APPLIED PHYSICS LETTERS 93, 174107 共2008兲
Measurement of temperature after hypervelocity collision of microparticles in the range from 10 to 40 km/s Takashi Miyachi,1,a兲 Masayuki Fujii,1 Nobuyuki Hasebe,1 Mitsuhiro Miyajima,1 Osamu Okudaira,1 Seiji Takechi,2 Toshiyuki Onishi,2 Shigeyuki Minami,2 Hiromi Shibata,3 Hideo Ohashi,4 Takeo Iwai,5 Ken-ichi Nogami,6 Sho Sasaki,7 Eberhard Grün,8 Ralf Srama,8 and Nagaya Okada9 1
Advanced Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan Graduate School of Engineering, Osaka City University, Osaka 558-8585, Japan 3 Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan 4 Faculty of Marine Science, Tokyo University of Marine Science and Technology, Tokyo 108-8477, Japan 5 Nuclear Professional School, School of Engineering, University of Tokyo, Ibaraki 319-1106, Japan 6 Department of Physics, Dokkyo Medical University, Tochigi 321-0293, Japan 7 National Astronomical Observatory of Japan, Iwate 023-0861, Japan 8 Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany 9 Honda-Electronics Co., Ltd., Aichi 441-3193, Japan 2
共Received 4 July 2008; accepted 14 October 2008; published online 31 October 2008兲 The temperature recorded immediately after hypervelocity collision of microparticles comprising iron and nickel with a silver-coated piezoelectric plate was analyzed using photomultipliers of different spectral response characteristics. The conversion rate between the velocity and temperature is estimated to be ⬃900 K / km/ s in the velocity range of 10–40 km/s. This rate is greater than that reported earlier. © 2008 American Institute of Physics. 关DOI: 10.1063/1.3013313兴 In previous reports,1–4 a piezoelectric lead-zirconatetitanate 共PZT兲 element was studied by bombardment with hypervelocity microparticles. The response of the PZT element immediately after collision depended on the microparticle velocity. Currently, no reliable theories exist that can explain the PZT output signal as a function of velocity. If the PZT element is to be used as a dust/debris detector in the future, reliable procedures for analyzing its behavior must be established. The temperature during collision is considered as one of the primary parameters for calibration purpose. Past studies have presented the temperatures for the collision of hypervelocity microparticles with several materials.5,6 These studies assumed that the site of impact acted as a blackbody. The number of photons emitted was measured using photomultipliers with applying several corrections for solid angle calculation, reflection of light, gain control systems, emissivity of a radiator, and other sources of errors or ambiguities in the measurements. On the other hand, if the amplitude is intercalibrated between the velocity and the temperature, the temperature can be defined as a function of the velocity during collision. This method needs at least one point, which is hereafter considered the standard point, where the temperature and velocity values 共T0 and v0, respectively兲 can be simultaneously determined. Since there have been few studies that have dealt with the evaluation of the temperature during collision of hypervelocity microparticles with various materials in the velocity range of 10–40 km/s, this paper aims to experimentally determine the temperature. The number of photons emitted with an energy h from the site of impact is proportional to the function f共x兲 = x2 / 共ex − 1兲, where x = h / kT and = c / . Here, h, , k, c, , and T are the Planck constant, photon frequency, Boltzmann constant, light velocity, wavelength, a兲
Electronic mail:
[email protected].
0003-6951/2008/93共17兲/174107/3/$23.00
and temperature, respectively. Then, the amplitude of the photomultiplier output signal 共T兲 at T is
共T兲 ⬀
冕
f ⫻ gdx,
共1兲
where g is the spectral response characteristic function of the photomultiplier. The collision of a microparticle with the PZT element leads to the emission of light quanta from the collision area. The photomultiplier detects a part of the light and generates a single sharp signal with a rise time of ⬃5 ns. This report discusses the evaluation of the temperature immediately after the collision by using this sharp signal. The amplitude of the output signal ␣共v兲 at a velocity v is experimentally measured. Thus, the relation 共T兲 / 共T0兲 = ␣共v兲 / ␣共v0兲 is valid. Four types of photomultipliers were used in the experiment. The function g, as given in Eq. 共1兲, was measured for each photomultiplier, as shown in Fig. 1共a兲. The photomultipliers are designated as u, b, v, and w for convenience. The u-photomultiplier acts as a threshold detector because of its narrow response characteristics. In Fig. 1共b兲, the calculated values are plotted as a function of T. By extrapolating these points, it is estimated to be ⬃18 000 K at zero amplitude. If this threshold point is employed as the standard point, the temperature of the standard point is determined: T0 ⬃ 18 000 K. The five photomultipliers were arranged such that they were directed toward the PZT element placed at a distance of 60 mm. Two v-type photomultipliers were used: one 共v1兲 was used to measure the flashes and the other 共v2兲 was used as a monitor. All the photomultipliers were biased such that the amplitudes of the output signals were less than 150 mV in order to avoid a possible deviation from linearity. The hypervelocity particles comprising nickel and iron particles were supplied by the Van de Graaff accelerator at the Max-Planck-Institut für Kernphysik. The surface of a
93, 174107-1
© 2008 American Institute of Physics
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
174107-2
Miyachi et al.
