IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 50, NO. 3, JUNE 2001 781

Simultaneous Measurement of Time-Resolved 2-DTemperature Distribution of Evaporation Surface

Heated by Swept Electron BeamYen-Wei Chen, Member, IEEE

Abstract—The temporal variation and spatial distribution ofmetallic gadolinium surface temperature during electron beamevaporation have been measured simultaneously by a high-speedvideo camera with a band-pass filter. The temperature was de-termined from the radiation intensity recorded by the bandpass,high-speed video camera coupled with a band-pass filter, aftercalibration with a two-color thermometer. Analytical resultsindicate that temporal variation of the surface temperature willcause a significant fluctuation of the atomic beam.

Index Terms—Atomic beam, band-pass filter, evaporation sur-face, high-speed video camera, Planck’s law, swept electron beam,temporal variation, time-resolved 2-D temperature distribution.

I. INTRODUCTION

I N atomic vapor laser isotope separation (AVLIS) [1], theelectron beam heating technique, is used to produce the

metal atomic vapor containing isotope species selectivelyphotoionized by a pulsed laser beam. Recently, a new sweepingmode electron beam heating technique was proposed to producea long-distance atomic vapor with high evaporation efficiency[2]. In order to maximize the laser beam efficiency and atomicvapor utilization, the atomic beam must be stable and uniform[3]. Since the qualities of the evaporated atomic beam mainlydepend on electron beam heating, it is important to know thespatial and temporal characteristics of the evaporation surfacetemperature.

To date, there are very few reports on measuring surface tem-perature distribution. Ohbaet al.reported measuring the surfacetemperature distributions of copper (Cu) [4] and gadolium (Gd)[5] heated by an electron beam in nonsweeping mode. In theirexperiments, the surface radiation distribution during the evap-oration was taken using a charge-coupled device (CCD) cameracoupled with a band-pass filter. The temperature distributionwas then determined from the measured radiation distributionusing Planck’s law. Since the temporal resolution of the mea-surements is very limited, the relationship between the evapo-rated atomic beam and the temporal characteristics of the evapo-ration surface temperature cannot be clearly established. In thispaper, we report simultaneous measurement of the spatial dis-tribution and temporal variation of the surface temperature of

Manuscript received May 26, 1998; revised January 18, 2001.The author is with the Faculty of Engineering, University of the Ryukyus,

Okinawa 903-0213, Japan.Publisher Item Identifier S 0018-9456(01)04927-0.

metallic Gd heated by a swept electron beam. The evaporatingsurface was imaged by the use of a high-speed video camera(Kodak Ekatapro HS Processor, Model 4540) which can recordup to 4500 full frame images/s. The dependence of the atomicbeam on the spatial and temporal characteristics of surface tem-perature has also been studied.

II. EXPERIMENTAL

A. Experimental Setup

The atomic vapor system in the vacuum chamber is shown inFig. 1. Metallic Gd in a water-cooled carbon crucible was heatedby an electron beam to generate the atomic vapor. The electronbeam was focused on a spot of cm and scanned across theGd surface over an area 2 cm long and 2 cm wide with a variablesweeping rate. The maximum power of the electron beam is 30kW (maximum acceleration voltage: 30 kV; maximum emissioncurrent: 1 A). In the experiments, the acceleration voltage wasfixed at 15 kV, and the output power was controlled by changingthe emission current in the range 0.1 A–2 A. The atomic vaporemitted from the heated surface flows upwards with thermalvelocity through a collimator slit 18 cm in length and 9 cm inwidth.

Atomic density was monitored by a quartz crystal thicknessmeter. Three thickness meters were located at positions indi-cated by , , and in Fig. 1. The temporal fluctuation ofatomic vapor was monitored by laser-induced fluorescence witha photo multiplier tube (PMT) coupled with an oscilloscope. Adye laser, resonant with the absorption line (215–17 618 cm)of Gd [6], was used to produce the laser-induced fluorescence.The laser beam was maintained at a height of 43 cm from thesurface of the metallic Gd. The signal of the laser-induced flu-orescence is proportional to the atomic density [6], [7].

