In inertial confinement fusion experiments, the neutron yield is an important metric for thermonuclear fusion performance. Neutron activation diagnostics can be used to infer neutron yields. The material used for neutron activation diagnostic undergoes a threshold reaction so that only neutrons having energies above the threshold energy are observed. For thermonuclear experiments using deuterium (D) and tritium (T) fuel constituents, neutrons arising from D + D reactions (DD-neutrons) and neutrons resulting from D + T reactions (DT-neutrons) are of primary interest. Indium has two neutron activation reactions that can be used to infer yields of DD-neutrons and DT-neutrons. One threshold is high enough that only DT-neutrons can induce activation, the second reaction can be activated by both DD-neutrons and DT-neutrons. Thus, to obtain the DD-neutron yield, the contribution made by DT-neutrons to the total induced activity must be extracted. In DD-fuel experiments, DT-neutrons arise from secondary reactions, which are significantly lower in number than primary DD-neutrons, and their contribution to the inferred DD-neutron yield can be ignored. When the DD- and DT-neutron yields become comparable, such as when low tritium fractions are added to DD-fuel, the contribution of DT-neutrons must be extracted to obtain accurate yields. A general method is described for this correction to DD-neutron yields.
I. INTRODUCTION
At the Sandia National Laboratories Z-facility, historically deuterium-fueled inertial confinement fusion (ICF) experiments have been conducted. The thermonuclear reactions in these experiments are dominated by the primary reactions of the deuterium fuel reacting with itself, which produces 2.45 MeV neutrons. A small fraction of the time, a secondary reaction takes place in which tritium (T), a product of a primary reaction, reacts with the deuterium (D) in the fuel and produces neutrons having energies centered about 14.1 MeV. The specific reactions are given in Table I.
Neutron yields have been inferred using the activation of indium (In) and copper (Cu). The activation reactions of interest are given in Table II. Since these are threshold reactions, only neutrons above the threshold energy are capable of inducing activity. The elastic scattering nuclear reaction with indium1 has a threshold energy of 0.38 MeV and is used to measure neutrons arising from D + D reactions (DD-neutrons). The In115(n,2n) reaction and the Cu63(n,2n) reaction have thresholds of 9.66 MeV and 11 MeV, respectively. Thus, these reactions can be used to measure the secondary D + T reaction neutrons (DT-neutrons) and are not sensitive to DD-neutrons. We measure the induced activity of the In114 by measuring the 190 keV gamma rays that are emitted. To measure the activity of the Cu62 produced, a coincidence system is used to detect the 511 keV annihilation gamma rays in coincidence, which are produced following the positron decay.
Activation reactions of inferring neutron yields.
| Reaction | Threshold energy (MeV) | Photon energy (keV) | Half-life (τ1/2) |
|---|---|---|---|
| 115In(n,n’)115mIn(γ) | 0.38 | 336 | 4.49h |
| 115In(n,2n)114In(γ) | 9.66 | 190 | 49.5d |
| 63Cu(n,2n)62Cu(β+) | 11 | 511 | 9.6m |
| Reaction | Threshold energy (MeV) | Photon energy (keV) | Half-life (τ1/2) |
|---|---|---|---|
| 115In(n,n’)115mIn(γ) | 0.38 | 336 | 4.49h |
| 115In(n,2n)114In(γ) | 9.66 | 190 | 49.5d |
| 63Cu(n,2n)62Cu(β+) | 11 | 511 | 9.6m |
These secondary DT-neutrons will also drive the In115(n,n′) inelastic scattering reaction, and therefore, the DT-neutron contribution to the total In115m activity must be extracted before the DD-neutron yield can be determined. Fortunately, we can reasonably assume that the secondary DT-neutron contribution to the total In-115m activity can be ignored in determining the DD-neutron yield. This assumption is justified because maximum observed secondary DT-neutron yields are about 1% of the DD-neutron yield in a given experiment and often much less due to the ion temperatures present in these experiments, which are approximately 2–4 keV.2 Thus, the corrections to the DD-neutron yield due to DT reaction neutrons are at most 1%, while the overall uncertainty of the measurement is on the order of 20% (see Sec. IV).
