Nuclear Instruments and Methods 216 (1983) 219-226 219 North-Holland Publishing Company

T H E R M A L N E U T R O N D R I V E N , 14.1 M e V N E U T R O N G E N E R A T O R S

W i l l i a m H. M I L L E R , W.S. L A W and R o b e r t M. B R U G G E R

Nuclear Engineering, University of Missouri, Columbia, Missouri 65211, USA

Received 7 October 1982 and in revised form 1 March 1983

A detailed theoretical and experimental study of the production of 14.1 MeV neutrons from thermal neutrons using simple convertors has been performed. These convertors rely on the absorption of a thermal neutron resulting in a triton which interacts with deuterium producing a 14.1 MeV neutron. Three different systems have been studied: 6 LiD, 6 LiOD_D20 and 3 He D 2. In general the agreement between theory and experiment is good and demonstrated efficiencies of approximately 2 x 10 4 are observed. Based upon these results, theoretical optimization studies have been performed and possible applications have been discussed.

1. Introduction

There exists a variety of needs for high energy neu- trons (above approximately 10 MeV) for basic neutron studies. These include fusion-related research efforts (including neutron damage studies), neutron transport and shielding studies, and neutron detector calibration studies. There are also interesting applications in the area of fast neutron activation analysis. To satisfy these needs several fast neutron sources are available, based upon accelerator devices. This work describes and evaluates an alternative source of fast neutrons.

The deuter ium-tr i t ium ( D - T ) fusion reaction is a well-known source of 14.1 MeV neutrons and is used in some of the accelerator devices mentioned above. Ther- mal neutrons can be used to create energetic tritons which can subsequently interact with deuterium to also produce 14.1 MeV neutrons, thus creating an alternative source of fast neutrons. Thermal neutron reactions which lead to tritons include:

nth + 3 H e ---, t + p + 764 keV, (1)

nth +6Li ~ t + 4 H e + 4.79 MeV. (2)

If one of these reactions also takes place in a deuterium-containing material, there is a probability that a 14.1 MeV neutron will be produced. Such materi- als include: D 2, 6LiD and 6 L i O D - D 2 0 . The total reac- tions may then be written:

3He + D2 + nth ~ n14.1MeV -~- P +4He , (3)

6LiD + n t h ~ n14.1 MeV + 2(4He), (4)

6LiOD + DzO + nth --* n|4.1 MeV q- 2(4He) + " ' " (5)

Preliminary theoretical evaluations of reactions (4) and (5) have already taken place. Frigerio [1] has theo- retically studied reactions (4) and (5) and reported

efficiencies of 1.7 x 10 -4 and 2.1 x 10 5, respectively. (The efficiency is defined as the number of 14.1 MeV neutrons produced per thermal neutron incident upon the sample.) Almquist [2] reported a theoretical ef- ficiency of reaction (5) of 1.2 x 10 - 4 . Based upon these data, Napier et al. [3] reported the design of an in-core fast-neutron generator based upon reaction (5). An ex- periment was conducted and an efficiency of 2.5 x 10 - 4

was reported. Unfortunately, an error in these measure- ments was noted by Wysocki and Griffin [4] and acknowledged by Eckhoff [5]. Some work has also been reported by Greenspan [6] at Princeton, which indicated "marg ina l" efficiencies (specific data from this report have not been obtained by the authors of this work).

Based upon this survey of the literature, it is difficult to ascertain the efficiency of these reactions and their potential as useful devices. In particular, reaction (3) has not been studied and may have some advantages. This paper describes new theoretical and experimental work in the evaluation of these fast neutron sources.

2. Theory

To obtain a useful thermal neutron to fast neutron convertor, it is important to maximize the conversion efficiency (i.e., the ratio of the number of 14.1 MeV neutrons produced per thermal neutron incident upon the convertor). This efficiency is a function of the thermal neutron cross-section, the slowing down poten- tial of tritons in the deuterium containing material, and the D - T interaction cross-section of the sample.

The cross-section for the D - T reaction [7] (where the triton is the projected particle) is shown in fig. 1. This cross-section peaks at approximately 160 keV and decreases with increasing triton energy to a negligible

0167-5087/83/0000-0000/$03.00 © 1983 North-Hol land

220 PlLH. Miller et al. / 14.1 M e V neutron generators

7~ Z

If}

Z 0 t - U b~ o,)

0

(J

/

o o

f 5\\\ / \ \ / I ~, ~ . . . . T(d,n) 4 He (WHERE THE ENERGY IS THAT OF THE DEUTERON)

V \ o ,

i l i I = I i I i I

200 400 600 800 I000

ENERGY (keY)

Fig. 1. Cross section for the D - I reactmn.

value above 1 MeV. The D - T interaction probability is proportional to the area under the curve in fig. 1 integrated from the initial triton energy down to zero. To maximize this probability, it is advantageous to have an initial triton energy as large as possible, although energies above approximately 1 MeV contribute little additional interaction probability.

