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Reactor physics

Reactor physics. Reactor training course Institut für Kernchemie. www.kernchemie.uni-mainz.de. Binding energy. Binding energy E B = E  - E = - E E  Energy of the free nucleus; E  = 0 E Energy of the compound nucleus E  > E Mass defect m = E B / c² Mass of the nuclei

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Reactor physics

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  1. Reactor physics Reactor training course Institut für Kernchemie www.kernchemie.uni-mainz.de

  2. Binding energy • Binding energy • EB = E - E = - E • E Energy of the free nucleus; E = 0 • E Energy of the compound nucleus • E > E • Mass defect • m = EB / c² • Mass of the nuclei • m = Z mp + N mn – EB / c² Fission Fusion Fusion: 1 to3.5 MeV / nucleus ca. 20 MeV / fusion Fission: about 1 MeV / nucleon  ca. 200 MeV / fission

  3. Neutron induced fission • Ef = limit for fission • Ef 5 MeV for Z > 90 • Neutron induced fission • Capture of a free neutron •  excited compound nucleus (ZK) with excitation energy • EA = EB + Ekin,n Ef • EB(gg-ZK) > EB(ug-,gu-ZK) • ug-nuclei: uneven number of n and even number of p or opposite • gg–nuclei: even number of n and p Abstand Potentielle Energie

  4. slow neutrons Nucleus Compound nucleus Necessary neutron energy for fission in MeV fast neutrons Fission of heavy nucleons with neutrons

  5. Neutron energies • Slow (thermal) neutrons Etherm≤ 0.4 e V • typical thermal energy Etherm = 0.025 eV • Epithermal neutrons 0.4 eV < Eepi < 10 keV • Fast neutrons Efast≥ 10 keV Application of research reactors

  6. Uranium • 1 g 238U • 20 spontaneous fissions per hour (tunnel effect) • 106 times more -decays • Natural Uranium • 0.72 % 235U • 99.28 % 238U • Enrichment of 235U • Power reactors: 3-4% • Research reactors:  20 % (LEU) • > 20 % (HEU) fuel development

  7. U235 Fission products Number of fission products nf for 235U Fission product nf [%] 131I (8.05 d) 3.1 132Te (77 h) 4.7 133Sb (4.1 min) 4.0 133Te (63 min) 4.9 133I (21 h) 6.9 133Xe (5.27 d) 6.6 134Te (44 min) 6.9 135I (6.7 h) 6.1 137Cs (29 a) 6.15 140Ba (12.8 d) 6.44 143Ce (33 h) 5.7 144Ce (285 d) 6.0 • thermal fission of 233U and 239Pu • thermal und 14 MeV-fission of 235U • fission by prompt neutrons of 232Th and 238U

  8. Activation • Structural components of the reactor • Aluminum • Stainless steel • Concrete • Air, water

  9. Fission of 235U – operation of reactors

  10. Prompt fission neutrons • = average number of prompt neutrons produced by the fission For U-235: • (E)= 2.43 + 0.106 x E with E = excitation energy for the neutrons

  11. Fission spectrum Maxwellverteilung mit EW = 0,7 MeV Ē = 2 MeV Energy spectrum of the prompt neutrons by thermal fission of 235U

  12. Delayed neutrons After the emission of the 2 n the excitation energy of the nucleus is too small to emit an other neutron. The stability for the decay products is reached by - decay.

  13. Properties of delayed neutrons

  14. Cross section  Probabilities for the neutron Total cross section = Probabilities for the interaction Neutron - nucleus Unit: Barn (b), 1 b = 10-24 cm² Different microscopic cross sections for the different processes

  15. Microscopic cross sections elastic scattering inelastic Cross section fission capture -radiation absorption p-emission 2n-emission For small neutron energies in thermal reactors is , p and 2n  0

