Measurement of the local radiation field in a nuclear reactor by microwave interferometric techniques

NUCLEAR INSTRUMENTS

AND METHODS

95 (I97I) 3~3-325; © N O R T H - H O L L A N D

P U B L I S H I N G CO.

MEASUREMENT OF THE LOCAL RADIATION FIELD IN A NUCLEAR REACTOR BY M I C R O W A V E I N T E R F E R O M E T R I C T E C H N I Q U E S * A. K. BHATTACHARYAt, J. T. VERDEYEN, F. T. ADLER and L. GOLDSTEIN

Gaseous Electronics Laboratory and Nuclear Engineering Program, University of Illinois, Urbana, Illinois, U.S.A. Received 13 April 1971

The results of a study of the radiation field intensity in the core of a pulsed nuclear reactor by means of microwave propagation through an appropriately chosen noble gas placed within the reactor is reported. It is shown that the microwave propagation techniques are capable of measuring the reactor power, the local radiation flux and the dynamic reactor response instantaneously over a wide range of power levels. The technique is virtually

unlimited in its ability to follow fast transients in reactor power. The technique was used to measure reactor power from 40 kW to 560 MW. It was also used to measure the spatial gamma flux profile in the core of Triga Mark II reactor. It is shown that the technique is suitable for measurements of both high (> 101°R/h) and low (~, 104 R/h) gamma dose rates.

1. Introduction The exploratory experiments reported earlier ~) established the usefulness of guided microwave propagation techniques t h r o u g h ionized gases for measuring and monitoring fast power changes in a reactor. In this paper we describe the results of such experiments in some detail and also show the application of such techniques for the measurement of "local" radiation flux. We thereby, report the development of a radiation detector very m u c h suitable for reactor instrumentation, especially, where fast changes in the reactor power is to be monitored. Using this microwave technique the g a m m a flux profiles in the direction of the length of fuel elements as well as at different positions in the core of a M a r k I[ Triga Reactor at the University of Illinois have been measured and reported here. The study o f the characteristics of rare gas plasma produced by the radiation field in the core of a reactor has been reported elsewhere2). II is k n o w n that in the fission of a 235U nucleus about 200 MeV of energy is released on the average3). O f 1:his total energy about 12 MeV is carried away by g a m m a radiation alone. The fraction (7/12) of the total g a m m a energy appears as p r o m p t g a m m a rays at the time of the fission and the rest appear as delayed gammas. Measurement of the p r o m p t g a m m a radiation gives us a means of monitoring the rate o f nuclear fission and thereby measure the reactor power level.

The present work presents a technique of measuring the reactor power by monitoring the ionization produced by the p r o m p t g a m m a radiation. It will be clear f r o m discussions presented here that the m e t h o d is not limited to the detection o f g a m m a radiation alone. Obvious modifications (such as fill gas, nature of container wall, etc.) of the system will allow the detection o f both fast and slow neutrons and also the fission fragments. Therefore, with the present technique the reactor power level could be measured either by monitoring the neutron flux or the g a m m a radiation. The principle underlying the present investigation is quite simple. Ionization produced in an appropriately chosen gaseous medium by penetrating nuclear radiation present in the reactor was monitored by studying the propagation of low level, high radio frequency electromagnetic waves through such a medium. In the following, we present in turn a brief discussion of the nature of plasmas produced, the experimental arrangement together with the microwave diagnostic technique, and then report typical experimental results.

* This work supported in part by a University of Illinois research grant. t This work represents a part of the thesis submitted for the partial fulfillments for the Ph.D. degree in Nuclear Engineering at the University of Illinois. Present address: Lighting Research Laboratory, General Electric Company, Nela Park, Cleveland, Ohio 44112, U.S.A.

