Arn 01-0-nuclear fission

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Mata kuliah Analisis Reaktor Nuklir , bahan ajar Dr-Ing Sihana

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Arn 01-0-nuclear fission

  1. 1. Nuclear Fission 2011
  2. 2. Fission Reactions <ul><li>Spontaneous Fission </li></ul><ul><ul><li>Most heavy nuclei decay by  -emission. </li></ul></ul><ul><ul><li>Some can also spontaneously fission: </li></ul></ul><ul><ul><ul><li>252 Cf (2.638 y; fission prob. 3.09%). </li></ul></ul></ul><ul><ul><ul><li>250 Cm (6900 y; fission prob. 61.0%). </li></ul></ul></ul><ul><li>Neutron Induced Fission </li></ul><ul><ul><li>Neutron can induce fission: </li></ul></ul><ul><ul><ul><li>Produce a COMPOUND NUCLEUS . </li></ul></ul></ul><ul><ul><ul><li>Highly Excited State </li></ul></ul></ul><ul><ul><ul><li>One of the decay modes is FISSION . </li></ul></ul></ul>Possible neutron Interactions with U-235
  3. 3. Fission Reactions <ul><li>Neutrons are released in Fission Reactions </li></ul><ul><ul><li>The fission products are “neutron rich”. </li></ul></ul><ul><ul><li>Some of the subatomic particles emitted (y 1 ,y 2 ,…) are neutrons: chain reaction. </li></ul></ul><ul><ul><li>Self sustaining fission reaction releases fission energy. </li></ul></ul><ul><li>Fission depends on Neutron Energy: </li></ul><ul><ul><li>Fission at very low energy (thermal ~0.025 eV): FISSILE NUCLEI. </li></ul></ul><ul><ul><ul><li>235 U, 233 U, 239 Pu. </li></ul></ul></ul><ul><ul><li>Fission at higher energies (MeV): FISSIONABLE NUCLEI. </li></ul></ul><ul><ul><ul><li>238 U, 240 Pu. </li></ul></ul></ul><ul><li>Conversion to Fissile Nuclei (BREEDING): </li></ul><ul><ul><li>Nuclei can be converted to fissile nuclei by absorbing slow neutrons. </li></ul></ul>232 Th and 238 U are FERTILE nuclides
  4. 4. Characteristics of the Fission Reaction <ul><ul><li>Scission Explained by the “Liquid Drop” Model </li></ul></ul><ul><ul><ul><li>Compound Nucleus Highly Excited. </li></ul></ul></ul><ul><ul><ul><li>Large oscillations of shape of “Nuclear Fluid”. </li></ul></ul></ul><ul><ul><ul><li>Elongated shape breaks in two (10 -20 s): </li></ul></ul></ul><ul><ul><li>Primary Fission Products Y H , Y L </li></ul></ul><ul><ul><ul><li>Highly Excited States. </li></ul></ul></ul><ul><ul><ul><li>Neutrons “evaporate” from surface (10 -17 s): PROMPT NEUTRONS  p . </li></ul></ul></ul><ul><ul><ul><li>Reduce excitation by  emission (~10 -14 s): PROMPT GAMMAS  p . </li></ul></ul></ul><ul><ul><li>Fission Fragments Transfer Kinetic Energy to the surrounding medium in ~10 -12 s. </li></ul></ul>Coulomb Repulsion >> Nuclear Forces
  5. 5. Fission Products <ul><li>Fission Product Decay Chains </li></ul><ul><ul><li>Several Hundred different nuclides can be produced </li></ul></ul><ul><ul><li>They are all neutron rich and decay by  - emission until a stable nuclide is reached: DECAY CHAIN . </li></ul></ul><ul><li>Important Decay Chains </li></ul>Hahn and Strassman discovered fission Characterization of Promethium and production of Samarium. Very effective thermal neutron absorbers Discovery and Production of Technetium for medical applications Production of Xe-135, largest low energy neutron absorption X-section
