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Nuclear Fission

Nuclear Fission. 1/ v. Fast neutrons should be moderated. 235 U thermal cross sections  fission  584 b.  scattering  9 b.  radiative capture  97 b. Fission Barriers. Nuclear Fission. Fissile. Q for 235 U + n  236 U is 6.54478 MeV.

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Nuclear Fission

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  1. Nuclear Fission 1/v Fast neutrons should be moderated. 235U thermal cross sections fission  584 b. scattering  9 b. radiative capture  97 b. Fission Barriers Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  2. Nuclear Fission Fissile • Q for 235U + n 236U is 6.54478 MeV. • Table 13.1 in Krane: Activation energy EAfor 236U 6.2 MeV (Liquid drop + shell)  235U can be fissioned with zero-energy neutrons. • Q for 238U + n 239U is 4.??? MeV. • EA for 239U  6.6 MeV  MeV neutrons are needed. • Pairing term:  = ??? (Fig. 13.11 in Krane). • What about 232Pa and 231Pa? (odd Z). • Odd-N nuclei have in general much larger thermal neutron cross sections than even-N nuclei (Table 13.1 in Krane). Fissionable Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  3. Nuclear Fission Why not use it? f,Th584 2.7x10-6 700 0.019 b Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  4. Nuclear Fission • 235U + n  93Rb + 141Cs + 2n • Q = ???? • What if other fragments? • Different number of neutrons. • Take 200 MeV as an average. 66 MeV 98 MeV Light fragments Heavy fragments miscalibrated Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  5. Nuclear Fission • Mean neutron energy  2 MeV. •  2.4 neutrons per fission (average)   5 MeV average kinetic energy carried by prompt neutrons per fission. HW 45 • Show that the average momentum carried by a neutron is only  1.5 % that carried by a fragment. • Thus neglecting neutron momenta, show that the ratio between kinetic energies of the two fragments is the inverse of the ratio of their masses. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  6. Nuclear Fission Enge Distribution of fission energy Krane sums them up as  decays. Lost … ! Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  7. Nuclear Fission Segrè Distribution of fission energy a b c Lost … ! • How much is recoverable? • What about capture gammas? (produced by -1 neutrons) • Why c < (a+b) ? Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  8. Nuclear Fission • Recoverable energy release  200 MeV per 235U fission. • Fission rate = 2.7x1021P fissions per day. P in MW. • Burnup rate: 1.05 P g/day. P in MW. • Capture-to-fission ratio: • Consumption rate: 1.05(1+) P g/day. • 1000 MW reactor. • 3.1x1019 fissions per second, or 0.012 gram of 235U per second. • Two neutrinos are expected immediately from the decay of the two fission products, what is the minimum flux of neutrinos expected at 1 km from the reactor. HW 46 Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). 4.8x1012 m-2s-1

  9. Nuclear Fission • 3.1x1010 fissions per second per W. • In thermal reactor, majority of fissions occur in thermal energy region,  and  are maximum. • Total fission rate in a thermal reactor of volume V • Thermal reactor power (quick calculation) Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). 9

  10. Controlled Fission Fast second generation neutrons • 235U + n  X + Y + (~2.4)n • Moderation of second generation neutrons  Chain reaction. • Net change in number of neutrons from one generation to the next k (neutron reproduction factor). • k  1  Chain reaction. • Water, D2O or graphite moderator. • k < 1  subcritical system. • k = 1  critical system. • k > 1  supercritical system. • For steady release of energy (steady- • state operation) we need k =1. Infinite medium (ignoring leakage at the surface). Chain reacting pile Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  11. Controlled Fission • Probability for a thermal neutron to cause fission on 235U is 235U thermal cross sections fission  584 b. scattering  9 b. radiative capture  97 b. Not all  neutrons cause fission…! If each fission produces an average of  neutrons, then the mean number of fission neutrons produced per thermal neutron =   < Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  12. Controlled Fission • Assume natural uranium: • 99.2745% 238U, 0.7200% 235U. • f / N = (0.992745)(0) + (0.0072)(584) • = 4.20 b. •  / N = (0.992745)(2.75) + (0.0072)(97) • = 3.43 b. 235U Thermal f = 0 b 584 b Thermal  = 2.75 b 97 b 238U Doppler effect? Using the experimental elastic scattering data the radius of the nucleus can be estimated. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  13. Moderation (to compare x-section) 2H 1H (n,n) (n,n) (n,) (n,) Timeout..! • Resonances?