2. Kinetics of plasma A volume of gas contained in a vessel which is placed in the core of a reactor will be ionized by the radiation field. A more detailed description of the kinetics of the plasma produced is given in refs. 2, 4 and 5. Suffice it to say here that the electron number density obeys the following relation

dn (r,t) _ S ( P , Z , p , t ) - en 2, dt

(1)

where the source term S ( P , Z , p , t ) represents the rate of production of electron-positive ion pairs (primary,

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BHATTACHARYA

secondary, tertiary, etc.) by the incident radiation and is the electron-positive ion recombination coefficient. The ionization rate S varies linearly with the reactor power P, and is a function of the nature of the gas Z and the pressure (p). The above relation (1) is valid at high pressures where the electron loss by diffusion can be neglected. The steady-state (dn/dt=O) electron density is given by

n = [S(P,Z,p)/c~] +.

(2)

Since the ionization rate S is directly proportional to reactor power, the electron number density varies as the square root of the reactor power. At low gas pressures and low charged particle densities where diffusion losses are not negligible n varies as S ~, where x < 1. When the charged particles are lost by diffusion alone the electron number density n is proportional to S, i.e. to the reactor power. When the reactor is operated in the pulse mode the steady-state condition (dn/dt =0), is certainly valid near the peak of the pulse. However, for most cases

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considered here, S changes slowly with time in particular at a rate much smaller than the microscopic processes occurring in the volume of the plasma. Thus the ionized medium can be considered to be in a quasisteady state and the relation (2) is approximately valid. Therefore, the instantaneous measurement of the electron density by microwave interferometric techniques will give information about the build-up and the subsequent decay of the ionization of the gas during slowly rising and falling reactor power pulser). Moreover, since the relation (2) is true at the peak of the pulse the maximum value of the ionization rate S(P,Z,p) can be determined from the measured value of the peak electron number density if the recombination coefficient ~ is known6).

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3. Experimental arrangement anti theory of the experiment

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Fig. 1. Cross sectional view of the core showing the positions of different paise rods and fuel elements.

The measurements were performed in the University of Illinois Mark I[ Triga ReactorT). In this type of reactor the active core is located at the bottom of a pool under approximately 16 ft of water. The core forms a right circular cylinder and consists of a lattice of cylindrical fuel-moderator elements and graphite dummy elements. A one foot thick radial graphite reflector surrounds the core. The fuel elements are

LOCAL RADIATION

FIELD IN A N U C L E A R

supported between two circular grid plates. The top grid plate has holes through which the fuel elements can be removed from the core. The fuel-moderator element, including the top and bottom fixtures is 28.44 inch long. The active fuel element is 1.42 inch in diameter by 14 inch long. Four-inch sections of graphite in the fuel can above and below the fuel region serve as top and bottom reflectors for the core. The layout of the grid plate indicating the positions of the fuel elements, graphite d u m m y elements, the pneumatic transfer tube (rabbit) and the control rods, etc., is schematically shown in fig. i. The three boron carbide control rods which are approximately 20 inch long have maximum travel from full "in" position to full "out" positions of about 15 inch. The mechanical counter readings corresponding to the in and out positions of the two control rods are shown in fig. 2. The reactor could be operated at a steady state power level of 250 kW or lower. By rapid insertion of excess reactivity, which is achieved by expelling the pulse rod from the core, the reactor power can be pulsed to high peak powers for a short interval of time. The insertion of 2.00 and 2.50 dollars a) of excess reactivities produced peak power bursts of 250 and 500 MW, respectively. Within a time interval of about 30 sec, following a transient, the power level returns to an equilibrium value determined by the amount of excess reactivity. The typical shape of a reactor power pulsed to 250 MW peak power is shown in fig. 3. The well-known diagnostic techniques based on the propagation of guided microwaves through an ionized medium were utilized to measure the free electron number density and their m o m e n t u m transfer collision frequency8,9). Measurements were performed by propagating very low power ( < ½ mW) cw microwaves of frequency in the range of 5.9 to 6.3 GHz. In order to be assured that the gas was uniformly ionized along the axis of the container, the length of the gas-filled tube and its position in the reactor core were carefully cho.,;en. When the gas is ionized, the phase constant (/7) and the attenuation constant (~) for an electromagnetic wave propagating in the fundamental mode (TEll mode) are given by the relation 2' 9, 10) 7 z = (~ +1/7) 2 = - (coZ/cZ)ep - (1.84/a) 2 ,

