Measurement of temperature after hypervelocity collision of microparticles in therange from 10 to 40 km/sTakashi Miyachi, Masayuki Fujii, Nobuyuki Hasebe, Mitsuhiro Miyajima, Osamu Okudaira, Seiji Takechi,Toshiyuki Onishi, Shigeyuki Minami, Hiromi Shibata, Hideo Ohashi, Takeo Iwai, Ken-ichi Nogami, Sho Sasaki, Eberhard Grün, Ralf Srama, and Nagaya Okada Citation: Applied Physics Letters 93, 174107 (2008); doi: 10.1063/1.3013313 View online: http://dx.doi.org/10.1063/1.3013313 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/93/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Measurement of incident position of hypervelocity particles on piezoelectric lead zirconate titanate detector Rev. Sci. Instrum. 79, 043303 (2008); 10.1063/1.2908206 Guided wave propagation in 0.67 Pb ( Mg 1 ∕ 3 Nb 2 ∕ 3 ) O 3 – 0.33 Pb Ti O 3 single crystal plate poled along[ 001 ] c Appl. Phys. Lett. 91, 102907 (2007); 10.1063/1.2775093 Hypervelocity Impact Flash at 6, 11, and 25 KM/S AIP Conf. Proc. 845, 1349 (2006); 10.1063/1.2263574 Response from piezoelectric elements appearing immediately after collisions with silver particles J. Appl. Phys. 98, 014110 (2005); 10.1063/1.1978973 Dynamic failure of steel under hypervelocity impact of polycarbonate up to 9 km/s J. Appl. Phys. 93, 5983 (2003); 10.1063/1.1569979

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Measurement of temperature after hypervelocity collision of microparticlesin the range from 10 to 40 km/s

Takashi Miyachi,1,a� 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

1Advanced Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan2Graduate School of Engineering, Osaka City University, Osaka 558-8585, Japan3Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan4Faculty of Marine Science, Tokyo University of Marine Science and Technology, Tokyo 108-8477, Japan5Nuclear Professional School, School of Engineering, University of Tokyo, Ibaraki 319-1106, Japan6Department of Physics, Dokkyo Medical University, Tochigi 321-0293, Japan7National Astronomical Observatory of Japan, Iwate 023-0861, Japan8Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany9Honda-Electronics Co., Ltd., Aichi 441-3193, Japan

�Received 4 July 2008; accepted 14 October 2008; published online 31 October 2008�

The temperature recorded immediately after hypervelocity collision of microparticles comprisingiron and nickel with a silver-coated piezoelectric plate was analyzed using photomultipliers ofdifferent spectral response characteristics. The conversion rate between the velocity and temperatureis estimated to be �900 K /km /s in the velocity range of 10–40 km/s. This rate is greater than thatreported earlier. © 2008 American Institute of Physics. �DOI: 10.1063/1.3013313�

In previous reports,1–4 a piezoelectric lead-zirconate-titanate �PZT� element was studied by bombardment withhypervelocity microparticles. The response of the PZT ele-ment immediately after collision depended on the micropar-ticle velocity. Currently, no reliable theories exist that canexplain the PZT output signal as a function of velocity. If thePZT element is to be used as a dust/debris detector in thefuture, reliable procedures for analyzing its behavior must beestablished. The temperature during collision is consideredas one of the primary parameters for calibration purpose.

Past studies have presented the temperatures for thecollision of hypervelocity microparticles with severalmaterials.5,6 These studies assumed that the site of impactacted as a blackbody. The number of photons emitted wasmeasured using photomultipliers with applying several cor-rections for solid angle calculation, reflection of light, gaincontrol systems, emissivity of a radiator, and other sources oferrors or ambiguities in the measurements.

On the other hand, if the amplitude is intercalibratedbetween the velocity and the temperature, the temperaturecan be defined as a function of the velocity during collision.This method needs at least one point, which is hereafter con-sidered the standard point, where the temperature and veloc-ity values �T0 and v0, respectively� can be simultaneouslydetermined.