Competing with this D - T reaction is the loss of triton energy by ionization as it passes through the convertor material. In fact, this is the predominate reaction accounting for the slowing down or loss of most of the tritons. The loss of energy by ionization is defined by the Bethe equation [8] or by other semi-em- pirical slowing down models [9,10]. To minimize slow- ing down losses of tritons, one would like to reduce the number of atoms that are not deuterium (i.e., not a target for the D T reaction). The convertor material should also have an atomic number (which is propor- tional to the electron density) as low as possible.

Returning to the three possible convertor materials given by reactions (3), (4) and (5) in Sect. 1, the relative merits of each can be considered in light of the compet- ing effects of D - T interaction and triton slowing down. For reaction (3) the triton born with the absorption of a thermal neutron by 3He has an energy of 191 keV. From fig. 1 it is apparent that the D - T interaction probability will be only about 20% of that possible with a triton energy above 1 MeV. On the other hand, the materials in this convertor have atomic numbers of only 1 and 2 (resulting in a low electron density and there-

fore less triton loss through ionization). In addition, the materials in reaction (3) are both gases which can be mixed in any proportion to maximize 14.1 MeV neutron generation efficiency.

For reactions (4) and (5), the tritons have a maxi- mum energy of 2.74 MeV resulting in essentially the highest possible integral cross-section for the D T reac- tion. For 6 LiD the atomic numbers are now 1 and 3, so there will be more specific energy loss due to ionization as compared to the 3He + D 2 system. In the 6LiOD + D20 convertor with the high atomic number for oxygen there is an even greater loss due to ionization. However, in reaction (5) the ratio of 6Li to D can be varied [similar in this regard to reaction (3)], whereas the ratio cannot be changed for reaction (2).

To theoretically evaluate these various reactions, a theoretical model was developed to predict convertor efficiency. The conversion process involves several steps: 1) absorption of the thermal neutron and production of

a triton; 2) the slowing down of triton and possible interaction

with deuterium, resulting in a 14.1 MeV neutron; 3) the escape of the 14.1 MeV neutron from the conver-

tor. If the convertor thickness is assumed to be on the order

of 1 cm, then two simplifying assumptions can be made: 1) The range of the triton (usually less than 0.5 mm) is

small in comparison to the size of the sample, so triton leakage can be ignored.

2) The probability of the resulting 14.1 MeV neutron

I, KH. Miller et al. / 14.1 M e V neutron generators 221

being absorbed or scattered by the convertor is small. Thus the efficiency becomes:

eff = fo le - ~'X Y~ ad xP t )T , (6)

where S t = the thermal neutron total cross-section of the

convertor material; -Ya = t h e thermal neutron absorption cross-section of

the convertor material; l = the sample thickness; PDT = probability of a triton interacting with deuterium

during the slowing down process. Since PDT is not a function of x, the integration results in:

Y-a e z j ) . eff = ~ t PDT ( 1 -- (7)

The calculation of PDT requires numerical integra- tion of the cross-section given in fig. 1 along with a knowledge of the slowing down function. The semi-em- pirical formulation of Anderson [9] has been used to describe the loss of energy of tritons by ionization. Slowing down was calculated in many small energy steps (typically 1000) from its initial energy to zero energy. For each energy increment, the corresponding path length was calculated and the probability of inter-

action with a deuteron was calculated based upon the D - T cross-section at that energy. These probabilities were then summed to calculate POT'

3. Experimental measurements

To experimentally verify the results predicted by the theoretical model, measurements have been carried out using the " A " beam port of the University of Missouri Research Reactor (MURR). The " A " beam port is ideally suited for these measurements with an available t he rma l neu t ron b e a m of 3.5 × 10 8 the rmal neu t rons / cm 2 s. The experimental arrangement is shown in fig. 2. By using this geometry, any background of high energy neutrons from fission at the detector is essentially eliminated. The U M C NE-213 fast neutron spectrometer system [11] is used to accurately and effi- ciently detect 14.1 MeV neutrons from the convertor.