(3)

where 2a is the inner diameter of the cylindrical waveguide. The relative dielectric constant ~ p of the ionized medium is given by ~. = 1

(%/<~)2

(l -jvl~o)'

(4)

where COp= ne2/rneo, n is the electron density, v is the

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electron collision frequency for momentum transfer, and ~o is the angular frequency of the propagating electromagnetic wave. There are two groups of electrons present in the gaseous medium located in the nuclear reactor: (a) the high energy electrons liberated in the primary ionization processes by the interaction of the fission g a m m a radiation in the volume of the gas and at the walls of container, and (b) the slow electrons which are created in the primary, secondary and tertiary ionization processes. The primary ionization produced by the fission g a m m a radiation in the gaseous medium and at the walls of the quartz container discussed here is primarily due to the Compton s c a t t e r i n f l ) . Although the Compton recoil electrons are liberated with a distribution of energy 11' lZ), the electrons thus produced in the primary interaction process have nearly as much kinetic energy as the incident photon. These primary electrons are capable of producing further (secondary) ionization and excitation in the medium. These highly energetic electrons have mean free path of several meters and go through the gaseous medium without loosing much of their energy. They loose most of their kinetic energy in the walls of the container. However, these primary electrons produce several secondary

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A.K. BHATTACHARYA et al.

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electrons in the volume of the gas and at the walls of the quartz container. Some of these secondary electrons are in turn capable of producing further ionization (tertiary) in the gaseous medium. Without going onto the details of the exact mechanisms of the ionization processes occurring in the gas, suffice it to say that for every high energy Compton electron there will be several low energy electrons generated in the volume of the gas. In addition to their relative number being much smaller compared to that of the low energy electrons, the life time of the primary electrons, rf - because of their high kinetic energy - in the microwave field ( f = 6100 MHz) is very short (rf ~ 10 -~° sec). The life time of the slow electrons r~, limited only by the recombination life time (rs =dn ~ 10 -3 sec) is very much longer than that of the fast Compton electrons, and thus the interaction of the propagating microwaves is primarily determined by the group of slow electrons. Therefore, the contribution to the total microwave complex conductivity of the group of fast electrons because of their low number density (nra~t/n~low~ 10 -4) and very short life time in the microwave field is in a first approximation negligible with respect to that

of the slow electrons which are of higher number density and also in addition have large momentum transfer collision frequencies in the appropriate gaseous medium. This assumption is supported by the microwave noise temperature measurement reported elsewhereZ). The drawing of the quartz container (2.8 cm i.d.) of the gas to be ionized is shown in fig. 4. This container completely filled the interior of a cylindrical waveguide (3.17 cm i.d.) which was excited and operated in the dominant TEll mode. The noble gas filled tube was tapered at one end to effect a smooth transition for microwaves from air to plasma. The vessel was flat on the other end which was placed against the shorted end of the in-core section of the waveguide. The cylindrical waveguide was placed at different fuel element positions E-3, D-l, D-2, etc., in the core of the reactor under 16 ft of shielding water. The waveguide had a slight " S " bend at approximately 8 ft from the short to prevent direct leakage of radiation through the air-filled waveguide. The circular waveguide was connected to a WR-137 rectangular waveguide and then to the "unknown" arm of the "MagicT " bridge circuit ~3) shown in fig. 5. When the gas in the core section was ionized, the phase and the attenuation of the propagating electromagnetic wave changed. The unbalance of the bridge is a measure of the change in the phase and the attenuation undergone by the microwave. As the degree of ionization that is free electron density changed in time, the detected signal at the Magic-T deviated its initial value, showing a fringe pattern reflecting the changes in the dielectric constant of the medium and hence the time variation of the degree of ionization ~'2). A typical interferometric display is shown in fig. 6. Each time the pattern exhibits a complete cycle of modulation, the single-pass phase shift through the plasma has changed by n radians. The same measurements can be made using standing wave detectors instead of a Magic-T. The extra phase shift and attenuation introduced by the plasma would then be determined by measuring the shift in the minimum position of the standing wave and the change in the standing wave ratio, respectively 2' 8, 9, 13). The attenuation can also be monitored by detecting the transmitted signal. When the sensing microwave signal was propagated in the waveguide a standing wave was set up in the guide, as shown in fig. 7. The distance between two successive minima was (2gc/2), )ogcbeing the guide wavelength. Placing a short at any one of the minima B, C, D , . . . , does not affect the standing wave pattern

