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A measurement of the neutron spectrum in the thermal column of the power-station reactor
J. Nucl.
Energy,
Part A:
Reactor
Science.
1959,
Vol,
10, pp. 75-79.
Pergamon
Press Ltd.
Printed
in Northern
Ireland
A MEASUREMENT OF THE NEUTRON SPECTRUM IN THE THERMAL COLUMN OF THE POWER-STATION REACTOR* A. P. SENCHENKOV and F. M. KUZNETSOV (Received 11 January 19.58) Abstract-A high-transmission mechanical neutron-velocity selector suitable for spectrum measurements in the energy range below 0.5 eV is described, and the results are given of a determination with this selector of the neutron spectrum in the thermal column of the power-station reactor. Kinks are found in the spectrum at velocities of 600,lOOO and 1650 msec-I, and theircauses areanalysed. The inelastic scatteringcross-section of graphite is estimated. By least squares fitting of a Maxwell distribution the neutron temperature is shown to be 354°K for a graphite temperature of 304°K.
INTRODUCTION
THE neutron .velocity spectrum in a moderating medium has been studied by many authors.(l-6) To a first approximation it has a Maxwell distribution, usually with a characteristic temperature some 50-lOOoK above that of the medium. There are, however, wide discrepancies between the various determinations of this characteristic temperature, some authors(5-g) giving a figure 50-100°K above the temperature of the moderator, others(lO) finding that thermal equilibrium has been established. The lack of agreement is explained (sG”)by the fact that the different sets of measurements were taken under different conditions of moderator temperature, neutron beam width, and so on; the investigations were made at different reactors, the reactors all being powerful, all subject to cooling, and having different densities of absorbing material in the moderator. Results published hitherto, therefore, cannot strictly be compared, and it has remained an open question how closely the actual distribution approaches to a true Maxwellian. The problem is, of course, an important one, as its solution will not only give a check on current theories of moderation but will allow reactor calculations to be based on the actual thermal neutron spectra observed. It is evident that the measurements must be made under conditions that disturb the neutron flux as little as possible. This is most easily achieved either in the thermal column of a reactor or in an uncooled experimental reactor of the demountable type, working at low power. In either case a spectrometer of high transmission is required so that neutron fluxes of the order of IO*-10’ cm-2 set-l will be sufficient. It is impermissible to increase the neutron beam strength * Translated
from Atomnaya Energiya 5,
124(1958)
beyond a certain limit by enlarging the area or solid angle employed, because this expedient increases the size of the hole in the moderator and tends always to interfere with the spectral distribution under study. On the other hand, high resolution is not required as the neutron velocity distribution is a smoothly varying function. The instrumental specification is suitably met by a mechanical velocity selector of the type that employs a long cylindrical rotor having slots cut at a small angle to the axis of rotation. We have built the instrument shown in Fig. 1 and operated it at the thermal column of the power station reactor. THE
VELOCITY
SELECTOR
The essential component of the selector is a cylindrical rotor of length 53 cm, diameter 27 cm and weight 55 kg, composed of 19 pertinax and 2 brass disks plated with cadmium each having a profile close to the so called contour of uniform stress. Its maximum spinning speed is limited by the tensile strength of the brass, and after allowing for an appropriate safety factor is fixed at 12,000 rev min-l. 297 slots, 0.8 mm wide and 13 mm deep, have been cut along the length of the cylinder so as to form channels at the rotor periphery making an angle of 1.6” to the cylinder axis. The rotating element runs in a vacuum chamber which is pumped out by a fore-vacuum pump to a pressure below 0.5 mm Hg, the shaft being brought out through a rotary seal using brass and graphite as the surfaces in contact. It is arranged that a seizure of the gland will not fracture the shaft. The rotor is turned by means of a belt drive from a 2.5 kW three-phase asynchronous two-speed motor, energized by a threephase auto-transformer. Its bearings are continously lubricated by the action of a centrifugal pump operating within the vacuum system, and the bearing
76
A. P. SENCHENKOV and F. M. KUZNET~OV
temperatures are monitored. The revolutions are counted by a scaler operated by an electromagnetic device attached to the shaft, and the spinning speed is exhibited on a ratemeter. The complete spinning unit is mounted on a rotatable platform, and may be turned about a 17
12
34
5
6
The resolution of the selector is determined by the angular spread of the directions from which an incident neutron is able to pass through the collimator and slot system, and by the spread Au, in the actual slot velocity that results from the non-zero height of the slot. Writing d, and d, for the widths of the slot 18
4.
