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Lecture 13

Lecture 13. Applications of Nuclear Physics Fission Reactors and Bombs. off syllabus, only in notes at end of slides. 12.1 Overview. 12.1 Induced fission Fissile nuclei Time scales of the fission process Crossections for neutrons on U and Pu Neutron economy Energy balance

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Lecture 13

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  1. Lecture 13 Applications of Nuclear Physics Fission Reactors and Bombs Nuclear Physics Lectures, Dr. Armin Reichold

  2. off syllabus, only in notes at end of slides 12.1 Overview • 12.1 Induced fission • Fissile nuclei • Time scales of the fission process • Crossections for neutrons on U and Pu • Neutron economy • Energy balance • A simple bomb • 12.2 Fission reactors • Reactor basics • Moderation • Control • Thermal stability • Thermal vs. fast • Light water vs. heavy water • Pressurised vs. Boiling water • Enrichment • 12.3 Fission Bombs • Fission bomb fuels • Suspicious behaviour Nuclear Physics Lectures, Dr. Armin Reichold

  3. DEsep≈6MeV per nucleon for heavy nuclei Very slow n DEf =Energy needed to penetrate fission barrier immediately ≈6-8MeV Neutron 12.1 Induced Fission(required energy) Nucleus Potential Energy during fission [MeV] A= 238 Neutrons Nuclear Physics Lectures, Dr. Armin Reichold

  4. 12.1 Induced Fission(required energy & thermal fission) • Spontaneous fission rates low due to high coulomb barrier (6-8 MeV @ A≈240) • Slow neutron releases DEsepas excitation into nucleus • Excited nucleus has enough energy for immediate fission if Ef - DEsep >0 • We call this “thermal fission” (slow, thermal neutron needed) • But due to pairing term … • even N nuclei have low DEsepfor additional n • odd N nuclei have high DEsep for additional n • Fission yield in n -absorption varies dramatically between odd and even N Nuclear Physics Lectures, Dr. Armin Reichold

  5. 12.1 Induced Fission(fast fission & fissile nuclei) • DEsep(n,23892U)= 4.78 MeV only  • Fission of 238U needs additional kinetic energy from neutron En,kin>Ef-DEsep≈1.4 MeV • We call this “fast fission” (fast neutrons needed) • Thermally fissile nuclei, En,kinthermal=0.1eV @ 1160K • 23392U, 23592U, 23994Pu, 24194Pu • Fast fissile nuclei En,kin=O(MeV) • 23290Th, 23892U, 24094Pu, 24294Pu • Note: all Pu isotopes on earth are man made • Note: only 0.72% of natural U is 235U Nuclear Physics Lectures, Dr. Armin Reichold

  6. <# prompt n> nprompt=2.5 <n-delay> td=few s <# delayed n> nd=0.006 12.1 Induced Fission (Reminder: stages of the process up to a few seconds after fission event) t=0 t≈10-14 s t>10-10 s Nuclear Physics Lectures, Dr. Armin Reichold

  7. 12.1 Induced Fission (the fission process) Energy balance of 23592U induced thermal fission MeV: • Prompt (t<10-10s): • Ekin( fragments) 167 • Ekin(prompt n)5  3-12 from X+nY+g • E(prompt g)6 • Subtotal: 178 (good for power production) • Delayed (10-10<t<): • Ekin(e from b-decays) 8 • E(g following b-decay) 7 • Subtotal: 15 (mostly bad, spent fuel heats up) • Neutrinos: 12 (invisible) • Grand total: 205 Nuclear Physics Lectures, Dr. Armin Reichold

  8. 12.1 Induced Fission(n -induced fission crossections (n,f) ) • 23892U does nearly no n -induced fission below En,kin≈1.4 MeV • 23592U does O(85%) fission starting at very low En,kin • Consistent with SEMF-pairing term of 12MeV/√A≈0.8 MeV between • odd-even= 23592U and even-even= 23892U unresolved, narrow resonances unresolved, narrow resonances 235U 238U n-Energy

  9. energy range of prompt fission neutrons “good 235 ” 23892U(n,g) “bad-238” 23892U(n,g) 23592U(n,f) 23892U(n,g) 23892U(n,f) “good 238 ” 23592U(n,g) 23592U(n,f) “bad-235” 23592U(n,g) fast thermal 12.1 Induced Fission((n,f) and (n,g) probabilities in natural Uranium) neutron absorbtion probabilit per 1 mm