317

LOCAL R A D I A T I O N FIELD IN A N U C L E A R R E A C T O R

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for that region past the plasma tube. Hence, one can make measurements with the plasma tube at integral multiples of )~gc/2 from the true short-circuit and still use ~:he theory of a shorted plasma. The microwave determination of the ionization produced at different vertical positions at a fixed core location was carried out by placing the gas-filled tube at distances of integral multiples of (2;c/2) f r o m the bottom (shorted end) of the waveguide. For these measurements a 9.7 cm long quartz tube filled with neon-krypton gas mixture ( ~ 0.02% Kr) at a pressure of 89.4 torr was used. The tube was suspended inside the core section of thEe waveguide by means of a thin cotton string. The string passed inside and along the wall o f the long section of the waveguide and was brought out above the water level in the reactor tank through a small hole in the wall o f the waveguide.

4. Results and discussion

A typical experiment consisted of placing a 22.7 cm long quartz tube (28 m m i.d.) filled with neon at 30.4 torr in the D-2 position in the core. The core section of the waveguide was shorted at a distance of 16 cm from the top of the lower grid plate. It will be clear from the discussions presented later in this section that this assured a uniform ionization along the length of the gas container. It is important to mention that the free electron density in the atmospheric (air) filled portion of the waveguide exposed to the radiation field was found to be negligible compared to that in the rare gas filled tube 2' 9). Fig. 8 shows the outputs of standing wave detectors together with the independently measured neutron flux determined by an uncompensated ionization chamber (WL-8137) recorded by a visicorder oscillo-

318

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graph when the reactor was pulsed to a peak power of 560 MW. The microwave phase shift measured by probes 1 and 2 are respectively rn~ and (2rn+l)zr/2, where m = 0, 1,2,.... The fringe patterns displayed by the detected microwave signal are symmetrical about the peak of the reactor power pulse and shows the rise of the reactor to its peak power and also its decay. In neon at such gas pressures the electron-ion recombination is the dominant mechanism by which low energy electrons are lost from the volume of the gas. Since a quasi steady-state is established practically instantaneously as compared with the time constant of the reactor (6.0 sec), the ionization rate is given by S ~ n 2. Fig. 9 shows the build-up and the subsequent decrease in ionization determined from the recording shown in fig. 8. Fig. 9 also shows the plot of Socn 2 which is in excellent agreement with the reactor power as measured by the neutron flux monitored independently. It, therefore, shows that the ionization pro-

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duced in neon at these pressures varies as the square root of the reactor power. Fig. I0 displays a fringe pattern indicating the amount of ionization produced in a 85.7 cm long quartz tube filled with neon at 21.2 torr containing about 0.05% krypton. The peak electron number density obtained in this case was estimated to be between the limits 2.3 x 1 0 t ° < n < 2 . 6 × 1020 cm -3. In this particular case the waveguide containing the gas tube was placed in the reactor tank outside the graphite reflector and approximately at a distance of two feet from the active core. The gamma radiation level at the location of the waveguide is < 6 × 10s R/h at 500 MW of reactor power. The presence of large number of fringes indicated that the gas mixture cited above was very sensitive to the radiation flux. It also illustrates the benefit of using Penning mixtures in obtaining higher sensitivity. As mentioned earlier, a smaller quartz tube filled