327
8
lb
FIG. l.-Longitudinal section of the neutron velocity selector. I-aluminium window; 2-bearings; 3-balance weights; 4-brass disks; 5-pertinax disk; 6-the shaft; 7-revolution counter; 8-vacuum valve; g-base plate; IO-the swivel mechanism; 1 l-rotating carriage; 12-swivel bearing; 13-lubricating oil pump; 14-counter shield: 15-collimator 17-driving pulley; 1t3-the vacuum chamber. supporting bracket; 16-the electric motor;
vertical axis through the centre of the rotor by a selsyn drive at a control desk. One turn of the selsyn rotates the instrument by 0*000726 rad. The transmitted neutron energy depends on the angle between the neutron beam and the rotor slots, and on the spinning speed ; the former may be adjusted continuously over a certain range, the latter in steps between 2,500 and 9,500 rev min-l. A proportional counter of diameter 3.5 cm and working length 25 cm, filled to a pressure of 600 mm Hg with BF, 80 per cent enriched in 1°B, functioned as the detector. All adjustments are made and measurements taken at the control desk by a single operator. If v, be the effective transverse velocity of the slot measured at the centre of its vertical dimension, a, be the angle between the direction of the slot and the neutron beam and u2 the angle between the direction of the slot and the rotor axis, then the neutrons emerging from the instrument have a velocity
and the collimator respectively, 1, and Z, for their respective lengths, h, for the effective slot height and R for the radius of the rotor, the resolving power of the instrument is given by
AE being the total width of the resolution function at half-height. The transmitted intensity is approximately
where (D(E) is the incident neutron flux per unit energy interval, h, the height of the first pupil of the collimator, and D, is the distance between successive slots of the rotor.
MEASUREMENTS Our measurements at the thermal column were v = v, cos c&in u,. intended not only to allow a detailed study of the Since a, is not greater than 5” and u2 is only 1*6”, energy distribution of thermal neutrons diffusing in this expression reduces to graphite, but also to elucidate the effect of the beam hole diameter on the apparent spectrum. Accordingly v = v,/ul.
A measurement
of the neutron spectrum in the thermal column of the power-station
we extracted the beam in three different ways: from a cavity of dimension 40 x 40 x 60 cm3 and from holes of two different diameters, 10 cm and 6 cm. Fig. 2 shows the layout of the experiment. The observed counting rates N(a,) were corrected for resolution and for detector efficiency, and were
reactor
77
results were concordant. We have no explanation of this discrepancy, and do not consider that it is necessarily real. The true size of the three other irregularities in the spectrum is obscured in the curve of Fig. 3 by the effects of inadequate resolution. In the case of the
h
FIG. 2.-Layout of the experiment. l-the water shield of the reactor; 2-the graphite reflector; 3-a layer of lead, 20 cm in thickness; 4--graphite; 5-a removable insert; 6-the beam hole; 7-entrance pupil of the collimator; LX-exit pupil of the collimator; 9-the neutron velocity selector; IO-the detector; 1l-paraffin and cadmium shielding; 12-preamplifier.