Since there have been few studies that have dealt withthe evaluation of the temperature during collision of hyper-velocity microparticles with various materials in the velocityrange of 10–40 km/s, this paper aims to experimentally de-termine the temperature. The number of photons emittedwith an energy h� from the site of impact is proportional tothe function f�x�=x2 / �ex−1�, where x=h� /kT and �=c /�.Here, h, �, k, c, �, and T are the Planck constant, photonfrequency, Boltzmann constant, light velocity, wavelength,

and temperature, respectively. Then, the amplitude of thephotomultiplier output signal ��T� at T is

��T� �� f � gdx , �1�

where g is the spectral response characteristic function of thephotomultiplier.

The collision of a microparticle with the PZT elementleads to the emission of light quanta from the collision area.The photomultiplier detects a part of the light and generatesa single sharp signal with a rise time of �5 ns. This reportdiscusses the evaluation of the temperature immediately afterthe collision by using this sharp signal. The amplitude of theoutput signal ��v� at a velocity v is experimentally mea-sured. Thus, the relation ��T� /��T0�=��v� /��v0� is valid.

Four types of photomultipliers were used in the experi-ment. The function g, as given in Eq. �1�, was measured foreach photomultiplier, as shown in Fig. 1�a�. The photomulti-pliers are designated as u, b, v, and w for convenience. Theu-photomultiplier acts as a threshold detector because of itsnarrow response characteristics. In Fig. 1�b�, the calculatedvalues are plotted as a function of T. By extrapolating thesepoints, it is estimated to be �18 000 K at zero amplitude. Ifthis threshold point is employed as the standard point, thetemperature of the standard point is determined: T0�18 000 K.

The five photomultipliers were arranged such that theywere directed toward the PZT element placed at a distance of60 mm. Two v-type photomultipliers were used: one �v1�was used to measure the flashes and the other �v2� was usedas a monitor. All the photomultipliers were biased such thatthe amplitudes of the output signals were less than 150 mVin order to avoid a possible deviation from linearity.

The hypervelocity particles comprising nickel and ironparticles were supplied by the Van de Graaff accelerator atthe Max-Planck-Institut für Kernphysik. The surface of aa�Electronic mail: miyachi@waseda.jp.

APPLIED PHYSICS LETTERS 93, 174107 �2008�

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PZT element with dimensions of 40�40�1 mm3 wascoated with a layer of silver electrode that was several mi-crometers thick. All the incident microparticles were consid-ered to collide with the silver layer over an area of incidencewith diameter of �10 mm.7

The amplitudes of the output signals of the photomulti-pliers u, b, v1, and w were directly measured with a digitalscope S1, while the amplitudes of those from the PZT ele-ment were measured by another scope S2 to confirm the oc-currence of collision. The v2-photomultiplier signal wasmonitored on S2 as a time reference.

The velocity and mass of each particle were measuredusing another scope S3 by scanning the signals induced in anelectrostatic electrode.2 Their values ranged 10–50 km/s and1–50 fg, respectively. The v2-photomultiplier signal was alsomonitored on S3 as a time reference.

The maximum inherent ambiguity in the photomultipli-ers was estimated to be 20%. The signal forms in S1, S2, andS3 were measured visually. The maximum reading errors ofS1 and S3 were 20% and 10%, respectively. Therefore, themaximum overall margin of error was estimated to be 30%.

The signal form was varied not only among the photo-multipliers but also from event to event. Figure 2 showsthe typical signal forms observed in the u- andv1-photomultipliers. There are some cases in which the sig-nal form appears normal ��a� tagged as category I�. However,there are various forms that appear irregular ��b� category II�.Such variations are indicative of the wide distribution ofthe amplitudes of the output signals ��c� for thev1-photomultiplier�.

The characteristic behaviors shown in Fig. 2 can be ex-plained as follows. When a hypervelocity microparticlestrikes the PZT element, many secondary particles thatscreen the photomultipliers from the element are produced.This effect varies from one photomultiplier to another. The

irregular signal forms, as shown in Fig. 2�b�, are consideredto be a consequence of this screen effect.

Figure 2�a� shows an event wherein theu-photomultiplier signal is almost uninhibited by thescreening and, with a time offset of �9 ns, follows thev1-photomultiplier signal, which is slightly obstructed by thesecondary particles. In contrast, Fig. 2�b� illustrates the casewherein the v1-photomultiplier signal is significantly ob-structed by the secondary particles and the u-photomultipliersignal, which is separated from the v1-photomultiplier signalby the time offset mentioned earlier, almost disappears at anadvanced point in the signal path.