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with a neon-krypton gas mixture at 89.4 torr was used to measure the g a m m a flux profile in the core. Figs. 11 and 12 show a series of pictures displaying the detector outputs when the gas filled tube was placed at different vertical positions in the location D-2 of the core. The upper and the lower traces in these figures are the detector outputs indicating microwave phase shifts of m~ and ( 2 r n + l ) ~/2, where m = 0 , 1 , 2 , respectively. These measurements were performed by replacing the fuel element from D-2 by the waveguide. The fuel element from D-2 was then located in the F-5 position in the core. Table 1 gives the positions of the rf probed gas ionization tube together with the control rod positions for each reactor pulse and the reactor peak power measured by the linear power recorder at the control console (10% accuracy). A more accurate measurement of reactor peak power was obtained from the calibrated output of the uncompensated ionization (WL-0137) which monitored the neutron flux in the vicinity of the reactor core. The table also gives the

excess reactivity (in dollars 3) added to the core to produce each power pulse. Fig. 13 shows a plot of the measured electron number density, the normalized value of the measured S(t) oc n 2, and independently measured reactor power during the time the reactor power was pulsed to 250 MW. It indicates that in this case also the electrons are lost mainly by recombination and the peak electron density is given by the relation npeak =

constant x (reactor peak power)L

(5)

The peak electron number densities rtpeak measured with the gas-filled tube placed at the bottom of the waveguide and the reactor pulsed to peak powers of 500 and 250 MW were within the limits 8.2 x 101° > n > 6 . 6 x 101° and 6 . 6 x 1 0 1 ° > n > 4 . 8 x 101° cm -3, respectively. The peak electron densities determined from the data such as shown in figs. 11 and 12 are plotted in fig. 14. Also plotted are the normalized values of the square root of g a m m a dose at these locations measured in-

320

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ment of fast neutron flux profile determined from irradiation of aluminum foils and measuring the 2+Na activity17). Aluminum foils (1 inch diam) were taped on outside surface of the waveguide containing the cobalt dosimeters. The 24Na activity of these aluminum foils would represent the fast neutron flux profile in the core. The results of such measurements clearly indicated that LiF shields depressed the fast neutron flux by as much as 15 to 20% in its immediate neighborhoodg). Since the neutron flux distribution was distorted by the presence of LiF containers, the validity of the measurements made by the g a m m a dosimeters are open to question. Nevertheless the results obtained from the dosimeters and from the microwave data do agree qualitatively. It is worthwhile to mention that

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dependently. It is clear that the agreement between the microwave and the direct gamma dose measurements is excellent ~6). The integrated g a m m a dose was measured at different locations by means of commercially available Cobalt glass dosimeters (Edgerton, Germeshausen and Grier, Inc.) TM ~5). The dosimeters were irradiated by placing three at a time in the waveguide and pulsing the reactor to peak powers of 250 MW. In each case one position is kept common to different pulses as a reference for comparison. The cobalt glass plates used to measure g a m m a dose also exhibit a rather large thermal neutron response. Lithium fluoride shields were used to attenuate (approximately by a factor of 103) the thermal neutrons reaching the glass plates. The presence of LiF shields had quite an adverse effect on the characteristics of the core. Because of these LiF shields the reactor could not be operated in the pulse mode with more than three g a m m a dosimeters in the waveguide. Also the presence of the LiF shield drastically depressed the neutron flux in its neighborhood. This was substantiated by the measure-

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the results obtained by microwave technique are free from such defects. It may also be added that the dosimeter measures an integrated dose, whereas the microwave can measure the gamma dose rate. Once the system is calibrated the technique gives the instantaneous dose rate. The neutron flux profile measured by irradiating gold foils and also by measuring the 2 4 N a activity of aluminum waveguide indicated a shape of the fission neu~Lron flux similar to that of the gamma flux obtained by the microwave technique.

