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Fundamentals of Neutronics : Reactivity Coefficients in Nuclear Reactors. Paul Reuss Emeritus Professor at the Institut National des Sciences et Techniques Nucléaires. Contents. A – Neutron balance B – Temperature effects C – Examples of design problems. PART A. Neutron balance.

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fundamentals of neutronics reactivity coefficients in nuclear reactors

Fundamentals of Neutronics :Reactivity Coefficients in Nuclear Reactors

Paul Reuss

Emeritus Professor

at the Institut National des Sciences et Techniques Nucléaires

contents
Contents

A – Neutron balance

B – Temperature effects

C – Examples of design problems

part a

PART A

Neutron balance

fission chain reaction
Fission chain reaction
  • Fissions  Neutrons  Fissions  Neutrons  Fissions  Neutrons Etc.
  • Fission yields :
    • About 200 MeV of energy (heat)
    • About 2.5 fast neutrons (about 2 MeV)
    • 2 fission products
  • The scattering slows down the neutrons (thermalized neutron : about 1/40 eV)
reactor types
Reactor types
  • Fast neutron reactors :
    • Avoid the slowing down
    • Use a highly enriched fuel
    • Good neutron balance (breeding possible)
  • Thermal neutron reactors :
    • Slow down the neutrons thanks to a moderator
    • Great cross-sections of the fissile nuclei in the thermal range
    • Therefore possibility to use a low enriched fuel
    • Breeding impossible in practice
kinetics
Kinetics
  • N  kN  k2N k3N k4N  …
  • Equivalently : N(0) exp(wt)
  • Criticality : k = 1 or : r = (k - 1)/k = 0
  • Otherwise : see inhour equation
neutron balance
Neutron balance

The criticality is possible if the size is sufficient

part b

PART B

Temperature effects

temperature effects
Temperature effects
  • Doppler effect
    • Broadening of the resonances
    • Mainly of uranium 238 capture
    • Negative (stabilizing) prompt effect
  • Thermal spectrum effect
    • No-proportionality of the absorption cross-sections
    • Small effect (on f and h) for the PWRs
  • Water expansion effect
    • p decreases, f increases if Tm increases
    • Main moderator effect for the PWRs
part c

PART C

Examples

of design problems

main parameters of the pwr design
Main parameters of the PWR design
  • Radius of the fuel
    • Mainly thermal criteria
  • Moderation ratio
    • If it increases, p improves and f decreases
    • There is an optimum of moderation
    • A under-moderated design is chosen
  • Fuel enrichment
    • Get the adequate length of cycle
problem of the boron poisoning
Problem of the boron poisoning
  • Condition for a negative temperature coefficient : ln(1/p) > 1 – f
  • If CB increases, f decreases and this condition may be non fulfilled
  • Therefore a limit on the boron concentration
  • If the need of boron is greater than the limit, burnable poisons are used
burnable poisons
Burnable poisons
  • Solid : no positive expansion effect
  • Efficient : reduce the excess of reactivity at the beginning of cycle
  • Burnable : no more antireactivity at the end of cycle
  • Usual materials : B, Gd, Eu…
problem of plutonium recycling
Problem of plutonium recycling
  • Standard uranium fuel : about 1 % of plutonium after irradiation  recycling interesting
  • No FBR available  recycling in the water reactors
  • Great neutron absorption of the plutonium fuels  control less efficient  mixed core  zoning of the MOX assemblies
conclusions
Conclusions
  • Major concerns : criticality and negative temperature coefficients
  • Criticality  adjust the content in fissile material
  • Temperature coefficients  constraints on the design and the choice of materials
  • Strong interactions between neutronics, thermalhydraulics, sciences of materials, etc.
  • The safety analyses defines the limits
  • The margins must be as great as possible to anticipate the evolutions
  • Weight of history