  6. 6. Fission Products <ul><li>Mass Distribution of Fission Products </li></ul><ul><ul><li>The mass of fission fragments ranges from 70 to ~170. </li></ul></ul><ul><ul><li>100 different fission chains (with constant A) are formed. </li></ul></ul><ul><ul><li>Fission Chain Yield y(A) : </li></ul></ul><ul><ul><ul><li>Probability a fission fragment is a nuclide with mass number A. </li></ul></ul></ul><ul><ul><li>The fission yield curve is ASYMETRIC </li></ul></ul><ul><ul><ul><li>It depends on the fissioned nuclide. </li></ul></ul></ul><ul><ul><ul><li>It depends on the Neutron Energy: higher energy, less asymmetry. </li></ul></ul></ul>Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  7. 7. Fission Products <ul><li>Initial Energy of Fission Fragments </li></ul><ul><ul><li>The kinetic energy of the two fission fragments must equal: </li></ul></ul><ul><ul><ul><li>The kinetic energy of the neutron and </li></ul></ul></ul><ul><ul><ul><li>The Q-value of the fission reaction. </li></ul></ul></ul><ul><ul><li>For a fission induced by a thermal neutron: </li></ul></ul><ul><ul><ul><li>Conservation of Momentum </li></ul></ul></ul><ul><ul><ul><li>The sharing of Kinetic Energy is: </li></ul></ul></ul>
  8. 8. Neutron Emission in Fission <ul><li>Prompt Neutrons: </li></ul><ul><ul><ul><li>Released within 10 -14 s. </li></ul></ul></ul><ul><ul><ul><li>Number  p can vary from 0 to 8. </li></ul></ul></ul><ul><ul><ul><li>The average number is for thermal fission depends on nuclide and neutron energy. </li></ul></ul></ul><ul><li>Delayed Neutrons: </li></ul><ul><ul><ul><li>Small fraction (1% Thermal) of neutrons are emitted as delayed neutrons. </li></ul></ul></ul><ul><ul><ul><li>The come from the Decay of Fission Products. </li></ul></ul></ul><ul><ul><ul><li>The time is from some seconds to minutes. </li></ul></ul></ul><ul><ul><ul><li>The average number depends strongly on: </li></ul></ul></ul><ul><ul><ul><ul><li>Fissioning nucleus. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Energy of the inducing neutron. </li></ul></ul></ul></ul>DELAYED Neutrons are ESSENTIAL to control the Nuclear Reaction Average Number of PROMPT Neutrons DELAYED Neutron Fraction Average TOTAL Number of Neutrons
  9. 9. Delayed Neutron Emission Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  10. 10. Neutron Emission in Fission <ul><li>The neutron energy distribution is a continuous Maxwellian Distribution which depends on: </li></ul><ul><li>Material ( T w and E w ) </li></ul><ul><li>Neutron Energy: E </li></ul><ul><li>The AVERAGE energy is ~ 2 MeV </li></ul>Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  11. 11. Prompt Energy Released <ul><li>The amount of energy per fission can be estimated by using the BINDING energy per NUCLEON. </li></ul><ul><li>Energy is released in TWO TIME SCALES: </li></ul><ul><ul><ul><li>Prompt (10 -12 s): </li></ul></ul></ul><ul><ul><ul><ul><li>Kinetic Energy. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Prompt Neutrons. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Prompt Gammas </li></ul></ul></ul></ul><ul><ul><ul><li>Delayed (s to minutes): Decay of fission Products. </li></ul></ul></ul>6.7 MeV 5.2 MeV
  12. 12. Energy from Fission Products <ul><ul><li>Most Fission Products decay in a few years. </li></ul></ul><ul><ul><li>Some others have much larger half-lives. </li></ul></ul><ul><ul><li>The Decay Heat is of concern for: </li></ul></ul><ul><ul><ul><li>Nuclear Safety: Removal of Decay Heat. </li></ul></ul></ul><ul><ul><ul><li>Management of Spent Fuel. </li></ul></ul></ul><ul><ul><li>Calculations based on Empirical Models: </li></ul></ul>Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  13. 13. Delayed Energy Released Anti-neutrino Decay Chains Energy = Mass Defect c 2 Delayed Fission Energy Released