Fig. 15 shows the plot of the measured peak electron density at different vertical positions at the E-3 position of the core when the reactor was pulsed to peak powers of 500 MW. It also shows that the ionization is nonuniform along the length of the fuel element and weighed more towards the bottom part of the core. Also, the ionization produced at E-3 position is smaller than that at the D-2 position. The radial variation in the gamma flux could be measured by determining the change in ionization produced in the E, D, C,... rings. The electron densities

322

A.K. BHATTACHARYA et al.

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POWER = t65 Mw

Fig. 12. Photograph showing the detector outputs when the gas filled tube was placed at d = 4.9x cm, where x = 5, 7, 9, and l l at D-2 position. m e a s u r e d at E-3, D - l , D-2, D-7 and C-1 positions when the gas filled tube was p l a c e d at the b o t t o m o f the waveguide are given in table 2. Since the level of g a m m a r a d i a t i o n is p r o p o r t i o n a l to the square r o o t o f the electron density, the a b o v e figures can be used to estimate the radial variation in the g a m m a dose rate. The two limits o f densities are determined by the accuracy o f the p a r t i c u l a r experimental technique used. It is needless to say that the accuracy can be i m p r o v e d

by using additional standing wave detectors to determine the m i c r o w a v e phase shift m o r e precisely. The asymmetric shape o f the flux can be explained by referring to the discussion in section 3 and fig. 2. The control rods which are strong neutron absorbers, are inserted into the core f r o m the top. F o r the measurements reported here the control rods were partially inserted into the active fuel region from the t o p of the core. The presence o f such strong neutron a b s o r b e r s

LOCAL

RADIATION

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Fig. 13. Plot of measured electron density in Ne-Kr mixture (89.4 torr), normalized value of measured S(t) = kn"-, and independently measured reactor power pulsed to 250 M W . TABLE 2 Ionization measured at different core positions for reactor power of 250 MW.

Position in the core E-3 D-1 D-2 D-7 C-I

Electron density (cm-3) Lower limit Upper limit 4.7 5.1 4.8 3.3 5.4

x x × x ×

101° 10 l° 10 l° 10 lo 10l°

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at the top would tend to push the neutron flux downward and produce the asymmetrical thermal neutron

distribution, and hence the asymmetrical distribution of nuclei undergoing fissions. The spatial distributions o f thermal neutrons and the g a m m a radiation are closely related to each other. This would explain the asyrmnetrical shape of the g a m m a flux profile. The g a m m a flux profile obtained above could be taken as a representative of the spatial distribution of nuclei undergoing fissions. 5. Summary and conclusions The excellent agreement between the independent measurements of neutron flux, the 7-flux, and the free electron number density as measured by l o w level microwaves, indicate that the technique presented provides an excellent tool to measure and m o n i t o r the

324

A.K. BHATTACHARYA

instantaneous reactor response over several orders of magnitude in power. The technique is quite suitable for monitoring very fast transients in reactor power. The technique has been utilized for monitoring steady-state reactor power as low as 40 kW. A slight modification of the detection scheme will make it possible to extend the lower limit still further. For instance, a system employing a TEM mode of propagation at lower frequencies and the microwave cavity technique appear very promising in this respect 4' 5, ~8). It is evident that by selecting the appropriate frequency of the probing signal, the nature and the pressure of the gas, the system can be tailored to monitor both low as well as extremely high g a m m a dose rates. It has also been shown that the microwave technique presented is capable of measuring local high level g a m m a flux ( ~ 10 l° R/h or higher). This has been confirmed by employing other methods of measuring g a m m a radiation intensities. The technique presented has obvious advantages over the conventional radiation dosimetry. It does not require the shielding necessary to separate the effects of the fast and the thermal neutrons from that of the g a m m a radiations. The commercially available g a m m a dosimeters require a strong neutron absorber for neutron shielding, which tend to distort the radiation field under investigation. Moreover, most of these high level dosimeters are capable of measuring the integrated g a m m a dose only.

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,

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Fig. 15. Plot of measured peak electron density at various vertical distances at E-3 position for reactor power pulsed to 500 M W .