The temporal variation and spatial distribution of the evap-oration surface were monitored by a high-speed video camera(the maximum rate is 4500 frames/s) connected with a framememory with a viewing angle of 30. The camera was coveredby a band-pass filter (center frequency: 555 nm; bandwidth: 5nm) to record a monochromatic image, which can be used todetermine the temperature using Planck’s law.

B. Surface Temperature

Assuming radiation from the evaporation surface is theblack-body radiation, the recorded time and space resolved

0018–9456/01$10.00 © 2001 IEEE

782 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 50, NO. 3, JUNE 2001

Fig. 1. Schematic drawing of experimental setup.

radiation intensity by the camera can be related tosurface temperature with Planck’s law as follows:

(1)where

first Planck radiation constant;second Planck radiation constant;speed of light in a vacuum;radiation wavelength;Plank’s constant;emissivity of liquid Gd, which is assumed as aconstant [8] and and are the trans-mittance of the filter and camera response, re-spectively.

Since the bandwidth of the filter is only 5 nm, approxi-mates a delta function and (1) can be simplified as

(2)

or

(3)

Here, and is the center frequency (555 nm)of the band-pass filter. Sinceis an unknown constant, Ohbaetal. [5] used radiation intensity ratio of the evaporation surfaceand a reference light source to determine the surface tempera-ture. In our experiments, we used the following simpler methodto determine from the radiation intensity. We measured thetemperature of the evaporation surface center of the hot zonewith a calibrated two-color thermometer at the same time. Thedetection area of the thermometer was estimated as 1.51.5 cm and the response time is about 1/30 s. The measuredtemperature is the averaged value over theand , whichis expressed as

(4)

Since is assumed as a constant [6],is not a function of .and can also be considered uncorrelated. Thus,can

be estimated as

(5)By substituting (5) for (3), we have the relationship of surfacetemperature and recorded radiation intensity as follows:

(6)

CHEN: TIME-RESOLVED 2-D TEMPERATURE DISTRIBUTION 783

(a)

(b)

Fig. 2. Snap shots of the surface temperature distribution. The time intervalfor each snap shot is 1/700 (t = t + 1=700).

By using (6), we can determine the surface temperature distribu-tion from the recorded monochromatic image. In the calculationof temperature, the integration in (6) is performed digitally.

III. EXPERIMENTAL RESULTS

We did experiments with four different sweep ratesHz, Hz, Hz, and Hz. Typical snap shots of thesurface temperature distribution for Hz are shown inFig. 2 (the bright regions correspond to high-temperature re-gions). The sweeping method is also shown in Fig. 2 and, ,

correspond to each snap shot time. The time interval is1/700 s. Seven snap shots correspond to one cycle of the sweep.The camera shutter speed is 1s. It can be seen that surfacetemperature is not uniform in space, and there is significant tem-poral variation at one point because the sweeping rate is too slowcompared to thermal conduction time. The temperature at thecenter point of each snap shot (as shown in Fig. 2) is used to ana-lyze the temporal variation of the surface temperature. The tem-poral variation at the center point for different sweeping rates( ) is shown in Fig. 3. Each point in Fig. 3 is obtained fromthe center point of each snap shot, and the temperature is es-timated from the radiation indensity using (6). The curves inFig. 3 are fitting curves obtained using the least square method.It can be seen that the surface temperature varies periodicallywith the rate of electron beam sweeping. The temporal varia-tion is improved by increasing sweep rate of the electron beam.In the case of Hz, there is no periodically temporalvariation. In order to make a quantitative analysis, we define thetemporal fluctuation as . Thesweep rate dependence of the calculated from Fig. 3 (ex-perimental results) is shown in Table I.

The periodic temporal fluctuation of atomic beam density isalso observed by monitoring the laser-induced fluorescence [7].The sweep rate dependence of the atomic beam density fluctu-ation [ ] is also shown inTable I. The atomic beam density varies with surface tempera-ture.

IV. DISCUSSIONS

The evaporation rate per unit areais given by [8]

g/s cm (7)

whereatomic mass of the evaporant;

surface temperature;

saturated vapor pressure, determined by the surfacetemperature .