normalized to the same energy interval by division by Au - 9. The resulting figures are proportional to the desired neutron flux per unit velocity interval. For each type of hole in the graphite, sets of readings were taken several times and an average taken to establish O(v). An example is given in Fig. 3, which shows the curve appropriate to a spinning speed of 5000 rev/min-l and a single-slit collimator having d, = 15 mm and Z, = 5 m in conjunction with a hole of diameter 10 cm. The parameters of the Maxwell distribution Q(v) dv = Ae-RV2v3 dv giving the best fit to fifteen points of each curve were determined by the method of least squares. Examination of the results shows that the observed spectra do not have an unmodified Maxwellian form, the departures being outside the limit of experimental error. The deviations are of two sorts; kinks at the velocities 600, 1000 and 1650 m/set-l. and a smooth but significant departure in the region of 2800 mjsec-l. It might have been thought possible that the latter discrepancy was due to a failure to take into account a variation in the transmission of the selector resulting from the vertical divergence of the beam. To examine this point, measurements were taken at various spinning speeds between 2500 and 6300 rev/min-l, and with two different degrees of vertical divergence, obtained by setting h, at 4 and 7 cm in turn; the
irregularity at 1650 m/se+, a magnitude has been determined by the intersections of the tangents to the flux curve, extrapolating its directions at points to the left and right of the abrupt drop, with a vertical straight line erected at a point determined by the X-ray structure analysis data for graphite. The ratios of the intensities to the left and to the right were as follows for the three beams: neutrons from the 40 x 40 x 60 cm3 cavity 1.40 from the 10 cm dia hole 1.18 from the 6 cm dia hole 1.13 DISCUSSION
Explanations of the irregularity at 600 m/set-l have been discussed in detail in Pile Neutron Research,(8) while the kink at lOOOm/sec-r has been observed also by EGELSTAFF. fll) The phenomena at 1000 and 1650 m/set-l may be ascribed to the following three causes. (1) The neutron flux along the direction of the beam, taken to be the x-axis, is governed by J(v) = p.D(v) + go(v)
F
)
with D(v) the diffusion coefficient.02) If D(v) has a discontinuity, then even though D(v) may be continous throughout the moderator, J will exhibit a discontinuity of magnitude proportional to [D(V + Au) -
D(v - Au)] 2
.
78
A. P. SENCHENKOV and F. M. KUZNETSOV
It is a simple matter to calculate the size of this step, which at 1650 m/set-i (in the vicinity of the large jump in the cross-section of graphite) comes to 2 per cent of the total flux, or 10 per cent of the actual step deduced from the measurements with the 10 cm hole.
dependent of hole diameter, while effect (2) is proportional to its square, the contributions made by all three effects may be deduced from our previous estimate of the part played by effect (1). With the 10 cm hole it transpires that the three contributions
2.5
1000
2000
3000 Neutron
4000 velocity
5000 u,
6000
msec
-I
7000
8000
,
FIG. 3.-The neutron flux distribution as measured with the use of a 10 cm diameter hole. -the observed distribution. - - - - a Maxwell distribution with characteristic temperature 352’K.
(2) The boundary of the moderator where the beam is taken out is equivalent to a neutron sink, whose magnitude per unit area of the radiating surface is proportional to the square of the beam diameter. This sink has the effect of increasing &D(u)/&, and thereby enhancing the observed break in J in proportion to the square of the beam diameter, so long as that diameter be small compared to the diffusion length. (3) If there were no exchange of energy between the neutron beam and the graphite, i.e. if the inelastic scattering cross-section cm = 0, the neutrons of each energy interval would diffuse independently and the flux would fall off as exp [-x/L(v)], with L(v) the diffusion length. On the other hand, if there are jumps in L(v) there will be corresponding steps in the flux whose magnitude will increase with distance away from the radiating boundary of the moderator. A strong energy exchange between neutrons and graphite will not result in any observable effect; but with only a weak coupling, a constant flux discontinuity would be found at large distances from the boundary, situated in the same spectral region as the discontinuity in L(U), proportional to the size of the latter discontinuity and inversely proportional to cm. Bearing in mind that effects (1) and (3) are in-
to the observed break in the flux distribution are respectively 10, 35 and 55 per cent. It thus follows that the ratio J(u + Au)/J(u- Au) which should properly be ascribed to the weak energy exchange is 1.10. The ratio thus derived may now be employed to make an approximate calculation of the inelastic scattering cross-section of graphite, as follows. The mean number of elastic collisions which occur for every inelastic collision is
where ZS= &J,(u + Au) + cS(u - Au)]. The mean distance covered by the neutron in a straight line between two successive inelastic collisions is given by (s) 7 = 2FilI S t7 1, being the scattering length and 1, the transport mean free path, Now the step in the flux distribution is brought into existence only as a result of the diffusion that takes place between successive inelastic scattering events. Knowing L(u + Au) and L(u - Au) it is
A measurement
possible
to calculate
the known
J(u -
the mean
‘cleavage’
4~ + Au) AD)
of the neutron spectrum in the thermal column of the power-station
takes
distance
I over
which
place:
exp[--I/G + exp [-l/L(v
WI
=
REFERENCES
.
1. RAINWATER J. and
In the present instances we obtain I = 14 i 3 cm. Equating further 1 and l/(7) it is found that n = 10 f 4 ; whence
2. 3. 4.
