Lecture 13 Applications of Nuclear Physics Fission Reactors and Bombs Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 1 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 off syllabus, only in notes at end of slides Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 2
12.1 Induced Fission (required energy) ΔE sep 6MeV per nucleon for heavy nuclei Very slow n Nucleus Potential Energy during fission [MeV] A= 238 Neutron ΔE f =Energy needed to penetrate fission barrier immediately 6-8MeV Neutrons Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 3 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 ΔE sep as excitation into nucleus Excited nucleus has enough energy for immediate fission if E f - ΔE sep >0 We call this thermal fission (slow, thermal neutron needed) But due to pairing term even N nuclei have low ΔE sep for additional n odd N nuclei have high ΔE sep for additional n Fission yield in n -absorption varies dramatically between odd and even N Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 4
12.1 Induced Fission (fast fission & fissile nuclei) ΔE sep (n, 238 92U) = 4.78 MeV only Fission of 238 U needs additional kinetic energy from neutron E n,kin >E f -ΔE sep 1.4 MeV We call this fast fission (fast neutrons needed) Thermally fissile nuclei, E thermal n,kin =0.1eV @ 1160K 233 92U, 235 92U, 239 94Pu, 241 94Pu Fast fissile nuclei E n,kin =O(MeV) 232 90Th, 238 92U, 240 94Pu, 242 94Pu Note: all Pu isotopes on earth are man made Note: only 0.72% of natural U is 235 U Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 5 12.1 Induced Fission (Reminder: stages of the process up to a few seconds after fission event) t=0 <# prompt n> ν prompt =2.5 t 10-14 s t>10-10 s <n-delay> τ d =few s <# delayed n> ν d =0.006 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 6
12.1 Induced Fission (the fission process) Energy balance of 235 92U induced thermal fission MeV: Prompt (t<10-10 s): E kin ( fragments) 167 E kin (prompt n) 5 3-12 from X+n Y+γ E(prompt γ) 6 Subtotal: 178 (good for power production) Delayed (10-10 <t< ): E kin (e from β-decays) 8 E(γ following β-decay) 7 Subtotal: 15 (mostly bad, spent fuel heats up) Neutrinos: 12 (invisible) Grand total: 205 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 7 12.1 Induced Fission (n -induced fission crossections (n,f) ) 238 92U does nearly no n -induced fission below E n,kin 1.4 MeV 235 92U does O(85%) fission starting at very low E n,kin Consistent with SEMF-pairing term of 12MeV/ A 0.8 MeV between odd-even= 235 92U and even-even= 238 92U unresolved, narrow resonances 238 U unresolved, narrow resonances 235 U n -Energy 8
12.1 Induced Fission ((n,f) and (n,γ) probabilities in natural Uranium) neutron absorbtion probabilit per 1 μm good 235 238 92 U(n,γ) 235 92 U(n,γ) bad-235 238 92 U(n,γ) 235 92 U(n,f) 235 92 U(n,γ) bad-238 238 92 U(n,γ) 238 92 U(n,f) 235 92 U(n,f) energy range of prompt fission neutrons good 238 thermal Dec 2006, Lecture 13 9 fast Uranium mix 235 U: 238 U =c:(1-c) 12.1 Induced Fission (a simple bomb) ρ nucl (U)=4.8*10 28 nuclei m -3 235 238 average n crossection: σ tot = cσtot + (1 + c) σtot mean free path for fission n: λ = 1( ρ σ ) 3 cm mean time between collisions =1.5*10-9 s @ E kin (n)=2mev Simplify to c=1 (the bomb mixture) prob( 235 U(n prompt,f)) @ 2MeV 18% (see slide 8) rest of n scatter, loosing E kin prob( 235 U(n,f)) grows most probable #collisions before 235 U(n,f) = 6 (work it out!) 6 random steps of λ=3cm l mp = 6*3cm 7cm in t mp =10-8 s nucl tot Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 10
12.1 Induced Fission (a simple bomb) After 10-8 s 1n is replaced with ν=2.5 n, ν=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 (νq-1) new such n in t mp =10-8 s (ignoring delayed n as bombs don t last for seconds!) nt ( + δt) = nt ( ) + ( νq 1) nt ( ) ( δttmp ) dn() t ν q 1 lim = nt ( ) δt 0 dt t mp ( ν q 1) t t mp solved by: nt ( ) = n(0) e if νq>1 exponential growths of neutron number For 235 U, ν=2.5 if q>0.4 you get a bomb Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 11 12.1 Induced Fission (a simple bomb) If object dimensions << l mp =7 cm most n escape through surface νq << 1 If R sphere ( 235 U) 8.7cm M( 235 U) 52 kg νq = 1 explosion in < t p =10-8 s little time for sphere to blow apart significant fraction of 235 U will do fission The problem is how to assemble such a sphere in less than 10-8 seconds Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 12