The amplitudes of the output signals were randomly de-creased due to the screening effect, as shown in Fig. 2�c�.There are some samples that comprise an upper boundary ofthe distribution and there exist many samples beneath theboundary. The former signal forms belong to category I,while the latter belong to category II. Similar distributionswere observed in other photomultipliers.

Therefore, the amplitude ��v� /��v0� should be mea-sured using only signal forms of category I. Figure 3 showsthe amplitudes of these signal forms obtained using theu-photomultiplier. By extrapolating these points to zero am-plitude, the threshold velocity v0 was estimated to be�19 km /s. This value corresponds to T0 of �18 000 K, as

FIG. 1. �a� Spectral response characteristic functions in quantum efficiencyvs wavelength. The nominal curve code and line type used to designate theu-, b-, v-, and w-photomultipliers are 100 M and solid-thick line, 200 S anddot-thin line, 400 K and solid-thin line, and 500 U and dot-thick line, re-spectively. �b� Relative amplitudes calculated from Eq. �1� using the solid-thick line as a function of the temperature. T0 is estimated as �18 000 K byextrapolation.

FIG. 2. Screening effect. �a� Events belonging to category I. �b� Eventsbelonging to category II. �c� Distribution of the amplitudes of thev1-photomultiplier output signals as a function of the velocity.

174107-2 Miyachi et al. Appl. Phys. Lett. 93, 174107 �2008�

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shown in Fig. 1�b�. By applying the same procedure to thesignal forms from the b-photomultiplier, these quantitiesare found to be �11 000 K and �11 km /s. By using therelation ��T� /��T0�=��v� /��v0�, they are found to be�12 000 K and �10 km /s, respectively, for thev1-photomultiplier.

By assuming that the function ��v� obtained from the u-,v1-, and w-photomultipliers is approximately linear in thevelocity range of 10–40 km/s, the relationship ��T� /��T0�=��v� /��v0� is plotted, as shown in Fig. 4, along with

the threshold points for the u- and b-photomultipliers.The temperature-velocity relationship appears slightlyconcave-up in shape. Here the relationship may be approxi-mated to be linear in the aforementioned velocity range.Using this approximation, the conversion rate was estimatedto be �900 K /km /s, which corresponds to a temperatureand a velocity of �36 000 K at 40 km/s, respectively.

According to Ref. 6, the conversion rate for collisions ofiron particles with a tungsten target was �140 K /km /s in avelocity range of 4–13 km/s. Although this range is differentfrom that in our study, this conversion rate value should bereevaluated by considering the influence of secondary par-ticles generated during collision.

In summary, the proposed method is useful for measur-ing the temperature immediately after the collision of hyper-velocity microparticles with solid materials. The conversionrate was found to be �900 K /km /s in a velocity range of10–40 km/s with an error of 30%. The temperature wasfound 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 theJapan Society for the Promotion of Science and On-groundexperimental Project from Japan Space Forum.

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5G. Eichhorn, Planet. Space Sci. 23, 1519 �1975�.6G. Eichhorn, Planet. Space Sci. 26, 463 �1978�.7T. Miyachi, G. Kuraza, A. Nagashimas, M. Fujii, N. Hasebe, N. Ya-mashita, K. Nogami, T. Iwai, H. Ohashi, H. Shibata, S. Minami, S. Take-chi, T. Onishi, E. Grün, R. Srama, and N. Okada, Jpn. J. Appl. Phys. 47,3772 �2008�.

FIG. 3. Amplitudes of the u-photomultiplier output signals as a function ofthe velocity. The measured points are extrapolated, as shown by the solidline. v0 and T0 were found to be �19 km /s and �18 000 K, respectively,as shown Fig. 1�b�.

FIG. 4. Velocity vs temperature, ��v� /��v0�=��T� /��T0�. The standardpoint observed by the u-photomultiplier is shown by ���, the points ob-tained by the eye-fit method and using the responses of the u-, v1−, andw-responses, and the threshold relation of the b-photomultiplier are alsoshown. The solid line is a guide for the eyes.

174107-3 Miyachi et al. Appl. Phys. Lett. 93, 174107 �2008�

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