Appl. Phys. Lett. 93, 174107 共2008兲
FIG. 1. 共a兲 Spectral response characteristic functions in quantum efficiency vs wavelength. The nominal curve code and line type used to designate the u-, b-, v-, and w-photomultipliers are 100 M and solid-thick line, 200 S and dot-thin line, 400 K and solid-thin line, and 500 U and dot-thick line, respectively. 共b兲 Relative amplitudes calculated from Eq. 共1兲 using the solidthick line as a function of the temperature. T0 is estimated as ⬃18 000 K by extrapolation.
PZT element with dimensions of 40⫻ 40⫻ 1 mm3 was coated with a layer of silver electrode that was several micrometers thick. All the incident microparticles were considered to collide with the silver layer over an area of incidence with diameter of ⬃10 mm.7 The amplitudes of the output signals of the photomultipliers u, b, v1, and w were directly measured with a digital scope S1, while the amplitudes of those from the PZT element were measured by another scope S2 to confirm the occurrence of collision. The v2-photomultiplier signal was monitored on S2 as a time reference. The velocity and mass of each particle were measured using another scope S3 by scanning the signals induced in an electrostatic electrode.2 Their values ranged 10–50 km/s and 1–50 fg, respectively. The v2-photomultiplier signal was also monitored on S3 as a time reference. The maximum inherent ambiguity in the photomultipliers was estimated to be 20%. The signal forms in S1, S2, and S3 were measured visually. The maximum reading errors of S1 and S3 were 20% and 10%, respectively. Therefore, the maximum overall margin of error was estimated to be 30%. The signal form was varied not only among the photomultipliers but also from event to event. Figure 2 shows the typical signal forms observed in the u- and v1-photomultipliers. There are some cases in which the signal form appears normal 关共a兲 tagged as category I兴. However, there are various forms that appear irregular 关共b兲 category II兴. Such variations are indicative of the wide distribution of the amplitudes of the output signals 关共c兲 for the v1-photomultiplier兴. The characteristic behaviors shown in Fig. 2 can be explained as follows. When a hypervelocity microparticle strikes the PZT element, many secondary particles that screen the photomultipliers from the element are produced. This effect varies from one photomultiplier to another. The
FIG. 2. Screening effect. 共a兲 Events belonging to category I. 共b兲 Events belonging to category II. 共c兲 Distribution of the amplitudes of the v1-photomultiplier output signals as a function of the velocity.
irregular signal forms, as shown in Fig. 2共b兲, are considered to be a consequence of this screen effect. Figure 2共a兲 shows an event wherein the u-photomultiplier signal is almost uninhibited by the screening and, with a time offset of ⬃9 ns, follows the v1-photomultiplier signal, which is slightly obstructed by the secondary particles. In contrast, Fig. 2共b兲 illustrates the case wherein the v1-photomultiplier signal is significantly obstructed by the secondary particles and the u-photomultiplier signal, which is separated from the v1-photomultiplier signal by the time offset mentioned earlier, almost disappears at an advanced point in the signal path. The amplitudes of the output signals were randomly decreased due to the screening effect, as shown in Fig. 2共c兲. There are some samples that comprise an upper boundary of the distribution and there exist many samples beneath the boundary. The former signal forms belong to category I, while the latter belong to category II. Similar distributions were observed in other photomultipliers. Therefore, the amplitude ␣共v兲 / ␣共v0兲 should be measured using only signal forms of category I. Figure 3 shows the amplitudes of these signal forms obtained using the u-photomultiplier. By extrapolating these points to zero amplitude, the threshold velocity v0 was estimated to be ⬃19 km/ s. This value corresponds to T0 of ⬃18 000 K, as
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
174107-3
Appl. Phys. Lett. 93, 174107 共2008兲
Miyachi et al.