The microwave technique has the advantage that it is quite suitable for measuring instantaneous dose rates as well as the integrated dosage. It is apparent that the device is quite flexible and can be adapted for the measurement of both the fast and the thermal neutron fluxes by utilizing well known principles. For example, a proper mixture of hydrogen and a noble gas can be used for detecting only the fast neutrons whereas the reaction ~°B (neutron, alpha) 7Li, or the fission of 235U can be utilized for measuring only the thermal neutron flux. Thus it is apparent that the microwave technique provides a tool which may be useful in monitoring fast changes in reactor power and for determining the power distribution within the core of a reactor as well as for probing high level radiation fields. It may prove to be a very convenient tool for monitoring spatially localized power oscillations in large power reactors. Also, in view of the possibility of transmitting microwave signals over large distances by the method described here enables remote indication and/or control of nuclear reactor operations.

TGP

,

O

et al.

70

(cm

Fig. 14. Plot of peak electron density at the various vertical distance at D-2 position for reactor power pulsed to 250 M W ; • - Electron density m e a s u r e d by microwave; y , • - normalized variation in ( g a m m a dose)<

The authors would like to thank Mr. G. P. Beck, Reactor Supervisor, for running the reactor and other members of the Reactor Laboratory for their invaluable cooperation and help during the course of the investigation. The cooperation of the members or the Gaseous Electronics Laboratory at the University of Illinois is also gratefully acknowledged.

LOCAL R A D I A T I O N FIELD IN A N U C L E A R R E A C T O R

References l) A. K. Bhattacharya, L. Goldstein, F. T. Adler, J. T. Verdeyen and E. P. Bialecke, Appl. Phys. Letters 5 (1964) 242. e) A. K. Bhattacharya, J. T. Verdeyen, F. T. Adler and L. Goldstein, J. Appl. Phys. 38 (1967) 527. 3) S Glasstone and A. Sesonske, Nuclear reactor engineering (D. van Nostrand Co., Princeton, N.J., 1963). 4) C. B. Leffert, D. B. Rees and F. E. Jamerson, Annual Report Nonr-3109(00) (Research Lab., General Motors Corp., Warren, Mich., 31 Oct. 1964); and Annual Report Nonr3][09(00) (31 Oct. 1965). .~) D. B. Rees, C. B. Leffert and D. J. Rose, J. Appl. Phys. 40 (1969) 1884. 6) E. W. McDaniel, Collision phenomena in ionized gases (J. Wiley and Sons, New York, 1964). 7) Hazard analysis for a T R I G A M A R K II training and research reactor (College of Engineering, University of Illinois, Urbana, Ill., Oct. 1959). ~) L. Goldstein, Advan. Electron. Electron Phys. 7 (1955) 399. ")) A. K. Bhattacharya, Ph.D. Thesis (University of Illinois, Urbana, II1., 1966).

325

10) E. C. Jordan, Electromagnetic waves and radiating systems (Prentice-Hall, Englewood Cliffs, N.J., 1960). 11) R. D. Evans, The atomic nucleus (McGraw-Hill, New York, 1955) p. 712. 12) C. M. Davisson and R. D. Evans, Rev. Mod. Phys. 24 (1952) 79. 13) E. L. Ginzton, Microwave measurements (McGraw-Hill, New York, 1957). 14) K. D. Fridell, IEEE Trans. Nucl. Sci. NS-II (1964) 155. 15) N. J. Kreidl and J. R. Hensler, Irradiation damage to glass, NYO-4780 and NYO-3784 (Bausch and Lomb Optical Co., Nov. 1954). 16) The electron densities corresponding to 250 MW of reactor power were computed from the measured values of the electron number densities at any other reactor power levels by using relation (5). 17) W. J. Price, Nuclear radiation detection (McGraw-Hill, New York, 1958). 18) M. H. Votti and E. S. Kenney, Nucl. Instr. and Meth. 63 (1968) 45.