, h and u are determined. The effect of multiple scattering is calculated using the E1, and then Dgmin(E) is obtained from Eqs. (4) and (5). As a result, the ambiguity of Dxmax is calculated as shown in Fig. 7. The angular resolution decreases with
0.5mm 1.0mm 1.5mm
Angular resolution, 50% (deg.)
20
10
0 0
2
4 6 Gamma-ray energy (MeV)
8
10
Fig. 7. The angular resolution Dxmax as a function of c-ray energy.
From the Section 4, we can see that the effect of the ambiguity of ~ e is the most significant. So it is thought that the angular resolution of HPXe-TPC is mostly dominated by the multiple scattering and position resolution and is corresponding to the Dxmax. We obtained 9° for 2 MeV as the angular resolution. This values is equivalent to a spatial resolution of 16 km for Lunar observations from 100-km altitude. Therefore, spatial resolution of a HPXe-TPC will be improved by a factor of 10 for 2-MeV c rays in comparison to c-ray spectrometers used in previous missions. There are some difficulties to realize the HPXe-TPC as a tool for a planetary mission. One of the technical problems is the method of measuring the 3D trajectory of the recoil electrons. The number of liberated electrons due to the recoil electron is very few to measure the trajectory. Hence, electron multiplication is necessary in the high-pressure xenon gas. Nowadays, some researchers concentrate on this kind of problem for their purpose and succeeds in measuring the 3D trajectory of the recoil electron in Ar + C2H6 gas (Miuchi et al., 2004). The second problem is the method of measuring the scintillation light of xenon gas. We have measured the scintillation yield in Xe and Xe with some dopants to resolve the problem (Kobayashi et al., 2004). The third issue is the detection efficiency of HPXeTPC for c-ray. The density of xenon gas is approximately 10 times smaller than a solid state c-ray spectrometer. However, the sensitivity of HPXe-TPC may be higher than the omnidirectional c-ray spectrometer because it is possible for HPXe-TPC to discriminate cray background from the composite material of the orbiter. This high sensitivity and the high atomic number of xenon somewhat compensate the disadvantage in the detection efficiency. Further experimental research and simulation study on the sensitivity are necessary. We would like to emphasize that the HPXe-TPC is the only tool which has the potential to determine the arrival direction of incident c-ray.
6. Concluding remarks The c-ray spectrometers carried on the previous planetary missions could not measure the arrival direction of
S. Kobayashi et al. / Advances in Space Research 37 (2006) 28–33
an incident c-ray. The spatial resolution, however, is improved by a HPXe-TPC which measures the recoil electron and the scattered c-ray of a Compton scattering and reconstructs the arrival direction. The simulation results show that the angular resolution of the HPXe-TPC is mostly affected by the multiple scattering of a recoil electron and the position resolution of the electrode. The HPXe-TPC in lunar mission has a spatial resolution of 16 km for 2-MeV c-ray at 100-km altitude. It is concluded that a new generation MeV c-ray imaging camera clearly distinguish the arrival direction of the incident c-ray to improve the spatial resolution. The imaging camera based on HPXe-TPC will provide means of precise global mapping of various chemical composition as a remote sensing spectrometer in future missions. Acknowledgements This work is financially supported in part by Institute of Space and Astronautical Science (ISAS) in the Japan Aerospace Exploration Agency (JAXA), the Tokyo Electric Power Company, and Scientific Research Grant-in-Aid from JSPS. This work is partly supported by a Grant-in-Aid for The 21st Century COE Program at Waseda University from the MEXT. References Agostinelli, S. et al. GEANT4 – a simulation toolkit. Nucl. Instrum. Meth. A506, 250–303, 2003. Boynton, W.V.24 colleagues Distribution of hydrogen in the near surface of Mars: evidence for subsurface ice deposits. Science 297, 81–85, 2002. Dmitrenko, V.V., Hasebe, N., Chernyshova, I.V., Batkov, O.B., Grachev, V.M., Kobayashi, S., Miyachi, T., Shibamura, E.,
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