Gin = 5,/n = 0.1~7~= 0.40 * O-16 barn 5.
in
good
agreement
with
the
determination
of
EGELSTAFF.‘~~) For
all three measured spectra the characteristic temperatures of the Maxwell distribution of best fit were consistent, being respectively 359,352 and 352°K each with a probable error of f 10°K. These results suggest a neutron temperature some 50°K higher than that of the moderator. In the case of the beam from the 10 cm hole the neutron temperature was also measured by the use of boron glass filters, giving the result 350 5 15°K. It is possible that the elevated temperature of the neutron gas may be caused in part by the presence of structural iron members within the graphite stack at a distance of 20 cm from the effective neutron source emnloved. I
J
79
Acknowledgements-Our thanks are due to A. K. KRASIN and B. G. DUBOVSKII for their interest and assistance, and to F. L. SHAPIROfor a valuable discussion of the early results.
1_1o
- AU)]
reactor
6. 7. 8. 9. 10.
HAVENS W. W., Phys. Rev. 70, 136 (1946). ZINN W. H., Phys. Rev. 71, 752 (1947). STURM W. J., Phys. Rev. 71, 751 (1947). Proceedings of the International Conference on the Peaceful Uses of Atomic Energy, Geneva 1955; Russian edition, p. 49 of Reaktorostroenie i Teoriya Reaktorov Academy of Sciences Publishing House (1955). ABOV Yu. G., Conference of the U.S.S.R. Academy of Sciences on the Peaceful Uses of Atomic Energy, Physical Sciences division, p. 209. Consultants Bureau (1955). LARSSON K. E., STEDMAN R. and PALEVSKY H., J. Nucl. Energy 6, 222 (1958). FERMI E., MARSHALL L. and MARSHALL J., Phys. Rev. 72, 193 (1947). HUGHES D. J., Pile Neutron Research. Addison Wesley (1953). HUGHES D. J., WALLACE J. R. and HOLTZMAN R. H., Phys. Rev. 73, 1217 (1948). TOLSTOV K.
D.,
SHAPIRO F.
L.
and SHTRANIKH I. V.,
Conference of the U.S.S.R. Academy of Sciences on the Peaceful Uses of Atomic Energy, Physical Sciences division, p. 95. Consultants Bureau (1955). 11. EGELSTAFFP. A., J. Nucl. Energy 1, 51 (1954). 12. GLASSTONES. and EDLUND M. C., Nuclear Reactor Theory. Macmillan, London (1953). 13. EGELSTAFFP. A., J. Nucl. Energy 5, 203 (1957).
Energy,
Part A:
Reactor
Science.
1959,
Vol,
10, pp. 75-79.
Pergamon
Press Ltd.
Printed
in Northern
Ireland
A MEASUREMENT OF THE NEUTRON SPECTRUM IN THE THERMAL COLUMN OF THE POWER-STATION REACTOR* A. P. SENCHENKOV and F. M. KUZNETSOV (Received 11 January 19.58) Abstract-A high-transmission mechanical neutron-velocity selector suitable for spectrum measurements in the energy range below 0.5 eV is described, and the results are given of a determination with this selector of the neutron spectrum in the thermal column of the power-station reactor. Kinks are found in the spectrum at velocities of 600,lOOO and 1650 msec-I, and theircauses areanalysed. The inelastic scatteringcross-section of graphite is estimated. By least squares fitting of a Maxwell distribution the neutron temperature is shown to be 354°K for a graphite temperature of 304°K.