  10. 12.1 Induced Fission(a simple bomb) • Uranium mix • 235U:238U =c:(1-c) • rnucl(U)=4.8*1028 nuclei m-3 • average n crossection: • mean free path for fission n: • mean time between collisions =1.5*10-9 s @ Ekin(n)=2MeV • Simplify to c=1 (the bomb mixture) • prob(235U(nprompt ,f)) @ 2MeV ≈ 18% (see slide 8) • rest of n scatter, loosing Ekin  prob(235U(n,f)) grows • most probable #collisions before 235U(n,f) = 6 (work it out!) • 6 random steps of l=3cm  lmp=√6*3cm≈7cm in tmp=10-8 s Nuclear Physics Lectures, Dr. Armin Reichold

  11. 12.1 Induced Fission(a simple bomb) • After 10-8 s 1n is replaced with n=2.5 n, n=average prompt neutron yield of this fission process • Let probability of new n inducing fission before it is lost = q • (others escape or give radiative capture) • Each n produces on average (nq-1) new such n in tmp=10 -8 s(ignoring delayed n as bombs don’t last for seconds!) • if nq>1 exponential growths of neutron number • For 235U, n=2.5  if q>0.4 you get a bomb Nuclear Physics Lectures, Dr. Armin Reichold

  12. 12.1 Induced Fission(a simple bomb) • If object dimensions <<lmp=7 cm  most n escape through surface  nq << 1 • If Rsphere(235U) ≥ 8.7cm M(235U) ≥ 52 kg  nq = 1  explosion in < tp=10-8 s  little time for sphere to blow apart  significant fraction of 235U will do fission • The problem is how to assemble such a sphere in less than 10-8 seconds Nuclear Physics Lectures, Dr. Armin Reichold

  13. 23892U(n,g) 23892U(n,g) 23592U(n,f) 23892U(n,g) 23892U(n,f) 23592U(n,g) 23592U(n,f) 23592U(n,g) 12.2 Fission Reactors(not so simple) • Q: What happens to a 2 MeV fission neutron in a block of natural Uranium (c=0.72%)? • A: In order of probability • elastic 238U scatter (slide 8) • Fission of 238U (5%) • rest is negligible • as Eneutron decreases via elastic scattering • s(23892U(n,g)) increases and becomes resonant • s(23892U(n,f)) decreases rapidly and vanishes below ~1 MeV • only remaining chance for fission is s(23592U(n,f)) which is much smaller then s(23892U(n,g)) • Conclusion: piling up natural U won’t make a reactor because n get “eaten” by (n,g) resonances. I said it is not SO simple

  14. 12.2 Fission Reactors(two ways out) • Way 1: Thermal Reactors • bring neutrons to thermal energies without absorbing them = moderate them • use low mass nuclei with low n-capture crossection as moderator. (Why low mass?) • sandwich fuel rods with moderator and coolant layers • when n returns from moderator its energy is so low that it will predominantly cause fission in 235U Nuclear Physics Lectures, Dr. Armin Reichold

  15. 12.2 Fission Reactors(two ways out) • Way 2: Fast Reactors • Use fast neutrons for fission • Use higher fraction of fissile material, typically 20% of 239Pu + 80% 238U • This is self refuelling (fast breeding) via: • 23892U+n  23992U + g • 23993Np + e- + ne • 23994Pu + e¯ + ne • Details about fast reactors later Nuclear Physics Lectures, Dr. Armin Reichold

  16. 12.2 Fission Reactors (Pu fuel) • 239Pu fission crossection slightly “better” then 235U • Chemically separable from 238U (no centrifuges) • More prompt neutrons n(239Pu)=2.96 • Fewer delayed n & higher n-absorbtion, more later

  17. 12.2 Fission Reactors (Reactor control) • For bomb we found: • “boom” if: nq > 1 where n was number of prompt n • we don’t want “boom”  need to get rid of most prompt n • Reactors use control rods with large n-capture crossection snc like B or Cd to regulate q • Lifetime of prompt n: • O(10-8 s) in pure 235U • O(10-3 s) in thermal reactor (“long” time in moderator) • not “long” enough Far too fast to control • … but there are also delayed neutrons Nuclear Physics Lectures, Dr. Armin Reichold

  18. Energy 12.2 Fission Reactors (Reactor control) • Fission products all n -rich  all b- active • Some b- decays have excited states as daughters • These can directly emit n (see table of nuclides, green at bottom of curve) • several sources of delayed n • typical lifetimes t≈O(1 sec) • Fraction nd ≈ 0.6% off syllabus

