1 Controlled Fission • 235 U + n X + Y + (~2.4)n • Moderation of second generation neutrons Chain reaction. • Water, D 2 O or graphite moderator. • Ratio of number of “neutrons” (fissions) in one generation to the preceding k (neutron reproduction or multiplication factor). • k 1 Chain reaction. • k < 1 subcritical. • k = 1 critical system. • k > 1 supercritical. For steady release of energy (steady- state operation) we need k =1. Fast second generation neutro Infinite medium (ignoring leakage at the surface). Chain reacting pile Chain reacting pile Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh).
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Controlled Fission
• 235U + n X + Y + (~2.4)n• Moderation of second generation neutrons Chain reaction.• Water, D2O or graphite moderator.• Ratio of number of “neutrons” (fissions) in one generation to the preceding k (neutron reproduction or multiplication factor).
• k 1 Chain reaction.• k < 1 subcritical.• k = 1 critical system.• k > 1 supercritical.For steady release of energy (steady-state operation) we need k =1.
Fast second generation neutrons
Infinite medium (ignoring leakage at the surface).
Using the experimental elastic scattering data the radius of the nucleus can be estimated.
Doppler effect?Doppler effect?
Moderation (to compare x-section)
1H
(n,) (n,)
(n,n)(n,n)2H
• Resonances?
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• Probability for a thermal neutron to cause fission in natural natural uraniumuranium
• If each fission produces an average of = 2.4 neutrons, then the mean number of fission neutrons produced per thermal neutron = = 2.4 x 0.55 1.3• This is close to 1. If neutrons are still to be lost, there is a danger of losing criticality. (Heavy water?).• For enriched uraniumenriched uranium (235U = 3%) = ????? (> 1.3). (Light water?).• In this case is further from 1 and allowing for more neutrons to be lost while maintaining criticality.
• Comment on the calculation for thermal neutrons and a mixture of fissile and non-fissile materials, giving an example.• Comment for fast neutrons and a mixture of fissionable materials, giving an example.
HW 11HW 11
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Converters: Convert non-thermally-fissionable material to a thermally-fissionable material.
Controlled Fission• N thermalthermal neutrons in one generation have produced have produced so far so far NN fast neutrons.fast neutrons.• Some of these fast neutrons can cause 238U fission more fast neutrons fast fission factor fast fission factor = (= 1.03 for natural uranium).• Now we have Now we have NN fast neutrons. fast neutrons.• We need to moderate these fast neutrons use graphite for 2 MeV neutrons we need ??? collisions. How many for 1 MeV neutrons?• The neutron will pass through the 10 - 100 eV region during the moderation process. This energy region has many strongstrong 238U capture resonances (up to ????? b) Can not mix uranium and graphite as powders.• In graphite, an average distance of 19 cm is needed for thermalization the resonance escape probability resonance escape probability p ( 0.9).Nuclear Reactors, BAU, 1st Semester, 2007-2008
(Saed Dababneh).
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Controlled Fission• Now we have Now we have ppN N thermal neutrons.thermal neutrons.• Graphite must not be too large to capture thermal neutrons; when thermalized, neutrons should have reached the fuel.• Graphite thermal cross section = 0.0034 b, but there is a lot of it present.• Capture can also occur in the material encapsulating the fuel elements.• The thermal utilization factor thermal utilization factor f ( 0.9) gives the fraction of thermal neutrons that are actually available for the fuel.• Now we have Now we have fpfpNN thermal neutrons thermal neutrons, could be > or < N thus determining the criticality of the reactor.
k = fp The four-factor formula.The four-factor formula.
k = fp(1-lfast)(1-lthermal)Fractions lost at surfaceNuclear Reactors, BAU, 1st Semester, 2007-2008
(Saed Dababneh).
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x 1.03x 1.03Fast fission Fast fission factor “factor “””
x 0.9x 0.9Resonance Resonance
escape escape probability ”p”probability ”p”
x 0.9x 0.9Thermal Thermal
utilization utilization factor “f”factor “f”
x
What is:• Migration length?• Critical size?How does the geometry affect the reproduction factor?