As ICF experiments have matured at the Z-facility, there has been an interest in adding trace amounts of tritium to the typical DD-fuel. Since the fusion cross section for DT reactions is approximately two orders of magnitude higher than the DD reaction cross section for the ion temperatures present in the experiment, introducing trace amounts of tritium (a few percent) to the DD fuel will result in comparable yields from the two reactions. There is utility in using the existing neutron activation infrastructure to determine neutron yields, however, the analysis becomes more complex due to the non-negligible contribution to the indium activation from the neutrons produced by the DT reactions. The remainder of this document will detail the problem and the proposed solution.
II. NEUTRON ACTIVATION ANALYSIS FOR TRITIUM FRACTION ADDED TO DD FUEL
As trace amounts of tritium are added to the DD fuel, the number of DT-neutrons produced in the experiment increases to the point where their contribution to the activity of indium becomes non-negligible. Hence, determining the DD-neutron yields becomes more complicated than for a pure DD-fueled experiments. Importantly, the scattering environment plays an important role in the DT contribution to that level of activation. Shown in Fig. 1, is the neutron activation cross-section for indium leads to the decay path where 336 keV gammas are emitted.3 Clearly, as DT-neutrons down-scatter to lower energies, the inelastic cross section for producing In115m increases, so the scattered DT-neutrons have a higher probability of producing In115m than do the primary 14.5 MeV DT-neutrons.
For a DT fuel mixture, the activity measured by counting the 336 keV gammas, cannot directly be used to infer the DD-neutron yield since the number of activated nuclei is the sum of the number activated by DD neutrons, DT neutrons and other neutron producing reactions [such as the 9Be(D,n) reaction arising from energetic D ions interacting with the beryllium target liner.] If we assume the contribution due to non-thermal neutrons is negligible and can be ignored, the number of activated nuclei is the sum of the DD-neutron activated nuclei and the DT-neutron activated nuclei,
To quantify the number of DT-neutron nuclei activated in indium resulting in 336 keV gammas (used to infer the DD-neutron yield), knowledge of the DT-neutron yield is needed.
III. CORRECTION TERM FOR DD-NEUTRON YIELDS WITH SMALL FRACTION OF TRITIUM ADDED TO DD FUEL
First, consider the expression used to infer neutron yield from an activation sample where there is only one activation channel of interest that is activated by one species of thermonuclear produced neutrons. The yield is given by the following expressions:
In those expressions, N0 is the number of activated nuclei at the end of implosion, m is the mass of the sample, F is the detector calibration, h is a scattering correction, ⟨d2⟩ is the mean of the distance squared (from the source to the sample), cnet is the number of counts in the peak minus the background, l is the decay constant (ln(2)/t1/2), t1 is the start of gamma collection with respect to the implosion, and t2 is when the gamma collection stopped with respect to the implosion. Re-writing this as an expression for the number of counts, one obtains the following expression:
In this expression, the yield is our source term. The remaining terms relate to geometrical, scattering, detector calibration, and data collection times. The manner in which this is written is important due to the method used for our detector calibrations, F, and scattering corrections, h. As shown in Table I, our calibration for a given detector is for the collection gamma energy (190, 336 keV) and for a specific source neutron type (DD or DT source neutrons). Similarly, our scattering corrections, h, are determined for a particular activation material and activation reaction, at a specific geometric location and a source neutron energy (either DD- or DT-neutrons) (Tables III and IV).
Calibration F-factors for each germanium detector counting system (Ge No. 1 – Ge No. 6) for either DD- or DT-neutrons inducing activity that results in either 190 or 336 keV gamma emission, as indicated in the column labels.
| Detector | DD 336 keV | DT 336 keV | DT 190 keV |
|---|---|---|---|
| Ge No. 1 | 3.078 × 10−5 | 6.522 × 10−6 | 4.752 × 10−5 |
| Ge No. 2 | 3.672 × 10−5 | 7.145 × 10−6 | 3.496 × 10−5 |
| Ge #3 | 3.210 × 10−5 | 7.200 × 10−6 | 3.160 × 10−5 |
| Ge No. 5 | 4.984 × 10−5 | 1.038 × 10−5 | 4.916 × 10−5 |
| Ge No. 6 | 2.910 × 10−5 | 7.786 × 10−6 | 3.990 × 10−5 |
| Detector | DD 336 keV | DT 336 keV | DT 190 keV |
|---|---|---|---|
| Ge No. 1 | 3.078 × 10−5 | 6.522 × 10−6 | 4.752 × 10−5 |
| Ge No. 2 | 3.672 × 10−5 | 7.145 × 10−6 | 3.496 × 10−5 |
| Ge #3 | 3.210 × 10−5 | 7.200 × 10−6 | 3.160 × 10−5 |
| Ge No. 5 | 4.984 × 10−5 | 1.038 × 10−5 | 4.916 × 10−5 |
| Ge No. 6 | 2.910 × 10−5 | 7.786 × 10−6 | 3.990 × 10−5 |
Estimate of errors for the quantities in yield expressions.