FIG. 3. Amplitudes of the u-photomultiplier output signals as a function of the velocity. The measured points are extrapolated, as shown by the solid line. v0 and T0 were found to be ⬃19 km/ s and ⬃18 000 K, respectively, as shown Fig. 1共b兲.
shown in Fig. 1共b兲. By applying the same procedure to the signal forms from the b-photomultiplier, these quantities are found to be ⬃11 000 K and ⬃11 km/ s. By using the relation 共T兲 / 共T0兲 = ␣共v兲 / ␣共v0兲, they are found to be ⬃12 000 K and ⬃10 km/ s, respectively, for the v1-photomultiplier. By assuming that the function ␣共v兲 obtained from the u-, v1-, and w-photomultipliers is approximately linear in the velocity range of 10–40 km/s, the relationship 共T兲 / 共T0兲 = ␣共v兲 / ␣共v0兲 is plotted, as shown in Fig. 4, along with
FIG. 4. Velocity vs temperature, ␣共v兲 / ␣共v0兲 = 共T兲 / 共T0兲. The standard point observed by the u-photomultiplier is shown by 共䊊兲, the points obtained by the eye-fit method and using the responses of the u-, v1−, and w-responses, and the threshold relation of the b-photomultiplier are also shown. The solid line is a guide for the eyes.
the threshold points for the u- and b-photomultipliers. The temperature-velocity relationship appears slightly concave-up in shape. Here the relationship may be approximated to be linear in the aforementioned velocity range. Using this approximation, the conversion rate was estimated to be ⬃900 K / km/ s, which corresponds to a temperature and a velocity of ⬃36 000 K at 40 km/s, respectively. According to Ref. 6, the conversion rate for collisions of iron particles with a tungsten target was ⬃140 K / km/ s in a velocity range of 4–13 km/s. Although this range is different from that in our study, this conversion rate value should be reevaluated by considering the influence of secondary particles generated during collision. In summary, the proposed method is useful for measuring the temperature immediately after the collision of hypervelocity microparticles with solid materials. The conversion rate was found to be ⬃900 K / km/ s in a velocity range of 10–40 km/s with an error of 30%. The temperature was found to be much higher than that reported earlier. We thank Mr. P. Sebastian for operating the accelerator. This work was partly supported by the Grant in Aid from the Japan Society for the Promotion of Science and On-ground experimental Project from Japan Space Forum. 1
T. Miyachi, N. Hasebe, H. Ito, T. Masumura, H. Okada, H. Yoshioka, K. Nogami, T. Iwai, H. Shibata, Y. Hamabe, S. Sasaki, S. Sugita, S. Hasegawa, H. Yano, H. Ohashi, K. Masunaga, M. Sato, and T. Tou, Adv. Space Res. 34, 935 共2004兲. 2 T. Miyachi, M. Fujii, N. Hasebe, M. N. Kobayashi, G. Kuraza, A. Nagashima, Y. Nakamura, K. Nogami, T. Iwai, S. Sasaki, H. Ohashi, S. Hasegawa, H. Yano, and H. Shibata, Adv. Space Res. 35, 1263 共2005兲. 3 T. Miyachi, M. Fujii, N. Hasebe, M. Kobayashi, G. Kuraza, A. Nagashima, Y. Nakamura, O. Okudaira, N. Yamashita, K. Nogami, T. Iwai, S. Sasaki, H. Ohashi, S. Hasegawa, H. Yano, H. Shibata, N. Okada, and T. Tou, J. Appl. Phys. 98, 014110 共2005兲. 4 T. Miyachi, M. Fujii, N. Hasebe, M. N. Kobayashi, G. Kuraza, K. Nogami, T. Iwai, S. Sasaki, K. Muranaga, H. Ohashi, S. Hasegawa, H. Yano, H. Shibata, E. Grün, R. Srama, N. Okada, and T. Tou, Appl. Phys. Lett. 86, 234102 共2005兲. 5 G. Eichhorn, Planet. Space Sci. 23, 1519 共1975兲. 6 G. Eichhorn, Planet. Space Sci. 26, 463 共1978兲. 7 T. Miyachi, G. Kuraza, A. Nagashimas, M. Fujii, N. Hasebe, N. Yamashita, K. Nogami, T. Iwai, H. Ohashi, H. Shibata, S. Minami, S. Takechi, T. Onishi, E. Grün, R. Srama, and N. Okada, Jpn. J. Appl. Phys. 47, 3772 共2008兲.
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