INTRODUCTION
THE neutron .velocity spectrum in a moderating medium has been studied by many authors.(l-6) To a first approximation it has a Maxwell distribution, usually with a characteristic temperature some 50-lOOoK above that of the medium. There are, however, wide discrepancies between the various determinations of this characteristic temperature, some authors(5-g) giving a figure 50-100°K above the temperature of the moderator, others(lO) finding that thermal equilibrium has been established. The lack of agreement is explained (sG”)by the fact that the different sets of measurements were taken under different conditions of moderator temperature, neutron beam width, and so on; the investigations were made at different reactors, the reactors all being powerful, all subject to cooling, and having different densities of absorbing material in the moderator. Results published hitherto, therefore, cannot strictly be compared, and it has remained an open question how closely the actual distribution approaches to a true Maxwellian. The problem is, of course, an important one, as its solution will not only give a check on current theories of moderation but will allow reactor calculations to be based on the actual thermal neutron spectra observed. It is evident that the measurements must be made under conditions that disturb the neutron flux as little as possible. This is most easily achieved either in the thermal column of a reactor or in an uncooled experimental reactor of the demountable type, working at low power. In either case a spectrometer of high transmission is required so that neutron fluxes of the order of IO*-10’ cm-2 set-l will be sufficient. It is impermissible to increase the neutron beam strength * Translated
from Atomnaya Energiya 5,
124(1958)
beyond a certain limit by enlarging the area or solid angle employed, because this expedient increases the size of the hole in the moderator and tends always to interfere with the spectral distribution under study. On the other hand, high resolution is not required as the neutron velocity distribution is a smoothly varying function. The instrumental specification is suitably met by a mechanical velocity selector of the type that employs a long cylindrical rotor having slots cut at a small angle to the axis of rotation. We have built the instrument shown in Fig. 1 and operated it at the thermal column of the power station reactor. THE
VELOCITY
SELECTOR
The essential component of the selector is a cylindrical rotor of length 53 cm, diameter 27 cm and weight 55 kg, composed of 19 pertinax and 2 brass disks plated with cadmium each having a profile close to the so called contour of uniform stress. Its maximum spinning speed is limited by the tensile strength of the brass, and after allowing for an appropriate safety factor is fixed at 12,000 rev min-l. 297 slots, 0.8 mm wide and 13 mm deep, have been cut along the length of the cylinder so as to form channels at the rotor periphery making an angle of 1.6” to the cylinder axis. The rotating element runs in a vacuum chamber which is pumped out by a fore-vacuum pump to a pressure below 0.5 mm Hg, the shaft being brought out through a rotary seal using brass and graphite as the surfaces in contact. It is arranged that a seizure of the gland will not fracture the shaft. The rotor is turned by means of a belt drive from a 2.5 kW three-phase asynchronous two-speed motor, energized by a threephase auto-transformer. Its bearings are continously lubricated by the action of a centrifugal pump operating within the vacuum system, and the bearing
76
A. P. SENCHENKOV and F. M. KUZNET~OV
temperatures are monitored. The revolutions are counted by a scaler operated by an electromagnetic device attached to the shaft, and the spinning speed is exhibited on a ratemeter. The complete spinning unit is mounted on a rotatable platform, and may be turned about a 17
12
34
5
6
The resolution of the selector is determined by the angular spread of the directions from which an incident neutron is able to pass through the collimator and slot system, and by the spread Au, in the actual slot velocity that results from the non-zero height of the slot. Writing d, and d, for the widths of the slot 18
4.
327
8
lb
FIG. l.-Longitudinal section of the neutron velocity selector. I-aluminium window; 2-bearings; 3-balance weights; 4-brass disks; 5-pertinax disk; 6-the shaft; 7-revolution counter; 8-vacuum valve; g-base plate; IO-the swivel mechanism; 1 l-rotating carriage; 12-swivel bearing; 13-lubricating oil pump; 14-counter shield: 15-collimator 17-driving pulley; 1t3-the vacuum chamber. supporting bracket; 16-the electric motor;
vertical axis through the centre of the rotor by a selsyn drive at a control desk. One turn of the selsyn rotates the instrument by 0*000726 rad. The transmitted neutron energy depends on the angle between the neutron beam and the rotor slots, and on the spinning speed ; the former may be adjusted continuously over a certain range, the latter in steps between 2,500 and 9,500 rev min-l. A proportional counter of diameter 3.5 cm and working length 25 cm, filled to a pressure of 600 mm Hg with BF, 80 per cent enriched in 1°B, functioned as the detector. All adjustments are made and measurements taken at the control desk by a single operator. If v, be the effective transverse velocity of the slot measured at the centre of its vertical dimension, a, be the angle between the direction of the slot and the neutron beam and u2 the angle between the direction of the slot and the rotor axis, then the neutrons emerging from the instrument have a velocity
and the collimator respectively, 1, and Z, for their respective lengths, h, for the effective slot height and R for the radius of the rotor, the resolving power of the instrument is given by
AE being the total width of the resolution function at half-height. The transmitted intensity is approximately
where (D(E) is the incident neutron flux per unit energy interval, h, the height of the first pupil of the collimator, and D, is the distance between successive slots of the rotor.