(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 238 238 92 U(n,γ) U scatter (slide 8) Fission of 238 U (5%) 238 92 U(n,γ) 235 rest is negligible 92 U(n,f) 235 92 U(n,γ) 238 92 U(n,γ) 238 92 U(n,f) 235 92 U(n,f) 235 92 U(n,γ) as E neutron decreases via elastic scattering σ( 238 92U(n,γ)) increases and becomes resonant σ( 238 92U(n,f)) decreases rapidly and vanishes below ~1 MeV only remaining chance for fission is σ( 235 92U(n,f)) which is much smaller then σ( 238 92 U(n,γ)) Conclusion: piling up natural U won t make a reactor because n get eaten by (n,γ) resonances. I said it is not SO simple 13 (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 235 U Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 14
(two ways out) Way 2: Fast Reactors Use fast neutrons for fission Use higher fraction of fissile material, typically 20% of 239 Pu + 80% 238 U This is self refuelling (fast breeding) via: 238 92U+n 239 92U + γ 239 93Np + e - + ν e 239 94Pu + e + ν e Details about fast reactors later Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 15 (Pu fuel) 239 Pu fission crossection slightly better then 235 U Chemically separable from 238 U (no centrifuges) More prompt neutrons ν( 239 Pu)=2.96 Fewer delayed n & higher n-absorbtion, more later 16
For bomb we found: (Reactor control) boom if: νq> 1where ν 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 σ nc like B or Cd to regulate q Lifetime of prompt n: O(10-8 s) in pure 235 U 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 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 17 (Reactor control) Fission products all n -rich all β - active Some β - 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 τ O(1 sec) Fraction ν d 0.6% Energy Delayed Neutron Precursor Groups for Thermal Fission in 235-U Delayed Average Half-Life Neutron Energy Group (sec) Fraction (MeV) 1 55.7 0.00021 0.25 2 22.7 0.00142 0.46 3 6.2 0.00127 0.41 4 2.3 0.0026 0.45 5 0.61 0.00075 0.41 6 0.23 0.00027 - Total - 0.0065 - off syllabus 18
(Reactor control) Since fuel rods hopefully remain in reactor longer then 10-2 s must include delayed n fraction ν d into our calculations New control problem: keep (ν+ν d )q = 1 to accuracy of < 0.6% at time scale of a few seconds Doable with mechanical systems but not easy Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 19 (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: Material State σ n-abs reduce E n chemistry other coolant H 2 O liquid small best reactive cheap good D 2 O C CO 2 press. He liquid solid gas gas none mild mild mild 2 nd best medium medium 3 rd best reactive reactive passive very passi. rare cheap cheap leaks good medium ok ok off syllabus Na liquid small medium very react. difficult excellent Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 20
Want dq/dt < 0 (Thermal Stability) Many mechanical influences via thermal expansion Change in n-energy spectrum Doppler broadening of 238 U(n,γ) resonances large negative contribution to dq/dt due to increased n -absorbtion in broadened spectrum Doppler broadening of 239 Pu(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 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 21 Isotope Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 430 12.3 Fission Bombs (fission fuel properties) Half-life a years 87.7 24,100 6,560 14.4 376,000 Bare critical mass kg, Alphaphase 10 10 40 10 100 100 a. By Alpha-decay, except Pu-241, which is by Beta-decay to Am-241. ideal bomb fuel = pure 239 Pu Spontaneous fission neutrons (gm-sec) -1 2.6x10 3 22x10-3 0.91x10 3 49x10-3 1.7x10 3 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 22 1.2 Decay heat watts kg -1 560 1.9 6.8 4.2 0.1 114