Thin aluminum-walled, cylindrical containers (ap- proximately 2.8 cm in diameter by 5.1 cm long) were built to hold the sample materials. For the 3He + D 2 system, a 3He partial pressure of 0.427 MPa (62 psia) was used in combination with D 2 partial pressures of 0.427, 0.855 and 1.28 MPa (62, 124 and 186 psia). Powdered 6LiD was loaded into another container un-

DETECTOR

co. t /

/ BIOLOGICAL SHIELD

THERMAL NEUTRONS

SHIELDING

SAMPLE 4eV NEUTRONS I I BEAMSTOP

Fig. 2. Experimental geometry.

222 VILH. Miller et al. / 14.1 M e V neutron generators

der an inert atmosphere. This sample was weighed to determine the densi ty of the powder which was signifi- cant ly less than that of solid 6LID. A saturated solution (13 wt%) of 6LiOD in D20 was formed by carefully adding 6LiD to D 2 0 under an inert atmosphere.

The magni tude of the thermal flux incident on the sample was checked using gold flux wires and found to be (3.66 + 0.20) × 108 n e u t r o n s / c m 2 s.

4. Results and discussion

Table 1 summarizes theoretical efficiencies obta ined in this work as compared to the results reported previ- ously by other authors. The new data presented here utilize sample thicknesses sufficient to stop essentially all of the thermal neutrons and therefore represent op t imum results.

In general 6LiD efficiencies calculated here are in reasonable agreement with the results from previous work. The 6 L i O D - D 2 0 results are quire variable. The new work is in good agreement with the result reported by Almquis t and is reasonably close to the retracted value reported by Napier. It does not agree well with the value reported by Frigerio. It is possible that these differences are due to different convertor composi t ions (i.e., natural Li vs. 6Li or the weight percent of 6LiOD in solution). The 3He + D 2 results are somewhat less than for the other convertors, but not enough so to rule out this system. In particular, as the D 2 to 3He ratio is increased, the efficiency improves and asymptotically approaches a value of about 0.6 X'I0 -4.

Other interesting convertor parameters are given in table 2. The tri ton path lengths in all convertors are less than 0.2 ram, which validates the assumption made in the theory section. The " o p t i m u m " thickness is defined as the thickness necessary to stop essentially all of the

thermal neutrons in the sample. Lesser thicknesses have lower conversion efficiencies. The sample thickness for the 3 H e + D 2 mixture is based upon a 3He partial pressure of 0.427 MPa (62 psia). The " o p t i m u m " path length is inversely proport ional to the pressure and could be easily reduced from 11.0 cm by raising the pressure.

Experimental ly measured neut ron spectra from the NE-213 spectrometer are shown in fig. 3 for the 3He + D 2 convertor. The presence of 14.1 MeV neutrons is obvious and demonst ra tes the ability of this experimen- tal procedure to accurately measure convertor efficien- cies. The increase in conversion efficiency as the D 2 part ial pressure is increased is apparent . A "back - g round" measurement was also taken using a 4 He + D 2 mixture to confirm that the peak in the spectrum at 14.1 MeV was actually from neutrons produced by the con- vertor.

Table 1 also summarizes a comparison between ex- per imental measurements and theoretical results. As can be seen, the agreement is reasonably good in all cases, a l though the experimental results for all convertors give a higher efficiency than predicted by the theory. Fig. 4 shows experimental and theoretical results for the 3He + D 2 convertors as the D 2 partial pressure is increased and calculated uncer ta inty bars have been shown.

Experimental uncertaint ies are calculated by propa- gating errors associated with the uncertainty of the measured thermal flux, the unfolded neut ron spectrum, and the geometry of the experiment (i.e., source to detector distance, partial detector i l luminat ion correc- t ion factor, non-uni form thermal neut ron i l luminat ion of the sample container, etc.). The total error is esti- mated to be +20%. For the theoretical results, two pr imary sources of uncer ta inty are identified: (1) the one-dimensional model assumption and (2) the accuracy of the slowing down model. The latter is most signifi-

Table 1 14 MeV conversion efficiencies.

Frigerio [ 1 ] Almquist [2] Napier [3] Miller,

theoretical

Miller, experimental

6 LiD

1.7 × 10 -4

1.5× 10 -4

2.1× 10 4

6LiOD-D20

0.21 x 10 4 1.2× 10 4 2.5× 10 4a)

0.92×10 4b)

1.7 × 10 -4 b)

3He-Dz

0.43 X 10 4(1:1) c) 0.54X 10 4(1:2) ~) 0.58 X 10 4(1:3)~)

0.63× 10-4(I :1) c) 0.87 × 10 4(1:2) c) 1.00× 10 4(1:3)c)

a) Later retracted (see ref. 4 and 5). b) Assumes 13 wt% LiOD in D20. c) (1 : l) denotes 3He to D 2 ratio.