  14. 14. Energy Released in Fission Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  15. 15. Energy Released in Fission <ul><li>How Much U-235 has to fission to generate 1 MWd ? </li></ul>
  16. 16. Nuclear Fission Chain Reaction <ul><ul><li>A Fissile atom (e.g 235 U) absorbs a neutron, and: </li></ul></ul><ul><ul><ul><li>fissions in two new atoms (fission fragments), </li></ul></ul></ul><ul><ul><ul><li>releasing three new neutrons </li></ul></ul></ul><ul><ul><ul><li>and energy. </li></ul></ul></ul><ul><ul><li>The neutrons can be </li></ul></ul><ul><ul><ul><li>Absorbed by an atom of 238 U (or other absorber), and does not continue the reaction: ABSORPTION . </li></ul></ul></ul><ul><ul><ul><li>Lost and does not collide with anything: LEAKAGE . </li></ul></ul></ul><ul><ul><ul><li>Collide with a fissile atom (e.g 235 U) which then fissions and releases additional neutrons: CHAIN REACTION . </li></ul></ul></ul>Leakage 2 nd generation 3 rd generation 1 st generation Non-Fission Absorption
  17. 17. The Neutron Cycle in a Thermal Reactor Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  18. 18. Quantification of the Thermal Cycle <ul><li>1. The FAST Fission Factor  </li></ul><ul><ul><li>Most fast fissions take place in 238 U ( E n > 1 MeV) </li></ul></ul><ul><ul><li>Natural or slightly enriched U cores:  between 1.02 and 1.o8. </li></ul></ul><ul><li>2. Resonance Escape Probability p </li></ul><ul><ul><li>Accounts for FAST neutron absorption during MODERATION. </li></ul></ul><ul><ul><li>p depends on the cross-sections in the resonance absorption region </li></ul></ul><ul><ul><li>For U fuelled reactors p varies depending on the moderator to fuel ratio: higher ratio increases p (most absorptions take place in U-238 .) </li></ul></ul>
  19. 19. Quantification of the Thermal Cycle <ul><li>3. Fast Non-Leakage Probability </li></ul><ul><ul><li>Probability that a FAST neutron does not leak from the core during moderation. </li></ul></ul><ul><ul><li>For a non-reflected core: </li></ul></ul><ul><li>Leakage probabilities depend on: </li></ul><ul><ul><li>Materials used in the Reactor: L (D,  a ) ,  . L,  increase  Leakage increases. </li></ul></ul><ul><ul><li>Geometry of the reactor: Buckling. Buckling increases  Leakage increases </li></ul></ul><ul><ul><li>Reactor Homogenous or Heterogeneous. </li></ul></ul><ul><ul><li>Use of a REFLECTOR of NEUTRONS: Decreases Leakage. </li></ul></ul>
  20. 20. Quantification of the Thermal Cycle <ul><li>4. Thermal non-Leakage Probability </li></ul><ul><ul><li>Probability that a thermal neutron does not leak out (escape) of the core before it is absorbed. </li></ul></ul><ul><ul><ul><li>L is the thermal diffusion length: one-half of the average distance difussed by a thermal neutron before it is absorbed. </li></ul></ul></ul><ul><ul><ul><li>B c 2 is the “Critical Buckling”: Related to the Geometry of the Reactor. </li></ul></ul></ul>Thermal Diffusion Coefficient Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  21. 21. Quantification of the Thermal Cycle <ul><li>5. The Thermal Utilization f </li></ul><ul><ul><li>Not all thermal neutrons are absorbed by the fuel. </li></ul></ul><ul><ul><li>f is the Probability that the neutrons are absorbed by the fuel. </li></ul></ul><ul><li>6. Thermal Fission Factor  </li></ul><ul><ul><li>Number of FAST neutrons produced per absorbed neutron in fuel. </li></ul></ul>Fuel Absorption rate Non-Fuel Absorption rate  MUST be > 1 for a self sustaining chain reaction