MEASUREMENTS Our measurements at the thermal column were v = v, cos c&in u,. intended not only to allow a detailed study of the Since a, is not greater than 5” and u2 is only 1*6”, energy distribution of thermal neutrons diffusing in this expression reduces to graphite, but also to elucidate the effect of the beam hole diameter on the apparent spectrum. Accordingly v = v,/ul.
A measurement
of the neutron spectrum in the thermal column of the power-station
we extracted the beam in three different ways: from a cavity of dimension 40 x 40 x 60 cm3 and from holes of two different diameters, 10 cm and 6 cm. Fig. 2 shows the layout of the experiment. The observed counting rates N(a,) were corrected for resolution and for detector efficiency, and were
reactor
77
results were concordant. We have no explanation of this discrepancy, and do not consider that it is necessarily real. The true size of the three other irregularities in the spectrum is obscured in the curve of Fig. 3 by the effects of inadequate resolution. In the case of the
h
FIG. 2.-Layout of the experiment. l-the water shield of the reactor; 2-the graphite reflector; 3-a layer of lead, 20 cm in thickness; 4--graphite; 5-a removable insert; 6-the beam hole; 7-entrance pupil of the collimator; LX-exit pupil of the collimator; 9-the neutron velocity selector; IO-the detector; 1l-paraffin and cadmium shielding; 12-preamplifier.
normalized to the same energy interval by division by Au - 9. The resulting figures are proportional to the desired neutron flux per unit velocity interval. For each type of hole in the graphite, sets of readings were taken several times and an average taken to establish O(v). An example is given in Fig. 3, which shows the curve appropriate to a spinning speed of 5000 rev/min-l and a single-slit collimator having d, = 15 mm and Z, = 5 m in conjunction with a hole of diameter 10 cm. The parameters of the Maxwell distribution Q(v) dv = Ae-RV2v3 dv giving the best fit to fifteen points of each curve were determined by the method of least squares. Examination of the results shows that the observed spectra do not have an unmodified Maxwellian form, the departures being outside the limit of experimental error. The deviations are of two sorts; kinks at the velocities 600, 1000 and 1650 m/set-l. and a smooth but significant departure in the region of 2800 mjsec-l. It might have been thought possible that the latter discrepancy was due to a failure to take into account a variation in the transmission of the selector resulting from the vertical divergence of the beam. To examine this point, measurements were taken at various spinning speeds between 2500 and 6300 rev/min-l, and with two different degrees of vertical divergence, obtained by setting h, at 4 and 7 cm in turn; the
irregularity at 1650 m/se+, a magnitude has been determined by the intersections of the tangents to the flux curve, extrapolating its directions at points to the left and right of the abrupt drop, with a vertical straight line erected at a point determined by the X-ray structure analysis data for graphite. The ratios of the intensities to the left and to the right were as follows for the three beams: neutrons from the 40 x 40 x 60 cm3 cavity 1.40 from the 10 cm dia hole 1.18 from the 6 cm dia hole 1.13 DISCUSSION
Explanations of the irregularity at 600 m/set-l have been discussed in detail in Pile Neutron Research,(8) while the kink at lOOOm/sec-r has been observed also by EGELSTAFF. fll) The phenomena at 1000 and 1650 m/set-l may be ascribed to the following three causes. (1) The neutron flux along the direction of the beam, taken to be the x-axis, is governed by J(v) = p.D(v) + go(v)
F
)
with D(v) the diffusion coefficient.02) If D(v) has a discontinuity, then even though D(v) may be continous throughout the moderator, J will exhibit a discontinuity of magnitude proportional to [D(V + Au) -
D(v - Au)] 2
.
78
A. P. SENCHENKOV and F. M. KUZNETSOV
It is a simple matter to calculate the size of this step, which at 1650 m/set-i (in the vicinity of the large jump in the cross-section of graphite) comes to 2 per cent of the total flux, or 10 per cent of the actual step deduced from the measurements with the 10 cm hole.
dependent of hole diameter, while effect (2) is proportional to its square, the contributions made by all three effects may be deduced from our previous estimate of the part played by effect (1). With the 10 cm hole it transpires that the three contributions
2.5
1000
2000
3000 Neutron
4000 velocity
5000 u,
6000
msec
-I
7000
8000
,
FIG. 3.-The neutron flux distribution as measured with the use of a 10 cm diameter hole. -the observed distribution. - - - - a Maxwell distribution with characteristic temperature 352’K.
