{"id":15560,"date":"2017-10-02T10:01:12","date_gmt":"2017-10-02T10:01:12","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=15560"},"modified":"2022-10-31T07:17:13","modified_gmt":"2022-10-31T07:17:13","slug":"neutron-leakage","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/neutron-leakage\/","title":{"rendered":"Neutron Leakage"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\">In general, neutrons may leak out of the system during the slowing down process or the neutron diffusion. <strong>Neutron leakage<\/strong> can be reduced using reflectors.<\/div><\/div>\n<p>In an infinite multiplication system, the leakage of the system is logically neglected. But all multiplying systems, all realistic <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor cores<\/a> are finite multiplying systems, and the leakage may not be neglected. In general, neutrons may leak out of the system during:<\/p>\n<ul>\n<li>During the <strong>slowing down process<\/strong>, some of the<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\"> neutrons<\/a> leak out of the boundaries of the reactor core before they become thermalized. This process and its impact on the <a title=\"Six Factor Formula \u2013 Effective Multiplication Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/six-factor-formula-effective-multiplication-factor\/\">effective multiplying factor<\/a> is characterized by the <a title=\"Fast Non-leakage Probability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/fast-non-leakage-probability\/\">fast non-leakage factor, P<sub>f<\/sub><\/a>, which is defined as the ratio of the number of fast neutrons that do not leak from the reactor core during the <strong>slowing down process<\/strong> to the number of fast neutrons produced by fissions at all energies.<\/li>\n<li>\n<figure id=\"attachment_15562\" aria-describedby=\"caption-attachment-15562\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/Two-Group-Method-Reflected-Reactor.png\"><img loading=\"lazy\" class=\"size-medium wp-image-15562\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/Two-Group-Method-Reflected-Reactor-300x169.png\" alt=\"two-group-method-reflected-reactor\" width=\"300\" height=\"169\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/Two-Group-Method-Reflected-Reactor-300x169.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/Two-Group-Method-Reflected-Reactor.png 574w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-15562\" class=\"wp-caption-text\">This figure shows the general effect of reflection in the thermal reactor system. Note that a reflector can raise the power density of the core-periphery and thus increase the core average power level without changing the peak power.<\/figcaption><\/figure>\n<p>During <strong>neutron diffusion<\/strong>, some of the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons<\/a> leak out of the boundaries of the reactor core before they are absorbed. This process and its impact on the effective multiplying factor is characterized by the <a title=\"Thermal Non-leakage Probability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/thermal-non-leakage-probability\/\">thermal non-leakage factor, Pt<\/a>, defined as the ratio of the number of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutrons<\/a> that do not leak from the reactor core during the <strong>neutron diffusion<\/strong> process to the number of neutrons that reach thermal energies.<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Fast Non-leakage Probability<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13667\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability.png\" alt=\"fast non-leakage probability\" width=\"751\" height=\"51\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability.png 751w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability-300x20.png 300w\" sizes=\"(max-width: 751px) 100vw, 751px\" \/><\/a><br \/>\nNote that there is consistency between the numerator in the definition of <a title=\"Fast Fission Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/fast-fission-factor\/\"><strong>\u03b5<\/strong><\/a> and the denominator in the definition of P<sub>f<\/sub>.<\/p>\n<p><span style=\"font-weight: 400;\">The fast non-leakage probability is for large reactor cores about <strong>0.92 &#8211; 0.98<\/strong>. This value is minimally affected (in comparison with the other factors) by operational changes except for changes in the moderator temperature. It can be derived from the Fermi age theory, the probability that a neutron will remain in\u00a0<\/span>the core and become a <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutron<\/a> without being lost by fast leakage is also <strong><span style=\"font-weight: 400;\">represented by the following equation:<\/span><\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_2.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13680\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_2.png\" alt=\"fast non-leakage probability_2\" width=\"189\" height=\"61\" \/><\/a><\/p>\n<p>where <strong>\u03c4<\/strong> is <strong>fermi age of a neutron<\/strong>, <strong>B<\/strong> is the <strong>geometrical buckling<\/strong> (in case of critical state B<sub>g<\/sub> = B<sub>m<\/sub>), which depends only on the shape and size of the core. The value of <strong>B<\/strong> <strong>for small cores is higher<\/strong> than the value for large cores. So that, it is obvious, the fast neutrons leakage is higher for small cores and depends on the <a title=\"Macroscopic Slowing Down Power \u2013 MSDP\" href=\"http:\/\/sitepourvtc.com\/glossary\/macroscopic-slowing-down-power-msdp\/\">macroscopic slowing down the power<\/a> of <a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">neutron moderator<\/a> (leakage is higher for poor moderators).<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Thermal Non-leakage Probability<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/thermal-non-leakage-probability.