  22. 22. Quantification of the Thermal Cycle Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  23. 23. Quantification of the Thermal Cycle <ul><li>Effective Multiplication Factor </li></ul><ul><li>Infinite Multiplication Factor </li></ul><ul><ul><li>In an infinite medium there is no leakage. </li></ul></ul>k ∞ depends only on the MATERIAL in the core
  24. 24. Core Design Estimates <ul><li>What fuel to use for a Thermal Reactor ? </li></ul><ul><ul><li>Only Natural Uranium ? </li></ul></ul><ul><ul><ul><li>With 0.72 atom-% of 235U and ~99.3% of 238U. </li></ul></ul></ul><ul><ul><ul><li>The probability of resonace absorption is very high </li></ul></ul></ul><ul><ul><ul><li>p , the probability of escaping the resonance is very low. </li></ul></ul></ul><ul><ul><ul><li>k ∞ << 1.0. </li></ul></ul></ul><ul><ul><li>Reactor design solutions: </li></ul></ul><ul><ul><ul><li>Increase p : Use an EFFECTIVE MODERATOR. </li></ul></ul></ul><ul><ul><ul><li>Increase f : Use more fissile material. </li></ul></ul></ul><ul><ul><ul><li>Increase  : use a fuel with more neutrons per fission and low </li></ul></ul></ul>
  25. 25. Core Design Estimates Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002 Increasing  But, there is no U-233 in Nature, one must “make” it.
  26. 26. Core Design Estimates <ul><li>If </li></ul><ul><ul><li>There is too little moderator , is small, p is very small and </li></ul></ul><ul><ul><li>There is too much moderator, is large, f is small and </li></ul></ul><ul><ul><li>There is an optimal that gives a maximum for </li></ul></ul>Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002 Only Heavy Water as a Moderator can be used for an homogeneous natural uranium reactor
  27. 27. Quantification of the Thermal Cycle Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
  28. 28. Core Design Estimates <ul><li>So, how can we build a nuclear reactor with Uranium without Heavy Water as Moderator ?. </li></ul><ul><ul><li>Increase f </li></ul></ul><ul><ul><ul><li>Increasing 235 U content from 0.72 % to > ~ 2.5% : ENRICHMENT </li></ul></ul></ul><ul><ul><ul><li>More fissile fuel will increase  more chance of absorption by fuel. </li></ul></ul></ul><ul><ul><ul><li>AND/OR </li></ul></ul></ul><ul><ul><li>Increase p </li></ul></ul><ul><ul><ul><li>Construct an HETEROGENEOUS core by separating fuel and moderator. </li></ul></ul></ul><ul><ul><ul><li>More Fast neutrons escape the fuel </li></ul></ul></ul><ul><ul><ul><li>They are thermalized away from 238 U resonances  more probability of escaping the resonances. </li></ul></ul></ul><ul><ul><ul><li>Heterogeneous reactors also have a higher  (more fast fissions in 238 U). </li></ul></ul></ul>
  29. 29. Core Design Estimates Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002 HETEROGENEOUS CORE Fuel Moderator Neutron moderation fast thermal More Heterogeneous: f decreases More heterogeneous: p increases There´s an optimum for k∞ max
  30. 30. Core Design Estimates <ul><li>Finally, we have to take care of the LEAKAGE </li></ul><ul><ul><li>Increase </li></ul></ul><ul><ul><ul><li>We surround the core with a material with a HIGH scattering-to-absorption cross section: REFLECTOR. </li></ul></ul></ul>Reflectors reduce Leakage Reflectors reduce Peak-to-average power Reflectors reduce Fast Neutron Flux outside the core  neutrons/cm 2 s center Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

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