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| Fig. 1: Schematic of the experimental setup used to measure the total kinetic energy of fission fragments from neutron-induced fission of U-235. A thin uranium fissioning source is positioned between two symmetrically placed silicon surface-barrier detectors. (Image source: N. Ly, after N. N. Ajitanand and J. W. Boldeman. [3]) |
Nuclear fission is among the most energy-dense processes accessible to modern technology, releasing far more energy per reaction than chemical combustion. When a heavy nucleus such as U-235 undergoes fission, approximately 200 MeV of energy is released, with nearly 80% appearing as the kinetic energy of the resulting fission fragments. [1] Although theoretical models provide estimates for the average total kinetic energy released in U-235 fission, its magnitude will be addressed through experimental data. [1]
The energy released in a single fission event depends on the properties of the fission fragments and on how the energy is split among different forms, so it is not a fixed quantity. The excitation energy of the fully accelerated fragments consists of intrinsic excitation, collective excitations, and deformation energy, which arise at different stages of fission and determine the emission of neutrons and gamma rays. Because the mechanisms responsible for energy transfer experience fluctuations, experimental studies focus on characterizing energy distributions and behavior. [2]
In experiments, the energy released in nuclear fission is the kinetic energy of the fission fragments. The fission process releases approximately 200 MeV of energy, and the majority of this energy appears as the total kinetic energy (TKE) of the fragments. Experimental studies show that almost 80 % of the fission energy is carried by the fragment kinetic energy, while the remaining portion is distributed among prompt fission neutrons, gamma emission, delayed neutrons, and β decay. [1]
In a typical experimental setup Fig. 1, a fissioning source is positioned between two solid-state surface barrier detectors placed symmetrically on either side. The detectors, fabricated from n-type silicon, record pulse-height signals as charged fission fragments deposit energy in the detector material. A fast coincidence requirement ensures that only fragment pairs originating from the same fission event are recorded. The individual fragment kinetic energies are then reconstructed, and the total kinetic energy released in a single fission event is obtained from their sum. [3]
Repeating this measurement over many fission events shows that the energy follows a statistical distribution rather than a single value, shown in Fig. 2. For thermal and 500 keV neutrons, the most probable TKE value is approximately 170 MeV, while for 14 MeV incident neutrons this value shifts downward to about 166 MeV. Experimental results further indicate that the average TKE is energy-dependent, decreasing roughly from 170 MeV to 164 MeV as the incident neutron energy increases from 0.0253 eV to 17 MeV. [1]
Experimental data for U-235 show that this dependence can be described by the empirical fit
where En is the incident neutron energy in MeV.
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| Fig. 2: Total kinetic energy (TKE) distribution of post-neutron fission fragments for the 235U(n,f) reaction at an incident neutron energy of 14 MeV. The distribution is approximately Gaussian, with a most probable value near 166 MeV. (Image source: N. Ly, after C. Liu et al. [1]) |
To estimate the nuclear fuel mass required to sustain the electrical demand of a large metropolitan area, I consider the five-county Los Angeles metropolitan area, which has an average electrical consumption of approximately 14 GW. [4] The corresponding rate of U-235 mass consumption is
| 1.49 × 109 J s-1
× (235 × 1.67 × 10-27)
kg atom-1 1.70 × 108 eV atom-1 × 1.602 × 10-19 J eV-1 |
= | 2.14 × 10-4 kg s-1 |
The consumption per year is then
| 2.14 × 10-4 kg s-1 × 3600 s h-1 × 25 h d-1 × 365 d y-1 | = | 6.77 × 103 kg y-1 |
or 6.77 tonnes per year. In practical reactor operation, only a fraction of the uranium atoms in the fuel are fissioned before the fuel is discharged. In practical power reactor operation, typical end-of- irradiation burnup corresponds to fissioning only about 5% of the initial heavy-metal atoms, with the remaining fuel discharged despite still containing substantial unburned uranium. [5] The total mass of uranium fuel required per year is therefore
| 6.77 tonnes y-1 0.05 |
= | 135.4 tonnes y-1 |
Thus, sustaining a continuous electrical power output of 14 GW requires approximately 135 tonnes of unenriched uranium metal per year.
Even for a fixed initial isotopic composition, both the average energy released per fission and the heavy-metal mass change over the irradiation period due to breeding and transmutation of actinides. As new fissionable nuclides are produced, the ratio between fission energy release and heavy-metal mass is not constant. [5]
U.S. Nuclear Regulatory Commission guidance limits commercial reactor fuel enrichment to 5% U-235, making higher burnup and more complete fuel utilization challenging in licensed reactors. [6]
© Nathan Ly. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] C. Liu et al., "Calculation of the Fission Products For Neutron-Induced Fission of 235U," Nucl. Eng. Technol. 56, 1895 (2024).
[2] K. H. Schmidt and B. Jurado, "Erratum: Final Excitation Energy of Fission Fragments, Phys. Rev. C 83, 061061 (2011).
[3] N. N. Ajitanand and J. W. Boldeman, "Precise Measurements of the Average Kinetic Energy of Fragments in the Fission of 235U By Fast Neutrons," Nucl. Phys. A 144, 1 (1970).
[4] D. Burillo et al., "Forecasting Peak Electricity Demand For Los Angeles Considering Higher Air Temperatures Due to Climate Change," Appl. Energy 136, 1 (2019).
[5] G. Kepisty and J. Cetnar, "On the Discrepancies Between FIMA and Specific Burnup," Prog. Nucl. Energy 98, 187 (2017).
[6] I. O. Lindsay et al., "Fuel Performance Evaluation of Two High Burnup PWR Core Designs During Normal Operation, Control Rod Withdrawal, and Control Rod Ejection Scenarios," Nucl. Eng. Des. 415, 112730 (2023).