  16. Cross sections for 235U total fission total capture fission scattering

  17. Cross section for 238U capture total fission

  18. Cross section for Cadmium Measurements with and without Cd: Separation of thermal and epithermal neutrons

  19. Characteristics for fissionable materials • For fissionable materials in reactors three important characteristics are • = average number of neutrons produced per fission • = ratio of the number of neutrons captured by the fuel  = average number of neutrons produced per neutron capture by the fuel  =  / (1 + )

  20. Neutron regeneration for thermal neutrons Fuel   U( natural ) 2.47 0.837 1.33 U (5% U-235) 2.47 0.272 1.94 U (20% U-235) 2.47 0.202 2.05 U-235 2.47 0.183 2.09 U-233 2.55 0.132 2.29 Pu-239 2.91 0.416 2.02

  21. number of fissions in one generation number of fissions in previous generation k = Multiplication factor k k < 1  under critical power level k = 1  constant power level k > 1  over critical power level

  22. Reactivity ρ • Definition of the reactivity ρ: ρ = (k - 1) / k = k/k • Unit Percentage [% k/k] or number [k/k] or Dollar [$] and Cent [¢] • Calculation: 1 $ = 100 ¢ = 0,0073k/k • 1 k/k = 137 $ = 13699 ¢

  23. Reaktivität ρ  < 0  under critical power level  = 0  constant power level  > 0  over critical power level

  24. Four – factor formula For large reactors an infinite multiplication factor is defined k =  .  . p . f  =number of neutrons produced per neutron absorbed in the fuel  = fast fission factor, a correction factor to take into account the fact that some fissions will be produced by fast neutrons p = resonant escape probability, the probability that a neutron will escape from capture while it is being slowed through the resonance energy range (approximately 1 to 100 eV). f = the thermal utilization, the fraction of thermal neutrons which are absorbed in in the fuel

  25. Four – factor formula - examples Homogenous mixture of natural uranium and graphite, both being powder: Number of neutrons produced per absorbed neutron  = 1.33 Fast fission factor  1.0, Product of resonant escape probabilityp and thermal utilization f: p.f  0.6 k =  .  . p . f = 1.33 . 1 . 0.6 = 0.8  Impossible to use such a combination in a reactor If the uranium is used in rods with diameters of 1 to 2 inch in a matrix of solid graphite (heterogeneous system) p is increased and the product p.f  0.8 Fast fission factor  1.03 k = 1.33 . 1.03 . 0.8 = 1.09  Possible to construct such a reactor

  26. Effektive multiplication factor Real reactor: Escape of neutrons through the surface (neutron leakage), Absorption of neutrons in 238U or (n,) reactions keff = k. Ps. Pth Ps and Pthnumber of neutrons, which do not escape (probabilities for slow and fast neutrons) With the reactivity: ρ = (keff - 1) / keff in the unit $

  27. Reactor period T • Reactor operation at constant power level:  keff = 1,  = 0 • Suddenly multiplication factor changed by keff • Increase dn of the number of neutrons n per unit volume dn in the time dt : • dn/dt = keff . n / l • with l = mean lifetime of the neutrons (time between generations) Solution of the differential equation: n = n0. exp( keff. t / l) with l / keff = T = Reactor period or e-folding time Neutron flux: n = n0 . exp(t/T) without delayed neutrons

  28. Reactor period T Example : Fission neutrons in natural Uranium: l = 0.001 s Increase of power level of keff =½ % = 0.005 Reactor period: T = l / keff = 0.001 s / 0.005 = 0.2 s Neutron flux without delayed neutronsn = n0. exp(t/T) Increase of the power level per second of exp(5)  Control of the reactor is not possible

  29. Reactor period T Delayed neutrons caused an increase of the mean life time l of 0.1 s Increase of the power level of keff =½ % = 0. 005 Reactor period: T = l / keff = 0.1 s / 0.005 = 20 s With delayed neutrons Increase of the power per second of exp(0.05)  Control of the reactor is possible

  30. Reactor period T n = n0. exp(t/T) Reactor period T or e-folding time: Time, in which the neutron flux changed of the factor e = 2.72 Relative changes of the flux = (1 / T) . 100

  31. Inhour equation The „inhour equation“ gives the relationship between the reactivity and the reactor period in terms of the delayed neutrons (regarding 6 groups) and the prompt neutron lifetime.