  19. 12.2 Fission Reactors (Reactor control) • Since fuel rods “hopefully” remain in reactor longer then 10-2 s  must include delayed n fraction ndinto our calculations • New control problem: • keep (n+nd)q = 1 • to accuracy of < 0.6% • at time scale of a few seconds • Doable with mechanical systems but not easy Nuclear Physics Lectures, Dr. Armin Reichold

  20. 12.2 Fission Reactors (Reactor cooling) • As q rises during control, power produced in reactor rises  • we cool reactor and drive “heat engine” with coolant • coolant will often also act as moderator • Coolant/Moderator choices: off syllabus Nuclear Physics Lectures, Dr. Armin Reichold

  21. 12.2 Fission Reactors (Thermal Stability) • Want dq/dT < 0 • Many mechanical influences via thermal expansion • Change in n-energy spectrum • Doppler broadening of 238U(n,g) resonances  large negative contribution to dq/dT due to increased n -absorbtion in broadened spectrum • Doppler broadening of 239Pu(n,f) in fast reactors gives positive contribution to dq/dt • Chernobyl No 4. had dq/dT >0 at low power • … which proved that you really want dq/dT < 0 Nuclear Physics Lectures, Dr. Armin Reichold

  22. 12.3 Fission Bombs (fission fuel properties) • ideal bomb fuel = pure 239Pu Nuclear Physics Lectures, Dr. Armin Reichold

  23. 12.3 Fission Bombs (drawbacks of various Pu isotopes) • 241Pu : decays to 241Am which gives very high energy g-rays  shielding problem • 240Pu : lots of n from spontaneous fission • 238Pu : a-decays quickly (t1/2= 88 years)  lots of heat conventional ignition explosives don’t like that! • in pure 239Pu bomb, the nuclear ignition is timed optimally during compression using a burst of external n  maximum explosion yield • … but using reactor grade Pu, n from 240Pu decays can ignite bomb prematurely  lower explosion yield but still very bad if you are holding it in your hand • Reactor grade Pu mix has “drawbacks” but could be made into a bomb. Nuclear Physics Lectures, Dr. Armin Reichold

  24. 12.3 Fission Bombs(where to get Pu from? Sainsbury’s?) a. Pu-241 plus Am-241. d. Plutonium recovered from 3.64% fissile plutonium MOX fuel produced from reactor-grade plutonium and which has released 33 MWd/kg fission energy and has been stored for ten years prior to reprocessing (Plutonium Fuel: An Assessment(Paris:OECD/NEA, 1989) Table 12A). c. Plutonium recovered from low-enriched uranium pressurized-water reactor fuel that has released 33 megawatt-days/kg fission energy and has been stored for ten years prior to reprocessing (Plutonium Fuel: An Assessment (Paris:OECD/NEA, 1989) Table 12A). Nuclear Physics Lectures, Dr. Armin Reichold

  25. 12.3 Fission Bombs (suspicious behaviour) • Early removal of fission fuel rods  need control of reactor fuel changing cycle! • Building fast breaders if you have no fuel recycling plants • Large high-E g sources from 241Am outside a reactor • large n fluxes from 240Pu outside reactors very penetrating  easy to spot over long range Plutonium isotope composition as a function of fuel exposure in a pressurized-water reactor, upon discharge. Nuclear Physics Lectures, Dr. Armin Reichold

  26. End of Lecture 13 even more energetic fusion and radioactive dating can be found in Dr. Weidberg’s notes for lecture 14 Nuclear Physics Lectures, Dr. Armin Reichold

  27. energy range of fission neutrons “good 235 ” 23892U(n,g) “bad-238” 23892U(n,g) 23592U(n,f) 23892U(n,g) 23892U(n,f) “good 238 ” 23592U(n,g) 23592U(n,f) “bad-235” 23592U(n,g) fast thermal 12.1 Induced Fission ((n,f) and (n,g) probabilities in natural Uranium) reprinted to show high E end of better neutron absorbtion probabilit per 1 mm Nuclear Physics Lectures, Dr. Armin Reichold

  28. Appendix to lecture 13 More on various reactors Uranium enrichment Off Syllabus Nuclear Physics Lectures, Dr. Armin Reichold

  29. 12.2 Fission Reactors (Thermal vs. Fast) • Fast reactors • need very high 239Pu concentration   Bombs • very compact core   hard to cool   need high Cpcoolant likeliq.Na or liq. NaK-mix   don’t like water & air &  must keep coolant circuit molten &  high activation of Na • High coolant temperature (550C)  good thermal efficiency • Low pressure in vessel   better safety • can utilise all 238U via breeding   141 times more fuel • High fuel concentration + breading   Can operate for long time without rod changes • Designs for 4th generation molten Pb or gas cooled fast reactors exist. Could overcome the Na problems Nuclear Physics Lectures, Dr. Armin Reichold