| Quantity | Uncertainty (%) |
|---|---|
| cnet | 1–5 |
| d | 1 |
| m | 1 |
| t | 1 |
| h | 10 |
| F | 8 |
| Ydt | 17 |
| Quantity | Uncertainty (%) |
|---|---|
| cnet | 1–5 |
| d | 1 |
| m | 1 |
| t | 1 |
| h | 10 |
| F | 8 |
| Ydt | 17 |
For a DT mixed fuel implosion, the 115In(nDD,n′)115mIn activation, which results in the emission of 336 keV gammas, has contributions from both DD- and DT-neutrons (ignoring non-thermal nuclear neutron sources.) The data collected to determine the number of activated nuclei is the number of net counts (counts in peak minus background) in the gamma peak centered at E = 336 keV during the period between t1 and t2 and results from a combination of DD- and DT-neutrons,
In the expression above, the second term is determined by the DT-neutron yield. The F-factors are for are for 115In(nDD,n’)115mIn activation, the first being with DD source neutrons and second for DT source neutrons. The h terms are scalars that relate the 115In(nDD,n’)115mIn activation of the sample in the experiment to the calibration, and are found using MCNP®. The first term is for DD source neutrons and the second is for DT source neutrons. Factoring out the common terms and explicitly noting the DD and DT specific terms, we get
Then solving for YDD, we get
The equation above is the general formulation for determining the DD-neutron yield for fractional tritium added to DD-fuel. The first term on the right-hand side of the equation is the solution one would use when no tritium was added to the fuel. The second term is the correction based upon the DT-neutron yield, which can be determined using zirconium and copper activation, in addition to indium. We also note that the experiments fielded have significant mass and complex geometries that attenuate and scatter the fusion neutrons born in the center. These geometries are constantly evolving, which necessitates a continuous reevaluation of the h factors needed to determine the yields.
IV. INFERRING DD- AND DT-NEUTRON YIELDS FROM EACH INDIUM ACTIVATION SAMPLE FOR SMALL FRACTION OF TRITIUM ADDED TO DD FUEL
The indium neutron activation reactions shown in Table II can be used for inferring DD- and DT-neutron yields.1 The lower activation energy reaction has been discussed earlier in this document for inferring DD-neutron yields but is also activated by DT-neutrons. To determine the DD-neutron yield, the contribution due to DT-neutrons must be removed. The higher activation threshold energy nuclear reactions can be used to infer DT-neutron.
In the interesting case in which one would use each sample to measure both the DD- and DT-neutron yield and then report the yields for the experiment as the mean of those measurements, the following expressions could be used.
First, the DT-neutron yields are needed.
Reporting DT-neutron yield as the mean of those measurements,
Second, the DT-neutron yield corrections to obtain the DD neutron yield must be made,
Estimates for the uncertainties of quantities1,4 involved in the DD-neutron yield expression are given in the table below.
V. CONCLUSION
Indium neutron activation can be used to infer both DD- and DT-neutron yields. Although the (n, n′) reaction used to infer DD-neutron yield is also activated by DT-neutrons, a correction can be used to obtain a DD-neutron yield. This method relies on the DT-neutron yield, appropriate calibration factors, and neutron transport corrections. Due to the increased uncertainty of the correction term, there are limitations to this method, primarily driven by the tritium fraction and scattering environment present in the experiment.
ACKNOWLEDGMENTS
Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC (NTESS), a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration (NNSA) under Contract No. DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
M. A. Mangan: Formal analysis (equal). C. L. Ruiz: Conceptualization (equal). G. W. Cooper: Conceptualization (equal). G. A. Chandler: Resources (equal). D. J. Ampleford: Supervision (equal).
DATA AVAILABILITY
Data sharing is not applicable to this article as no new data were created or analyzed in this study.