  32. Inhour equation Using a time dependent diffusion equation and taking into account the delayed neutrons, it is possible to derive the following equation ρ = (keff - 1) / keff = l / (T keff) + i / (1 + T/i) i with i= number of delayed neutrons of the group i i= life time of the delayed neutrons of the group i System of 7 linear in-homogenous differential equations of first order, the differential equations of the reactor kinetics.

  33. Inhour equation Reactivity: ρ = l / (T keff) +  / (1 + T/  )  = mean lifetime of the delayed neutrons  = i i Case I: Large positive or negative T T >> , 1 << T, ρ <<  ρ =   / Tρ  1 / T

  34. Inhour equation Beispiel: TRIGAρ =   / T  = 0.0073  = 12.3 s T = 1 h  = 0.0073 . 12.3 / 3600  2.5 .10-5 (inverse hour)

  35. Inhour equation Reactivity: ρ = l / (T keff) +  / (1 + T/  ) Case II: Small positive T, large reactivities ρ 0 < T <<  , ρ >  ρ = l /( keff. T) +   T = l / ( keff ( -  )) If k is not too far from unit, then T = l / ( -  ) If k exceed 1+ß, then the reactor will be critical on prompt neutrons alone. The reactor is prompt critical.

  36. Inhour equation Für TRIGA 1 dollar [$] =  = 0.0073 , 1 cent = 0.01 dollar 2 Dollar - Puls ρ = 2  (2 $) = 0.0146, T = 13.5 ms

  37. Inhour equation for the TRIGA Rod calibration

  38. Fission of 235U with Thermal Neutrons 0.025 eV 1 MeV • Neutron absorber rods (k=1, steady state) • Neutron moderator (1 MeV  0.025 eV)

  39. TRIGA Fuel Moderator Elements TRIGA Fuel: 91 % Zr 1 % H 8 % U (20% U-235) Atomic Ratio: Zr/H  1/1 Protons in U-Zr-Matrix act as Moderator

  40. TRIGA Fuel Moderator Elements Prompt negative temperature coefficient • Decrease of reactivity: • per °C  = -1,2 x 10-4keff/keff • . • at T = 100°C  = -1.2 x 10-2keff/keff = - 1.64 $ For comparision: 1 ¢ per kW increase of the power level

  41. Xenon poisoning • Reason for the Xenon poisoning: • Decay of I-135 into Xe-135 (large capture cross section for thermal neutrons) • Operation at constant power level: Production of I-135 and Xe • Increase of the power level: increase of I-135 and Xe • Decrease of the power level: Xe concentration increases due to the decay of the I-135 and neutrons will be captured by Xe. With a delay time of the half lifetime of I-135 the capture of neutrons decreases and also the power decreases slowly. • Operation of the reactor after the shut down is not possible when the absorption by Xe is too large. • Operation possible, when the Xe-135 production is negligible (about 20 h)

  42. a start of reactor operation with not poisoned core b after fast shut down of the reactor c after reduction of the power level d after increase of the power level to the previous level Xenon concentration Time (h) Xenon poisoning

  43. Core excess reactivity At a power level of 100 kW following contributions a necessary for the core excess reactivity: 0.40 $ for operation 0.50 $ for compensation of the temperature effect 0.60 $ for compensation of the poison (Xe-135) 0.20 $ for compensation of the burn-up Up to 1.00 $ for compensation of the neutron absorption in samples for irradiation positions __________  2.70 $

  44. Summary • Nuclear fission • Reactivity • Ideal (infinite) and real (finite) reactor • Inhour equation • TRIGA fuel (moderation, prompt negative temperature coefficient, inherent safe reactor) • Xenon poisoning

  45. More information to the operation of the TRIGA Mainz • Structure • Instrumentation • Cooling- and purification circuits • Radiation protection • Safety • Checks (internal – external) • Special incidents • Documentation • Organization

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