12.3 Fission Bombs (drawbacks of various Pu isotopes) 241 Pu : decays to 241 Am which gives very high energy γ-rays shielding problem 240 Pu : lots of n from spontaneous fission 238 Pu : α-decays quickly (τ 1/2 = 88 years) lots of heat conventional ignition explosives don t like that! in pure 239 Pu 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 240 Pu 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. Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 23 12.3 Fission Bombs (where to get Pu from? Sainsbury s?) Grade Isotope Super-grade Weaponsgrade b Pu- 238 -.00012.938.0035.00022 Reactor-grade c.013.603.243.091.050 MOX-grade d.019.404.321.178.078 FBR blanket e -.96.04 - - a. Pu-241 plus Am-241. 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). Pu- 239.98 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 24 Pu- 240.02.058 Pu- 241 a - Pu- 242 - d. Plutonium recovered from 3.64% fissile plutonium MOX fuel produced from reactorgrade 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).
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 γ sources from 241 Am outside a reactor large n fluxes from 240 Pu 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. Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 25 End of Lecture 13 even more energetic fusion and radioactive dating can be found in Dr. Weidberg s notes for lecture 14 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 26
12.1 Induced Fission ((n,f) and (n,γ) probabilities in natural Uranium) neutron absorbtion probabilit per 1 μm good 235 238 92 U(n,γ) 235 92 U(n,γ) bad-235 238 92 U(n,γ) 235 92 U(n,f) reprinted to show high E end of better bad-238 235 92 U(n,f) energy range of fission neutrons 238 92 U(n,γ) 238 92 U(n,f) good 238 235 92 U(n,γ) thermal Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 27 fast Appendix to lecture 13 More on various reactors Uranium enrichment Off Syllabus Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 28
(Thermal vs. Fast) Fast reactors need very high 239 Pu concentration Bombs very compact core hard to cool need high C p coolant like liq.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 238 U via breeding 141 times more fuel High fuel concentration + breading Can operate for long time without rod changes Designs for 4 th generation molten Pb or gas cooled fast reactors exist. Could overcome the Na problems Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 29 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 30
Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 31 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 32
Thermal Reactors (Thermal vs. Fast) Many different types exist BWR = Boiling Water Reactor PWR = Pressure Water Reactor BWP/PWR exist as LWR = Light Water Reactors (H 2 O) HWR = Heavy Water Reactors (D 2 O) (HT)GCR = (High Temperature) Gas Cooled Reactor exist as PBR = Pebble Bed Reactor other more conventional geometries Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 33 (Thermal vs. Fast) Thermal Reactors (general features) If moderated with D 2 O (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 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 34
Light Water it is cheap (Light vs. Heavy water thermal reactors) 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 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 35 Heavy Water (Light vs. Heavy water thermal reactors) 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 D 2 O moderation with different coolants to save D 2 O Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 36
(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 H 2 O 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 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 37 (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 (τ ½ ( 16 N)=7s, main contaminant) lower temperature lower efficiency if steam fraction too large (norm. 18%) Boiling crisis = loss of cooling Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 38
( cool reactors) Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 39 ( cool reactors) no boiling crisis no steam handling high efficiency 44% compact core low coolant mass Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 40
(enrichment) Two main techniques to separate 235 U from 238 U in gas form UF 6 @ 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 Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 41 1-2 m 15-20 cm O(70,000) rpm V max 1,800 km/h = supersonic! & g max =10 6 g difficult to build! Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 42
(enrichment) Dec 2006, Lecture 13 Nuclear Physics Lectures, Dr. Armin Reichold 43