Applied reactor Physics hebert

applied reactor physics hebert pdf download and fundamentals of nuclear reactor physics solution manual pdf
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Prepared by D. Hummel David Novog (Ph.D., P.Eng.) Associate Professor McMaster University (Canada) 1 m • Nucleus consists of: - protons (positive charge) - neutrons (no charge) • Surrounded by cloud of electrons - negative charge - memp,mn • of protons (Z) define the element • of protons + of neutrons (N) define the isotope (A) • Notation: X chemical symbol International Atomic Energy Agency .,) 2 efrici • The observed mass of a nucleus is smaller than the sum of its parts: L1 = zmP +(A- Z)mn _Amz • The mass deficit() has an equivalent energy (from E =mc2) called the binding energy ( 8 == 11 c2) • Nuclear reactions that result in a net release of energy (B) include: - fusion of two small nuclei - fission of a large nucleus International Atomic Energy Agency .,) 3 clear ergy 9 U25 Fess • .,..u2a - E released from - 1:: 0 6 fission ID (j =:1 1:: .._ 5 Q) c.. 4 ID E released from ;:;: a;. C) fusion 3 1:: H3 =c , He .5 ..0 2 a C) H:2 ()); 1 H1 0 90 0 .30 60 1:20 150 190 :210 :240 270 Number of nucleons In nucleus Original Image Source: Adriaan Buijs, EP704 Advanced Reactor Physics, Course Notes, McMaster Univetkf009. International Atomic Energy Agency 4 • • ce I I • It is possible for a heavy nucleus to fission on its own, but it is very rare (low probability of occurrence) • Many elements fission readily when the nucleus absorbs an additional neutron • Classify these materials as: - fissile: fissions readily with a low energy neutron e.g.: 233l/ 235ll 239JJL/ 92 92 94 - fissionable: fissions with a high energy neutron e.g.: 238l/ 92 - fertile: absorbs a neutron to become a fissile material e.g.: 232Th233ll 23sl/239fJll 90 92 92 94 International Atomic Energy Agency .,) 5 ele n • A neutron may undergo several different reactions with a nucleus, including: - Scattering (elastic or inelastic): there is a transfer of energy between the neutron and the nucleus - Absorption: the neutron is absorbed into the nucleus and lost - Fission: the neutron causes the nucleus to fission, releasing additional neutrons and fission products • The likelihood of an interaction occurring is represented 28 2 with a microscopic cross section (a) 1 barn (b)== l0- m - Dependent on the isotope of the interacting material (and its temperature) - Dependent on the incident neutron energy International Atomic Energy Agency ) 6 • • I I n I I -.. I -f ® -f I n .. n-.. International Atomic Energy Agency .,) 7 ergy • Neutron energies cover -10 orders of magnitude: - Fission spectrum - Delayed spectrum - Moderation • Interaction cross sections may change by 5+ orders of magnitude over this range of energy. • Need to solve neutron evolution over these ranges. • OPTIONS -7 - Full transport (absorption, moderation, fission) at each "point" in the reactor (i.e., continuous energy solution). - Transport over "Groupwise" energies (i.e., "multi-group cross sections). - Diffusion over "Few" groups (i.e., 2-group diffusion solvers such as SCALE) - What is the relative calculation times for these approaches? International Atomic Energy Agency ) 8 • the energies range up to several MeV, with a 0.4 maximum around 0.7 MeV. • The fission-neutron spectrum 0.2 has the form 0.1 036 x( E)== 0.453e-1. £ sinh .J2.29 E (1) 2 4 6 8 10 Energy (MeV) (a) where E is in MeV Energy Distribution of Fission Neutrons (Note: this is a distribution in Note - Illustration copyright: number of neutrons, not flux) Copyright 1985 by American Nuclear Society, La Grange Park, Illinois International Atomic Energy Agency .,) 9 • e erg1e • Neutronic energy distribution can be classified as: - the fission spectrum at energies above about 50-100 keV - the slowing-down spectrum to about 1 eV - the Maxwellian spectrum at thermal energies, below about 1 eV International Atomic Energy Agency ) 10 • • 235 I I r n E:HDF Request 92309. 