Arn 01-0-nuclear fission

Fission Reactions Spontaneous Fission Most heavy nuclei decay by  -emission. Some can also spontaneously fission: 252 Cf (2.638 y; fission prob. 3.09%). 250 Cm (6900 y; fission prob. 61.0%). Neutron Induced Fission Neutron can induce fission: Produce a COMPOUND NUCLEUS . Highly Excited State One of the decay modes is FISSION . Possible neutron Interactions with U-235

Fission Reactions Neutrons are released in Fission Reactions The fission products are “neutron rich”. Some of the subatomic particles emitted (y 1 ,y 2 ,…) are neutrons: chain reaction. Self sustaining fission reaction releases fission energy. Fission depends on Neutron Energy: Fission at very low energy (thermal ~0.025 eV): FISSILE NUCLEI. 235 U, 233 U, 239 Pu. Fission at higher energies (MeV): FISSIONABLE NUCLEI. 238 U, 240 Pu. Conversion to Fissile Nuclei (BREEDING): Nuclei can be converted to fissile nuclei by absorbing slow neutrons. 232 Th and 238 U are FERTILE nuclides

Characteristics of the Fission Reaction Scission Explained by the “Liquid Drop” Model Compound Nucleus Highly Excited. Large oscillations of shape of “Nuclear Fluid”. Elongated shape breaks in two (10 -20 s): Primary Fission Products Y H , Y L Highly Excited States. Neutrons “evaporate” from surface (10 -17 s): PROMPT NEUTRONS  p . Reduce excitation by  emission (~10 -14 s): PROMPT GAMMAS  p . Fission Fragments Transfer Kinetic Energy to the surrounding medium in ~10 -12 s. Coulomb Repulsion >> Nuclear Forces

Fission Products Fission Product Decay Chains Several Hundred different nuclides can be produced They are all neutron rich and decay by  - emission until a stable nuclide is reached: DECAY CHAIN . Important Decay Chains 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

Fission Products Mass Distribution of Fission Products The mass of fission fragments ranges from 70 to ~170. 100 different fission chains (with constant A) are formed. Fission Chain Yield y(A) : Probability a fission fragment is a nuclide with mass number A. The fission yield curve is ASYMETRIC It depends on the fissioned nuclide. It depends on the Neutron Energy: higher energy, less asymmetry. Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

Fission Products Initial Energy of Fission Fragments The kinetic energy of the two fission fragments must equal: The kinetic energy of the neutron and The Q-value of the fission reaction. For a fission induced by a thermal neutron: Conservation of Momentum The sharing of Kinetic Energy is:

Neutron Emission in Fission Prompt Neutrons: Released within 10 -14 s. Number  p can vary from 0 to 8. The average number is for thermal fission depends on nuclide and neutron energy. Delayed Neutrons: Small fraction (1% Thermal) of neutrons are emitted as delayed neutrons. The come from the Decay of Fission Products. The time is from some seconds to minutes. The average number depends strongly on: Fissioning nucleus. Energy of the inducing neutron. DELAYED Neutrons are ESSENTIAL to control the Nuclear Reaction Average Number of PROMPT Neutrons DELAYED Neutron Fraction Average TOTAL Number of Neutrons

Delayed Neutron Emission Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

Neutron Emission in Fission The neutron energy distribution is a continuous Maxwellian Distribution which depends on: Material ( T w and E w ) Neutron Energy: E The AVERAGE energy is ~ 2 MeV Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

Prompt Energy Released The amount of energy per fission can be estimated by using the BINDING energy per NUCLEON. Energy is released in TWO TIME SCALES: Prompt (10 -12 s): Kinetic Energy. Prompt Neutrons. Prompt Gammas Delayed (s to minutes): Decay of fission Products. 6.7 MeV 5.2 MeV

Energy from Fission Products Most Fission Products decay in a few years. Some others have much larger half-lives. The Decay Heat is of concern for: Nuclear Safety: Removal of Decay Heat. Management of Spent Fuel. Calculations based on Empirical Models: Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

Delayed Energy Released Anti-neutrino Decay Chains Energy = Mass Defect c 2 Delayed Fission Energy Released

Energy Released in Fission Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

Energy Released in Fission How Much U-235 has to fission to generate 1 MWd ?