For Gd, the saturated vapor pressurein a unit of mmHg isgiven by [8]

(8)

Thus, the atomic density (cm ) can be estimated as

(9)

784 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 50, NO. 3, JUNE 2001

(a)

(b)

(c)

Fig. 3. Temporal variations of surface temperature with different sweep rate.

where is the averaged velocity of the atom. Assuming thevelocity distribution of the Gd atoms obeys a Maxwellian dis-tribution, the averaged velocity can be estimated as

cm/s (10)

TABLE IDEPENDENCIES OF�T=T AND �N=N ON SWEEPINGRATE (f)

Fig. 4. Dependence of�N=N on�T=T .

By combining the above four equations, we can obtain the rela-tionship between and as

(11)

where . By differentiating with respectto and then dividing it by (11), we have the relationshipbetween and as follows:

(12)

The calculated dependence of a on is shown inFig. 4 with a solid line. In order to make a comparison, the ex-perimental results (Table I) are also shown in Fig. 4 with “,”which are in fairly good agreement with the calculation results.It can be seen that a small temperature variation will cause alarger fluctuation of atomic vapor. In order to reduce the fluctu-ation of atomic vapor to less than 10%, the temperature variationshould be less than 1%, and the sweep rate should be larger than500 Hz, as shown in Table I.

V. CONCLUSION

In conclusion, an imaging technique using a high-speedcamera coupled with a band-pass filter has been developedfor simultaneous measurement of the spatial distribution andtemporal variation of the surface temperature heated by a sweptelectron beam. The experimental results showed that a smalltemperature variation will cause a larger fluctuation of atomic

CHEN: TIME-RESOLVED 2-D TEMPERATURE DISTRIBUTION 785

vapor. The high-speed imaging technique is expected as animportant instrumentation technique for the investigation of thesweep rate scanning.

ACKNOWLEDGMENT

The author would like to thank Prof. Y. Izawa and Dr. K.Nomaru of the Institute of Laser Engineering, Osaka University,Japan, for their useful discussion and helpful advice through thisstudy. The author would also like to thank the reviewers for theirhelpful comments.

REFERENCES

[1] P. T. Greenland, “Laser isotope separation,”Contemp. Phys., vol. 31, pp.405–424, 1990.

[2] L. Blumenfeld and Soubbaramayer, “Power balance equation in elec-tron beam evaporation process,” inProc. 4th Workshop Separation Phe-nomena in Liquids and Gases, 1994, pp. 1–6.

[3] Y.-W. Chenet al., “Analysis of laser beam propagation effects in atomiclaser isotope separation,”Jpn. J. Appl. Phys., vol. 34, pp. 504–509, 1995.

[4] H. Ohba, K. Ogura, and T. Shibata, “Temperature distribution of evapo-ration surface heated by electron beam” (in Japanese),J. Vac. Soc. Jpn.,vol. 36, pp. 203–206, 1993.

[5] H. Ohba and T. Shibata, “Temperature profiles on the gadolium surfaceduring electron beam evaporation,” inProc. 6th Int. Symp. AdvancedNuclear Energy Research, 1994, pp. 963–969.

[6] H. Niki et al., “Hyperfine structure and isotope shift measurements onGadolinium levels by laser-induced fluorenscence spectroscopy,”Opt.Commun., vol. 70, pp. 16–20, 1989.

[7] K. Normaru, “Private communication,” unpublished.[8] S. Schilleret al., Electron Beam Technology. New York: Wiley, 1982.

Yen-Wei Chen (M’96) was born in Hangzhou,China, on August 25, 1962. He received the B.E.degree in 1985 from Kobe University, Kobe, Japan,the M.E. degree in 1987, and the D.E. degree in1990, both from Osaka University, Osaka, Japan.

From 1991 to 1994, he was a Research Fellow withthe Institute for Laser Technology, Osaka. From 1994to 1995, he was a Lecturer and, since 1996, he hasbeen an Associate Professor with the Department ofElectrical and Electronics Engineering, University ofthe Ryukyus, Okinawa, Japan. His research interests

include intelligent signal and image processing, radiological imaging, and op-tical instrumentation. He has written more than 100 research papers in thesefields.

Dr. Chen is a memeber of the IEICE and IEE of Japan.