W.H. Miller et aL / 14.1 M e V neutron generators

Table 2 Miscellaneous, calculated convertor parameters.

223

Reaction Material Mixture Triton Optimum Efficiency range thickness (calculated) (mm) (cm)

1 3He+ D 2 1 part 3He to 0.18 11.0 0.6× 10 4 3 parts D at 1.71 MPa

2 6LiD - 0.055 0. l 1.5x l0 4

3 6LiOD + D20 13.6 wt% LiOD 0.040 0.8 0.9 × 10 4 in D20

0 . 6

0 . 4

°'E 0 . 2

(/-) Z 0 n,* l--

14J Z

X

X

X

X

X

X

X I : t 3He:O 2 RATIO

0 1:2

1:5

4

0 I

0 5 I0

X

X ~

X \

x/ i o X

He:~ 2 B ACKGROUNO

/t /

N E U T R O N ENERGY ( M e V )

Fig. 3. Experimentally measured spectra using NE-213 spectrometer.

~IoA

15

224

1.5

W.H. Miller et al. / 14.1 M e V neutron generators

q.

b

Z " ' 0 . 5 (J b. b. LIJ

1.0

/ J

A E X P E R I M E N T A L

0 T H E O R Y

0 , I J I ~ I , •

I :1 1:3 1:5 1:7 1:9

3 H e : D 2 P A R T I A L P R E S S U R E R A T I O

Fig. 4. Comparison of experimental and theoretical results for the 3He-D2 system as a function of gas ratio.

cant. Preliminary theoretical work indicated that the model used (i.e., data from ref. 9 versus ref. 10) could vary the result by +20%. Thus a +25% theoretical uncer ta inty has been assumed. As a result, the experi- menta l and theoretical results agree within one s tandard deviation, but the trend in this data indicates a sys- tematic error. This is most likely due to either the slowing down model in the theoretical results or a systematic error in the normalizat ion of the experimen- tal results.

5. Further efficiency optimization

Based upon the results in the previous section, it appears that all of the convertors have approximately the same efficiency, with the 6LiD system showing somewhat of an advantage. The 3He + D 2 system has the inherent disadvantage of a low initial tr i ton energy but the decrease in the loss of tr i tons by ionization almost overcomes this deficiency. Al though the 6LiOD + D20 system allows variat ion of the deuter ium con- tent, the ionization losses due to oxygen seem to over- come this advantage. (This system may improve some- what with fur ther study.) The combina t ion of the higher tr i ton energy from 6Li along with the relatively smaller ionizat ion losses gives the 6LiD system the best overall efficiency.

Based upon these indications, it is possible to hypo- thesize systems which would have an even greater ef- ficiency. An op t imum system would have tri tons which were born from 6Li which would slow down entirely in a deuter ium gas. If the system were heterogeneous with small microspheres of 6Li (whose size is much less than the range of tr i t ium in 6Li) suspended in deuter ium gas, a higher efficiency could be realized. Such a hypothet i- cal system has been theoretically evaluated. Assuming an infinitely dilute system of 6Li in D 2 gas, an op t imum efficiency of 5.0 × 10 -4 has been calculated, an increase of a factor of three over the 6LiD result. This represents a theoretical op t imum value. A more "prac t i a l " system which assumes 200/~m 6Li microspheres of 6Li and 95% D 2 gas results in an efficiency of 2.6 × 10 -4. The prob- lem with the system is mainta in ing a " suspens ion" of 6Li in the D 2 gas, but these results do indicate that some addi t ional opt imizat ion may be possible. These results would be 30% higher based upon the experimen- tal measurements made in this study.

