Define 6th factor (relief)
Answers
Answered by
0
The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium.
six-factor formula: {\displaystyle k=\eta fp\varepsilon P_{FNL}P_{TNL}}[1]SymbolNameMeaningFormulaTypical Thermal Reactor Value{\displaystyle \eta }Thermal Fission Factor (Eta)The number of fission neutrons produced per absorption in the fuel.{\displaystyle \eta ={\frac {\nu \sigma _{f}^{F}}{\sigma _{a}^{F}}}}1.65{\displaystyle f}The thermal utilization factorProbability that a neutron that gets absorbed does so in the fuel material.{\displaystyle f={\frac {\Sigma _{a}^{F}}{\Sigma _{a}}}}0.71{\displaystyle p}The resonance escape probabilityFraction of fission neutrons that manage to slow down from fission to thermal energies without being absorbed.{\displaystyle p\approx \mathrm {exp} \left(-{\frac {\sum \limits _{i=1}^{N}N_{i}I_{r,A,i}}{\left({\overline {\xi }}\Sigma _{p}\right)_{mod}}}\right)}0.87{\displaystyle \varepsilon }The fast fission factor (Epsilon)total number of fission neutrons/number of fission neutrons from just thermal fissions{\displaystyle \varepsilon \approx 1+{\frac {1-p}{p}}{\frac {u_{f}\nu _{f}P_{FAF}}{f\nu _{t}P_{TAF}P_{TNL}}}}1.02{\displaystyle P_{FNL}}The fast non-leakage probabilityThe probability that a fast neutron will not leak out of the system.{\displaystyle P_{FNL}\approx \mathrm {exp} \left(-{B_{g}}^{2}\tau _{th}\right)}0.97{\displaystyle P_{TNL}}The thermal non-leakage probabilityThe probability that a thermal neutron will not leak out of the system.{\displaystyle P_{TNL}\approx {\frac {1}{1+{L_{th}}^{2}{B_{g}}^{2}}}}0.99
The symbols are defined as:[2]
{\displaystyle \nu }, {\displaystyle \nu _{f}} and {\displaystyle \nu _{t}} are the average number of neutrons produced per fission in the medium (2.43 for Uranium-235).
{\displaystyle \sigma _{f}^{F}} and {\displaystyle \sigma _{a}^{F}} are the microscopic fission and absorption cross sections for fuel, respectively.
{\displaystyle \Sigma _{a}^{F}} and {\displaystyle \Sigma _{a}} are the macroscopic absorption cross sections in fuel and in total, respectively.
{\displaystyle N_{i}} is the number density of atoms of a specific nuclide.
{\displaystyle I_{r,A,i}} is the resonance integral for absorption of a specific nuclide.
{\displaystyle I_{r,A,i}=\int _{E_{th}}^{E_{0}}dE'{\frac {\Sigma _{p}^{mod}}{\Sigma _{t}(E')}}{\frac {\sigma _{a}^{i}(E')}{E'}}}.
{\displaystyle {\overline {\xi }}} is the average lethargy gain per scattering event.
Lethargy is defined as decrease in neutron energy.
{\displaystyle u_{f}} (fast utilization) is the probability that a fast neutron is absorbed in fuel.
{\displaystyle P_{FAF}} is the probability that a fast neutron absorption in fuel causes fission.
{\displaystyle P_{TAF}} is the probability that a thermal neutron absorption in fuel causes fission.
{\displaystyle {B_{g}}^{2}} is the geometric buckling.
{\displaystyle {L_{th}}^{2}} is the diffusion length of thermal neutrons.
{\displaystyle {L_{th}}^{2}={\frac {D}{\Sigma _{a,th}}}}.
{\displaystyle \tau _{th}} is the age to thermal.
six-factor formula: {\displaystyle k=\eta fp\varepsilon P_{FNL}P_{TNL}}[1]SymbolNameMeaningFormulaTypical Thermal Reactor Value{\displaystyle \eta }Thermal Fission Factor (Eta)The number of fission neutrons produced per absorption in the fuel.{\displaystyle \eta ={\frac {\nu \sigma _{f}^{F}}{\sigma _{a}^{F}}}}1.65{\displaystyle f}The thermal utilization factorProbability that a neutron that gets absorbed does so in the fuel material.{\displaystyle f={\frac {\Sigma _{a}^{F}}{\Sigma _{a}}}}0.71{\displaystyle p}The resonance escape probabilityFraction of fission neutrons that manage to slow down from fission to thermal energies without being absorbed.{\displaystyle p\approx \mathrm {exp} \left(-{\frac {\sum \limits _{i=1}^{N}N_{i}I_{r,A,i}}{\left({\overline {\xi }}\Sigma _{p}\right)_{mod}}}\right)}0.87{\displaystyle \varepsilon }The fast fission factor (Epsilon)total number of fission neutrons/number of fission neutrons from just thermal fissions{\displaystyle \varepsilon \approx 1+{\frac {1-p}{p}}{\frac {u_{f}\nu _{f}P_{FAF}}{f\nu _{t}P_{TAF}P_{TNL}}}}1.02{\displaystyle P_{FNL}}The fast non-leakage probabilityThe probability that a fast neutron will not leak out of the system.{\displaystyle P_{FNL}\approx \mathrm {exp} \left(-{B_{g}}^{2}\tau _{th}\right)}0.97{\displaystyle P_{TNL}}The thermal non-leakage probabilityThe probability that a thermal neutron will not leak out of the system.{\displaystyle P_{TNL}\approx {\frac {1}{1+{L_{th}}^{2}{B_{g}}^{2}}}}0.99
The symbols are defined as:[2]
{\displaystyle \nu }, {\displaystyle \nu _{f}} and {\displaystyle \nu _{t}} are the average number of neutrons produced per fission in the medium (2.43 for Uranium-235).
{\displaystyle \sigma _{f}^{F}} and {\displaystyle \sigma _{a}^{F}} are the microscopic fission and absorption cross sections for fuel, respectively.
{\displaystyle \Sigma _{a}^{F}} and {\displaystyle \Sigma _{a}} are the macroscopic absorption cross sections in fuel and in total, respectively.
{\displaystyle N_{i}} is the number density of atoms of a specific nuclide.
{\displaystyle I_{r,A,i}} is the resonance integral for absorption of a specific nuclide.
{\displaystyle I_{r,A,i}=\int _{E_{th}}^{E_{0}}dE'{\frac {\Sigma _{p}^{mod}}{\Sigma _{t}(E')}}{\frac {\sigma _{a}^{i}(E')}{E'}}}.
{\displaystyle {\overline {\xi }}} is the average lethargy gain per scattering event.
Lethargy is defined as decrease in neutron energy.
{\displaystyle u_{f}} (fast utilization) is the probability that a fast neutron is absorbed in fuel.
{\displaystyle P_{FAF}} is the probability that a fast neutron absorption in fuel causes fission.
{\displaystyle P_{TAF}} is the probability that a thermal neutron absorption in fuel causes fission.
{\displaystyle {B_{g}}^{2}} is the geometric buckling.
{\displaystyle {L_{th}}^{2}} is the diffusion length of thermal neutrons.
{\displaystyle {L_{th}}^{2}={\frac {D}{\Sigma _{a,th}}}}.
{\displaystyle \tau _{th}} is the age to thermal.
Similar questions