  14. Controlled Fission • Probability for a thermal neutron to cause fission • For natural uranium • 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. • For enriched uranium (235U = 3%)  = ????? (> 1.3). • In this case  is further from 1 and allowing for more neutrons to be lost while maintaining criticality. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  15. Controlled Fission • Nthermal neutrons in one generation have produced so far N fast neutrons. • Some of these fast neutrons can cause 238U fission  more fast neutrons  fast fission factor =  (= 1.03 for natural uranium). • Now we have N 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 strong 238U capture resonances (up to 1000 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 p ( 0.9). Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  16. Controlled Fission • Now we have pN 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 f ( 0.9) gives the fraction of thermal neutrons that are actually available for the fuel. • Now we have fpN thermal neutrons, could be > or < N thus determining the criticality of the reactor. k = fp The four-factor formula. k = fp(1-lfast)(1-lthermal) Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). Fractions lost at surface

  17. Neutron reproduction factor k = 1.000 x 0.9 Thermal utilization factor “f” x x 0.9 Resonance escape probability ”p” • What is: • Migration length? • Critical size? • How does the geometry affect the reproduction factor? x 1.03 Fast fission factor “” Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  18. Controlled Fission • Time scale for neutron multiplication • Time  includes moderation time (~10-6 s) and diffusion time of thermal neutrons (~10-3 s). • TimeAverage number of thermal neutrons • tN • t +  kN • t + 2 k2N • For a short time dt • Show that Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  19. Controlled Fission • k = 1 N is constant (Desired). • k < 1 N decays exponentially. • k > 1 N grows exponentially with time constant  / (k-1). • k = 1.01 (slightly supercritical)  e(0.01/0.001)t = e10 = 22026 in 1s. • Cd is highly absorptive of thermal neutrons. • Design the reactor to be slightly • subcritical for prompt neutrons. • The “few” “delayed” neutrons • will be used to achieve criticality, • allowing enough time to • manipulate the control • rods. Dangerous Cd control rods Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  20. Fission Reactors • Essential elements: • Fuel (fissile material). • Moderator (not in reactors using fast neutrons). • Reflector (to reduce leakage and critical size). • Containment vessel (to prevent leakage of waste). • Shielding (for neutrons and ’s). • Coolant. • Control system. • Emergency systems (to prevent runaway during failure). Core Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  21. Fission Reactors • Types of reactors: • Used for what? • Power reactors: extract kinetic energy of fragments as heat  boil water  steam drives turbine  electricity. • Research reactors: low power (1-10 MW) to generate neutrons (~1013 n.cm-2.s-1 or higher) for research. • Converters: Convert non-thermally-fissionable material to a thermally-fissionable material. Fertile f,th = 742 b Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  22. Fission Reactors Fertile f,th = 530 b • If  = 2  Conversion and fission. • If  > 2 Breeder reactor. • 239Pu: Thermal neutrons ( = 2.1)  hard for breeding. • Fast neutrons ( = 3)  possible breeding  fast breeder reactors. After sufficient time of breeding, fissile material can be easily (chemically) separated from fertile material. Compare to separating 235U from 238U. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  23. Fission Reactors • What neutron energy? • Thermal, intermediate (eV – keV), fast reactors. • Large, smaller, smaller but more fuel. • What fuel? • Natural uranium, enriched uranium, 233U, 239Pu. How??? From converter or breeder reactor. HW 47 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  24. Fission Reactors • What moderator? • Cheap and abundant. • Chemically stable. • Very low mass (~1). • High density. • Minimal neutron capture cross section. • Graphite (1,2,4,5) increase amount to compensate 3. • Water (1,2,3,4) but n + p d + enriched uranium. • D2O (heavy water) has low capture cross section  natural uranium, but if capture occurs, produces tritium. • Be and BeO, but poisonous. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  25. Fission Reactors • What assembly? • Heterogeneous: moderator and fuel are lumped. • Homogeneous: moderator and fuel are mixed together. • In homogeneous systems, it is easier to calculate p and f for example, but a homogeneous natural uranium-graphite mixture can not go critical. • What coolant? • Coolant prevents meltdown of the core. • It transfers heat in power reactors. • Why pressurized-water reactors. • Why liquid sodium? Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  26. Boiling water reactor Pressurized water reactor • Light water reactors. • Both use “light” water as coolant and as moderator, thus enriched (2-3%)uranium is used. • Common in the US. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  27. CANDU reactor • Canada has D2O and natural uranium. Gas cooled reactor • Most power reactors in GB are graphite moderated gas-cooled. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  28. Liquid sodium cooled, fast breeder reactor. • Blanket contains the fertile 238U. • Water should not mix with sodium. Breeder reactor Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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