2009-Jul-17.1l :S1:11 5 to- ao 10- 1 Fast range Epi-thermal energy range Thermal energy range to 1 1. 1 Incident Energy ( IMeU) Original Image Source: Adriaan Buijs, EP704Advanced Reactor Physics, Course Notes, McMaster Univl 2009. International Atomic Energy Agency 11 • erma I I Fast Neutrons Thermal Neutron 1 eV 3 -10 m/s Heat 1 MeV Fission 7 -10 m/s Products Original Image Source: Jeremy Whitlock, Powering Ontario: The Nuclear Solution, Presentation to the UofT Nuclear Power Group, 2005. . International Atomic Energy Agency (y) 12 e KEVCQ • Most neutrons born from fission are in the fast range (high energy) • To sustain a fission chain reaction, the fast neutrons must be brought down to a lower energy (where a fission is higher) via interaction with a moderator • Thermal reactor • Neutrons transfer their "excess" energy to the moderator through series of scattering interactions I collisions • Good moderators have: - Low absorption cross sections cr absorption - Low atomic masses (to maximize E in a single interaction) International Atomic Energy Agency ) 13 Fast Thermal Neutrons Neutrons 235U Fission Products Original Image Source: Jeremy Whitlock, Powering Ontario: The Nuclear Solution, Presentation to the UofT Nuclear Power Group, 2005. ) International Atomic Energy Agency 14 e ergy N- tl\fJ1,wJ.t""' r"c.K 1\.&A.-"" N'\,0"' F £ p:., k..-.w-. c..l (A A,:.. l'ie........kiV''"') ) I -1 IO . 0 International Atomic Energy Agency ) 15 • The reactor is critical when the number of neutrons produced in each generation is equal to the number lost • The multiplication factor is defined as: k= rateot neutron production rate of neutron loss - k 1 : the reactor is subcritical - k = 1 : the reactor is critical - k 1 : the reactor is supercritical International Atomic Energy Agency .,) 16 an elaye e • Neutrons that are released immediately after the fission occurs are referred to as prompt neutrons • Most fission products are unstable nuclei that undergo radioactive decay • Following radioactive decay, some daughter nuclei may have sufficient energy to release additional neutrons called delayed neutrons - Time constants for release of delayed neutrons are dominated by the half life of the unstable fission product • Delayed neutrons must be included in analysis International Atomic Energy Agency ) 17 ce e • Direct fission neutrons have a "lifetime" - Neutrons born in fission interact with • moderator (scatter/absorption) • core materials (absorption). • Fast fission materials - Their "lifetime" is very short. - Control of such a system is very difficult (mechanical and I&C systems cannot respond on this timeframe). • Delayed neutrons have time scales much longer (order of seconds) . - A thermal reactor is designed such that the reactor is slightly "subcritical" based on direct fission neutrons alone. - The delayed neutrons provide the remaining neutrons to make the core critical. • Therefore control of the reactor can be achieved through changes in the delayed neutron absorption. International Atomic Energy Agency ) 18 • Define reactivity as the relative distance from criticality: 1 p==l k - p 0 : the reactor is subcritical - p = 0 : the reactor is critical - p 0 : the reactor is supercritical • Units of reactivity 1 mk == 0.001, or 1 pcm == 0.01 mk are typically viewed as being added or removed from the reactor International Atomic Energy Agency .,) 19 • IC The goal of reactor physics calculations is to track neutrons as they evolve in space, energy and time. This allows redictions of ower, radiation levels, decay heat. ... etc .. • Fundamental assumptions of most reactor physics analysis: - The average behaviour of neutrons is descriptive - Neutrons do not interact with one another International Atomic Energy Agency ) 20