  30. Nuclear Physics Lectures, Dr. Armin Reichold

  31. Nuclear Physics Lectures, Dr. Armin Reichold

  32. Nuclear Physics Lectures, Dr. Armin Reichold

  33. 12.2 Fission Reactors (Thermal vs. Fast) • Thermal Reactors • Many different types exist • BWR = Boiling Water Reactor • PWR = Pressure Water Reactor • BWP/PWR exist as • LWR = Light Water Reactors (H2O) • HWR = Heavy Water Reactors (D2O) • (HT)GCR = (High Temperature) Gas Cooled Reactor exist as • PBR = Pebble Bed Reactor • other more conventional geometries Nuclear Physics Lectures, Dr. Armin Reichold

  34. 12.2 Fission Reactors (Thermal vs. Fast) • Thermal Reactors (general features) • If moderated with D2O (low n-capture)   can burn natural U   now need for enrichment (saves lots of energy!) • Larger reactor cores needed   more activation • If natural U used  small burn-up time   often need continuous fuel exchange   hard to control Nuclear Physics Lectures, Dr. Armin Reichold

  35. 12.2 Fission Reactors (Light vs. Heavy water thermal reactors) • Light Water •  it is cheap •  very well understood chemistry •  compatible with steam part of plant • can not use natural uranium (too much n-capture)   must have enrichment plant   bombs • need larger moderator volume   larger core with more activation • enriched U has bigger n-margin   easier to control Nuclear Physics Lectures, Dr. Armin Reichold

  36. 12.2 Fission Reactors (Light vs. Heavy water thermal reactors) • Heavy Water •  it is expensive •  allows use of natural U • natural U has smaller n-margin   harder to control • smaller moderator volume   less activation • CANDU PWR designs (pressure tube reactors) allow D2O moderation with different coolants to save D2O Nuclear Physics Lectures, Dr. Armin Reichold

  37. 12.2 Fission Reactors (PWR = most common power reactor) • Avoid boiling   better control of moderation • Higher coolant temperature   higher thermal efficiency • If pressure fails (140 bar)   risk of cooling failure via boiling • Steam raised in secondary circuit   no activity in turbine and generator • Usually used with H2O   need enriched U •  Difficult fuel access  long fuel cycle (1yr)   need highly enriched U • Large fuel reactivity variation over life cycle   need variale “n-poison” dose in coolant Nuclear Physics Lectures, Dr. Armin Reichold

  38. 12.2 Fission Reactors (BWR = second most common power reactor) • lower pressure then PWR (70 bar)   safer pressure vessel •  simpler design of vessel and heat steam circuit • primary water enters turbine   activation of tubine   no access during operation (t½(16N)=7s, main contaminant) • lower temperature   lower efficiency • if steam fraction too large (norm. 18%)   Boiling crisis = loss of cooling Nuclear Physics Lectures, Dr. Armin Reichold

  39. 12.2 Fission Reactors (“cool” reactors) Nuclear Physics Lectures, Dr. Armin Reichold

  40. 12.2 Fission Reactors (“cool” reactors) • no boiling crisis • no steam handling • high efficiency 44% • compact core • low coolant mass Nuclear Physics Lectures, Dr. Armin Reichold

  41. 12.2 Fission Reactors (enrichment) • Two main techniques to separate 235U from 238U in gas form UF6 @ T>56C, P=1bar • centrifugal separation • high separation power per centrifugal step • low volume capacity per centrifuge • total 10-20 stages to get to O(4%) enrichment • energy requirement: 5GWh to supply a 1GW reactor with 1 year of fuel • diffusive separation • low separation power per diffusion step • high volume capacity per diffusion element • total 1400 stages to get O(4%) enrichment • energy requirement: 240GWh = 10 GWdays to supply a 1GW reactor with 1 year of fuel Nuclear Physics Lectures, Dr. Armin Reichold

  42. 1-2 m 15-20 cm O(70,000) rpm Vmax≈1,800km/h = supersonic! & gmax=106g  difficult to build! Nuclear Physics Lectures, Dr. Armin Reichold

  43. 12.2 Fission Reactors (enrichment) Nuclear Physics Lectures, Dr. Armin Reichold

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