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Neutron Chain Reaction Systems

Neutron Chain Reaction Systems. William D’haeseleer. Neutron Chain Reaction Systems. References : Lamarsh, NRT, chapter 4 Lamarsh & Baratta, chapter 4 Also Duderstadt & Hamilton § 3.I. Concept of chain reaction.

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Neutron Chain Reaction Systems

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  1. Neutron Chain Reaction Systems William D’haeseleer

  2. Neutron Chain Reaction Systems References: • Lamarsh, NRT, chapter 4 • Lamarsh & Baratta, chapter 4 • Also Duderstadt & Hamilton § 3.I

  3. Concept of chain reaction • Initially, reactor contains a certain amount of fuel, with initially Nf(0) fissile nuclei (e.g. U-235) • To get fission process started necessary to have an “external” neutron source → this source initiates fission process

  4. Concept of chain reaction • The by fission produced neutrons can be absorbed in U-235 → can lead to fission 2.5 n fission 2.5 n etc… etc…  CHAIN REACTION

  5. Concept of chain reaction Chain reaction 235 U

  6. Concept of chain reaction

  7. Concept of chain reaction • If “few” neutrons leak out, or parasitically absorbed: → exponentially run-away chain reaction  super critical reactor k > 1 • If “too many” neutrons leak out, or parasitically absorbed: → exponentially dying-out chain reaction  sub critical reactor k < 1

  8. Concept of chain reaction • If after one generation precisely 1 neutron remains, which “activates” again precisely 1 neutron, → stationary regime  critical reactor k = 1 k = multiplication factor number of neutrons in one generation number of neutrons in previous generation =

  9. Concept of chain reaction must be k=1

  10. Multiplication factor • Infinite reactor(homogeneous mixture of enriched U and moderator) • Assume at a particular moment n thermal neutrons absorbed in fuel • These produce n η fission neutrons • But sometimes also fissions due to fast neutrons → correction factor ε ≥ 1 (e.g., 1.03)  in fact n ηεfission neutrons

  11. Multiplication factor • These n ηεneutrons must be slowed down to thermal energies p ≡ resonance escape probability = probability for not being absorbed in any of the resonances during slowing down n ηε p thermalized neutrons • After thermalization, a fraction f will be absorbed in the fuel U-235; the remainder absorbs in structural material, moderator material, U-238, etc n ηε p f thermal neutrons absorbed in the fuel

  12. Multiplication factor • Hence, after the next generation:

  13. Multiplication factor Note: three-step approach for multiplication factor → mono-energetic infinite reactor → moderation in infinite thermal reactor → moderation in finite thermal reactor

  14. Multiplication factor • Mono-energetic infinite reactor

  15. Multiplication factor • Mono-energetic infinite reactor PAF = prob that neutron will be absorbed in the fuel “thermal utilization factor”

  16. Multiplication factor • Mono-energetic infinite reactor

  17. Multiplication factor Pf = prob that an absorbed neutron in the fuel leads to fission Number of neutrons in next generation:

  18. Multiplication factor • Moderation in infinite thermal reactor Now η identified with absorption of thermal neutrons Also f defined for thermal neutrons → reasons for name “thermal utilization factor” 

  19. Multiplication factor iii. Moderation in finite thermal reactor

  20. Multiplication factor • Moderation in finite thermal reactor PNL= non-leakage probability k ≡ keff = k∞ PNL k = multiplication factor for finite reactor

  21. Multiplication factor • Finite reactor  A critical reactor always has keff = 1 Influencing factors of keff : - leakage probability : geometry - amount of fuel: composition - presence/absence strong absorbers: composition non leakage probability

  22. Critical Mass • The larger the surface of a certain volume, the higher the probability to leak away • The larger R: • more fissile isotopes in volume • larger leak-through surface → relatively more production of neutrons than leakage But Vol ∕ Surf

  23. Critical Mass • Critical mass = minimal mass for a stationary fission regime • Examples: critical mass of U-235 ≤ 1 kg -when homogeneously dissolved as uranium salt in H2O -when concentration of U-235 > 90% in the uranium salt ≥ 200 kg -when U-235 is present in 30 tonnes of natural uranium embedded in matrix of C ! Natural uranium alone with 0.7% U-235 can never become critical, whatever the mass (because of absorption in U-238)

  24. Critical Mass

  25. Critical Mass

  26. Critical Mass

  27. Nuclear Fuels * fissile isotopesU-233 U-235 only this isotope is Pu239 available in nature * fertile isotopesTh-232U-233 U-238Pu-239 U-235 cannot be made artificially → to increase fraction of U-235 in a “U-mixture” → need to ENRICH “enrichment”

  28. Nuclear Fuels * consider reactor with 97% U-238 and 3% U-235 most of the U-235 fissions, “produces” energy, produces n U-238 absorbs neutrons Pu-239 an amount Pu-239 fissions…..energy…..n….. an amount Pu-239 absorbs n → Pu-240 … Pu-241 … Pu-242 an amount Pu-239 remains behind

  29. Production of Pu isotopes Evolution of 235U content and Pu isotopes in typical LWR

  30. Production of Pu isotopes

  31. Nuclear Fuels

  32. Nuclear Fuels * In a U-235 / U-238 reactor, Pu-239 production consumption of N U-235 atoms → NC Pu-239 atoms produced * In a Pu-239 / U-238 reactor, Pu-239 production consumption of N Pu-239 atoms →NC Pu atoms produced →(NC)C Pu atoms produced → (NC²)C Pu atoms produced →etc.

  33. Nuclear Fuels * C < 1 convertor C > 1 breeder reactor * η > 1for criticality write η = 1+ ζ (in addition to leakage, parasitary absorption) To be used for “conversion”

  34. Nuclear Fuels η(E) for U-233, U-235, Pu-239 & Pu-241 Ref: Duderstadt & Hamilton

  35. Slowing down (“moderation”) of neutrons • Fission neutrons are born with <E> ~ 2 MeV • Fission cross section largest at low E (0.025 eV) • →need to slow down neutrons as quickly as possible = “ moderation” • Mostly through elastic collisions (cf. billiard balls)

  36. Slowing down (“moderation”) of neutrons • Best moderator materials: → mass moderator as low as possible → moderator preferably low neutron-absorption cross section

  37. Slowing down (“moderation”) of neutrons Hence: * H2O -good moderator (contains much ) -but absorbs considerable amount of neutrons →U to be enriched -can also serve as coolant * D2O -still small mass: good moderator -absorbs fewer n than H2O →can operate with natural U: CANDU -can also serve as coolant

  38. Slowing down (“moderation”) of neutrons * graphite: -now need for separate cooling medium → other properties of moderator materials -good heat-transfer properties -stable w.r.t. heat and radiation -chemically neutral w.r.t. other reactor materials

  39. Slowing down (“moderation”) of neutrons • Time to “thermalize” from ~ 2 MeV → 0.025 eV in H2O:tmod ~ 1 μs tdiff ~ 200 μs = 2 x 10-4 s time that a neutron, after having slowed down, will continue to “random walk” before being absorbed. tgeneration ~ 2 x 10-4 s

  40. Reflector To reduce the leakage of neutrons out of reactor core → surround reactor core with “n-reflecting” material Usually, reflector material identical to moderator material Note: There exist also so-called “fast” reactors But most commercial reactors are “thermal” reactors (=reactors with thermal neutrons)

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