Nuclear Fission Chain Reaction A Fissile atom (e.g 235 U) absorbs a neutron, and: fissions in two new atoms (fission fragments), releasing three new neutrons and energy. The neutrons can be Absorbed by an atom of 238 U (or other absorber), and does not continue the reaction: ABSORPTION . Lost and does not collide with anything: LEAKAGE . Collide with a fissile atom (e.g 235 U) which then fissions and releases additional neutrons: CHAIN REACTION . Leakage 2 nd generation 3 rd generation 1 st generation Non-Fission Absorption

The Neutron Cycle in a Thermal Reactor Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

Quantification of the Thermal Cycle 1. The FAST Fission Factor  Most fast fissions take place in 238 U ( E n > 1 MeV) Natural or slightly enriched U cores:  between 1.02 and 1.o8. 2. Resonance Escape Probability p Accounts for FAST neutron absorption during MODERATION. p depends on the cross-sections in the resonance absorption region For U fuelled reactors p varies depending on the moderator to fuel ratio: higher ratio increases p (most absorptions take place in U-238 .)

Quantification of the Thermal Cycle 3. Fast Non-Leakage Probability Probability that a FAST neutron does not leak from the core during moderation. For a non-reflected core: Leakage probabilities depend on: Materials used in the Reactor: L (D,  a ) ,  . L,  increase  Leakage increases. Geometry of the reactor: Buckling. Buckling increases  Leakage increases Reactor Homogenous or Heterogeneous. Use of a REFLECTOR of NEUTRONS: Decreases Leakage.

Quantification of the Thermal Cycle 4. Thermal non-Leakage Probability Probability that a thermal neutron does not leak out (escape) of the core before it is absorbed. L is the thermal diffusion length: one-half of the average distance difussed by a thermal neutron before it is absorbed. B c 2 is the “Critical Buckling”: Related to the Geometry of the Reactor. Thermal Diffusion Coefficient Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

Quantification of the Thermal Cycle 5. The Thermal Utilization f Not all thermal neutrons are absorbed by the fuel. f is the Probability that the neutrons are absorbed by the fuel. 6. Thermal Fission Factor  Number of FAST neutrons produced per absorbed neutron in fuel. Fuel Absorption rate Non-Fuel Absorption rate  MUST be > 1 for a self sustaining chain reaction

Quantification of the Thermal Cycle Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002

Quantification of the Thermal Cycle Effective Multiplication Factor Infinite Multiplication Factor In an infinite medium there is no leakage. k ∞ depends only on the MATERIAL in the core

Core Design Estimates What fuel to use for a Thermal Reactor ? Only Natural Uranium ? With 0.72 atom-% of 235U and ~99.3% of 238U. The probability of resonace absorption is very high p , the probability of escaping the resonance is very low. k ∞ << 1.0. Reactor design solutions: Increase p : Use an EFFECTIVE MODERATOR. Increase f : Use more fissile material. Increase  : use a fuel with more neutrons per fission and low

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.

Core Design Estimates If There is too little moderator , is small, p is very small and There is too much moderator, is large, f is small and There is an optimal that gives a maximum for 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

Core Design Estimates So, how can we build a nuclear reactor with Uranium without Heavy Water as Moderator ?. Increase f Increasing 235 U content from 0.72 % to > ~ 2.5% : ENRICHMENT More fissile fuel will increase  more chance of absorption by fuel. AND/OR Increase p Construct an HETEROGENEOUS core by separating fuel and moderator. More Fast neutrons escape the fuel They are thermalized away from 238 U resonances  more probability of escaping the resonances. Heterogeneous reactors also have a higher  (more fast fissions in 238 U).

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

Core Design Estimates Finally, we have to take care of the LEAKAGE Increase We surround the core with a material with a HIGH scattering-to-absorption cross section: REFLECTOR. 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

Arn 01-0-nuclear fission

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Arn 01-0-nuclear fission