(2) The boundary of the moderator where the beam is taken out is equivalent to a neutron sink, whose magnitude per unit area of the radiating surface is proportional to the square of the beam diameter. This sink has the effect of increasing &D(u)/&, and thereby enhancing the observed break in J in proportion to the square of the beam diameter, so long as that diameter be small compared to the diffusion length. (3) If there were no exchange of energy between the neutron beam and the graphite, i.e. if the inelastic scattering cross-section cm = 0, the neutrons of each energy interval would diffuse independently and the flux would fall off as exp [-x/L(v)], with L(v) the diffusion length. On the other hand, if there are jumps in L(v) there will be corresponding steps in the flux whose magnitude will increase with distance away from the radiating boundary of the moderator. A strong energy exchange between neutrons and graphite will not result in any observable effect; but with only a weak coupling, a constant flux discontinuity would be found at large distances from the boundary, situated in the same spectral region as the discontinuity in L(U), proportional to the size of the latter discontinuity and inversely proportional to cm. Bearing in mind that effects (1) and (3) are in-
to the observed break in the flux distribution are respectively 10, 35 and 55 per cent. It thus follows that the ratio J(u + Au)/J(u- Au) which should properly be ascribed to the weak energy exchange is 1.10. The ratio thus derived may now be employed to make an approximate calculation of the inelastic scattering cross-section of graphite, as follows. The mean number of elastic collisions which occur for every inelastic collision is
where ZS= &J,(u + Au) + cS(u - Au)]. The mean distance covered by the neutron in a straight line between two successive inelastic collisions is given by (s) 7 = 2FilI S t7 1, being the scattering length and 1, the transport mean free path, Now the step in the flux distribution is brought into existence only as a result of the diffusion that takes place between successive inelastic scattering events. Knowing L(u + Au) and L(u - Au) it is
A measurement
possible
to calculate
the known
J(u -
the mean
‘cleavage’
4~ + Au) AD)
of the neutron spectrum in the thermal column of the power-station
takes
distance
I over
which
place:
exp[--I/G + exp [-l/L(v
WI
=
REFERENCES
.
1. RAINWATER J. and
In the present instances we obtain I = 14 i 3 cm. Equating further 1 and l/(7) it is found that n = 10 f 4 ; whence
2. 3. 4.
Gin = 5,/n = 0.1~7~= 0.40 * O-16 barn 5.
in
good
agreement
with
the
determination
of
EGELSTAFF.‘~~) For
all three measured spectra the characteristic temperatures of the Maxwell distribution of best fit were consistent, being respectively 359,352 and 352°K each with a probable error of f 10°K. These results suggest a neutron temperature some 50°K higher than that of the moderator. In the case of the beam from the 10 cm hole the neutron temperature was also measured by the use of boron glass filters, giving the result 350 5 15°K. It is possible that the elevated temperature of the neutron gas may be caused in part by the presence of structural iron members within the graphite stack at a distance of 20 cm from the effective neutron source emnloved. I
J
79
Acknowledgements-Our thanks are due to A. K. KRASIN and B. G. DUBOVSKII for their interest and assistance, and to F. L. SHAPIROfor a valuable discussion of the early results.
1_1o
- AU)]
reactor
6. 7. 8. 9. 10.
HAVENS W. W., Phys. Rev. 70, 136 (1946). ZINN W. H., Phys. Rev. 71, 752 (1947). STURM W. J., Phys. Rev. 71, 751 (1947). Proceedings of the International Conference on the Peaceful Uses of Atomic Energy, Geneva 1955; Russian edition, p. 49 of Reaktorostroenie i Teoriya Reaktorov Academy of Sciences Publishing House (1955). ABOV Yu. G., Conference of the U.S.S.R. Academy of Sciences on the Peaceful Uses of Atomic Energy, Physical Sciences division, p. 209. Consultants Bureau (1955). LARSSON K. E., STEDMAN R. and PALEVSKY H., J. Nucl. Energy 6, 222 (1958). FERMI E., MARSHALL L. and MARSHALL J., Phys. Rev. 72, 193 (1947). HUGHES D. J., Pile Neutron Research. Addison Wesley (1953). HUGHES D. J., WALLACE J. R. and HOLTZMAN R. H., Phys. Rev. 73, 1217 (1948). TOLSTOV K.
D.,
SHAPIRO F.
L.
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