6. Applications

Assuming the efficiencies for 14.1 MeV conversion which have been demons t ra ted in the laboratory, some est imates can be made as to practical applicat ions of

HCH. Miller et aL / 14.1 M e V neutron generators 225

i0 ~e

u FAST-FISSION SPECTRUM ~ ~ A / P L U S 14 MeV NEUTRON

~E X , " ~ ~ GENERATED SOURCE

x _ THREE METERS FROM

"J ~ FIRST WALL u_ 10 8 z 0 n- k-

tu ~, / A T TF COIL z

I ' i0 4 I I I I I i 0 2 10 4 10 6 10 8

NEUTRON ENERGY ( e V I

Fig. 5. Hypothetical "mixed field" spectrum as compared to fusion device spectra.

these generator systems. One area is that of fast neu t ron act ivat ion analysis. In the central th imble of the M U R R the thermal flux is 6 × 1014 n / c m 2 s and the result ing 14.1 MeV flux from a conver tor would be approxi- mately 1.0 × 10 I1 n / c m 2 s. This represents an approxi- mate increase of 5 in the n u m b e r of neut rons above 14 MeV (due to fission alone) and a factor of 25 increase in the n u m b e r of neutrons in the 14.0-14.2 MeV energy band . This increase in fast neut rons results in an in- crease in the act ivat ion of 14N and 19F on the order of a factor of 50 (due to the high neu t ron energy thresholds of these reactions). Similar results are obta ined in sam- ple i r radiat ion posit ions in the M U R R al though all fluxes are reduced by a factor of 3.

The beam port geometry used in this work to de- te rmine the efficiencies of these conver tors can also be used for detector cal ibra t ion work. As shown in fig. 3, the resulting neu t ron spect rum is quasi -monoenerget ic at 14.1 MeV down to about 5 MeV (at which point background neut rons are detected). All that is required for this source is a small sample of 6LiD and a thermal neu t ron source. By modifying the geometry and placing

the convertor near the core end of the beam tube, a mixed field of neut rons can be produced. This neut ron spectrum will consist of 14.1 MeV neutrons superim- posed upon the fission neu t ron spectrum as shown in fig. 5. As can be seen, this spect rum closely resembles a fusion device spectrum and, with some spectrum tailor- ing, can be modif ied to represent different points in a fusion energy device. Such a beam could be used for neu t ron t ranspor t studies. The absolute n u m b e r of 14.1 MeV neut rons present at the experimental area end of the beam tube at the M U R R would be on the order of 6 x 10 6 n / s which is more than sufficient for the highly efficient NE-213 spectrometer used in this work. Thus, such a system could be used for integral t ranspor t measurements of 14.1 MeV neutrons through materials of interest. Al though the flux magni tude may not be great enough for actual material damage studies in a fusion device neu t ron envi ronment (a l though some re- searchers are now observing damage in Si at these levels), some work on damage coefficients could be performed.

226 W.H. Miller et al. / 14.1 M e V neutron generators

7. Conclusion References

Theoretical calculat ions and experimental measure- ments have been performed to evaluate the effectiveness of producing 14.1 MeV neutrons f rom thermal neutrons in a simple convertor. In general, the agreement be- tween theory and exper iment is good for three different types of convertors. This includes the 3He + D 2 system which had not been studied previously.

Maximum demonst ra ted conversion efficiencies of between 1.5 and 2.1 x 10 -4 are readily available for the LiD system. Fur ther theoretical calculations suggest an absolute maximum efficiency of 5.0 x 10 -4. Assuming the demonst ra ted efficiency of approximately 2 x 10 4 several potent ial applicat ions have been discussed which include neut ron activation analysis, detector calibration, neu t ron t ranspor t and possibly neut ron damage. In particular, the neut ron activation of ~4N and 19F are

significantly enhanced. It is recognized that the efficiencies demonst ra ted

here may provide only marginal utility for these conver- tors. However, now that these efficiencies have been accurately quantified, the assessment of utility can be made on a sound basis.

[1] N.A. Frigerio, Division of Biological and Medical Re- search Annual Report, ANL-7870, Argonne National Laboratory (1971).

[2] E. Almquist, Can. J. Res. A28 (1950) 433. [3] B.A. Napier et al., Nucl. Instr. and Meth. 138 (1976) 463. [4] C.M. Wysocki and H.C. Griffin, Nucl. Instr. and Meth.

156 (1978) 605. [5] N.D. Eckhoff and J.G. Marklin, Nucl. Instr. and Meth.

156 (1978) 607. [6] E. Greenspan, Report MATT-923, Princeton University

(Sept., 1972). [7] H. Liskien and A. Paulson, Nucl. Data Tables 11 (1973)

569. [8] E. Segr+ and H.A. Bethe, Experimental nuclear physics,

vol. 1, part 2 (Wiley, New York, 1960). [9] H.H. Andersen and J.G. Ziegler, Hydrogen: stopping

powers and ranges in all elements (Pergamon, New York, 1977).

[10] C.F. Williamson et al., Report CEA-R 3042 (1966). [11] W.H. Miller and W. Meyer, NSF-GK-40728-UMC-2

(Available from NTIS) (1975).