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13665\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/thermal-non-leakage-probability.png\" alt=\"thermal non-leakage probability\" width=\"803\" height=\"54\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/thermal-non-leakage-probability.png 803w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/thermal-non-leakage-probability-300x20.png 300w\" sizes=\"(max-width: 803px) 100vw, 803px\" \/><\/a><br \/>\n<strong><span style=\"font-weight: 400;\"><strong>The thermal non-leakage probability<\/strong> is for large reactor cores about <strong>0.95 &#8211; 0.98<\/strong><\/span><\/strong><span style=\"font-weight: 400;\">. This<\/span><strong><span style=\"font-weight: 400;\"> value is minimally affected (in comparison with the other factors) by operational changes except for changes in the<strong> moderator temperature<\/strong>. The only parameter that influences <strong>the thermal non-leakage probability<\/strong> is the moderator temperature. It can be derived from the neutron diffusion theory. The probability that a thermal neutron will remain in the core is also represented by the following equation:<\/span><\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/thermal-non-leakage-probability-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13721\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/thermal-non-leakage-probability-equation.png\" alt=\"thermal non-leakage probability\" width=\"131\" height=\"69\" \/><\/a><\/p>\n<p>in which <strong>L<sub>d<\/sub><\/strong> is the <strong>diffusion length<\/strong>, <strong>B <\/strong>is the<strong> geometrical buckling<\/strong> (in case of critical state <strong>B<sub>g<\/sub> = B<sub>m<\/sub><\/strong>), which depends only on the shape and size of the core. The value of B for small cores is higher than the value for large cores. So that, it is obvious, the thermal neutrons <strong>leakage is higher for small cores <\/strong>and depends on the <a title=\"Macroscopic Slowing Down Power \u2013 MSDP\" href=\"http:\/\/sitepourvtc.com\/glossary\/macroscopic-slowing-down-power-msdp\/\">macroscopic slowing down the power<\/a> of <a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">neutron moderator<\/a> (leakage is higher for poor moderators). <strong>The diffusion length<\/strong> is given by the following equation:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/diffusion-length.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13723\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/diffusion-length.png\" alt=\"diffusion length\" width=\"108\" height=\"43\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Neutron Life Cycle - Thermal Reactor<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13834\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula.png\" alt=\"Six Factor Formula - Four Factor Formula\" width=\"839\" height=\"790\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula.png 839w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula-300x282.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Six-Factor-Formula-Four-Factor-Formula-52x50.png 52w\" sizes=\"(max-width: 839px) 100vw, 839px\" \/><\/a><\/div><\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Total Non-leakage Probability<\/h2>\n<p><a title=\"Fast Non-leakage Probability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/fast-non-leakage-probability\/\"><strong>The fast non-leakage probability<\/strong><\/a> (P<sub>f<\/sub>) and <a title=\"Thermal Non-leakage Probability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/thermal-non-leakage-probability\/\"><strong>the thermal non-leakage probability<\/strong><\/a> (P<sub>t<\/sub>) may be combined into one term that gives the fraction of <strong>all neutrons<\/strong> that do not leak out of the reactor core. This term is called<strong> the total non-leakage probability <\/strong>and is given the symbol P<sub>NL<\/sub>, and may be expressed by the following equation:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_3.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13679\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_3.png\" alt=\"fast non-leakage probability_3\" width=\"264\" height=\"117\" \/><\/a><\/p>\n<p>We can rewrite this equation without a substantial loss of accuracy <strong>for large reactors<\/strong> simply by replacing the <a title=\"Diffusion Length\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/diffusion-length\/\"><strong>diffusion length L<sub>d<\/sub><\/strong><\/a> and the fermi age\u00a0<strong>\u03c4<\/strong> with the <strong>migration length M<\/strong> in the one group equation. The term <strong>B<\/strong><strong><sup>4<\/sup><\/strong> is very small for large reactors, and therefore it can be neglected. We may then write.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_4.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13678\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_4.png\" alt=\"fast non-leakage probability_4\" width=\"135\" height=\"173\" \/><\/a><\/p>\n<p>where M is the <a title=\"Migration Length \u2013 Migration Area\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/migration-length-migration-area\/\"><strong>migration area (m<\/strong><strong><sup>2<\/sup><\/strong><\/a><strong><a title=\"Migration Length \u2013 Migration Area\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/migration-length-migration-area\/\">)<\/a><\/strong>, the migration length is defined as the square root of the migration area. As can be seen, the total non-leakage probability of large reactors is primarily a function of the migration area.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13684\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png\" alt=\"Neutron Moderators - Parameters\" width=\"666\" height=\"510\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png 666w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters-300x230.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters-180x138.png 180w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><\/a><\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Main operational changes, that affect the neutron leakage<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Since both (<strong>P<sub>f<\/sub> and P<sub>t<\/sub><\/strong>) are affected by a change in <strong>moderator temperature<\/strong> in a heterogeneous water-moderated reactor, and the directions of the feedbacks are the same, the resulting<strong> total non-leakage probability<\/strong> is also sensitive on the change in the moderator temperature. As a result, an<strong> increase in the moderator temperature<\/strong> causes that the probability of<strong> leakage to increase<\/strong>. This effect is one of two main effects causing the <a title=\"Moderator Temperature Coefficient \u2013 MTC\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/moderator-temperature-coefficient-mtc\/\"><strong>moderator temperature coefficient (MTC)<\/strong><\/a> of most\u00a0<a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWRs<\/a> to be negative.<\/p>\n<p><strong>The thermal neutron leakage<\/strong> is dependent on the core temperature (or moderator temperature). The moderator temperature influences <a title=\"Macroscopic Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/macroscopic-cross-section\/\">macroscopic cross-sections<\/a> for <a title=\"Neutron Elastic Scattering\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/\">elastic scattering reaction<\/a>, especially <a title=\"Atomic Number Density\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/atomic-number-density\/\">the atomic number density<\/a> \u2013\u00a0<strong>N<sub>H2O<\/sub><\/strong>(<strong>\u03a3<sub>s<\/sub>=\u03c3<sub>s<\/sub>.N<sub>H<sub>2<\/sub>O<\/sub><\/strong>) due to the<strong> thermal expansion<\/strong> of water. Also, the <a title=\"Microscopic Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/microscopic-cross-section\/\">microscopic cross-section<\/a>\u00a0(<strong>\u03c3<sub>a<\/sub><\/strong>) for <a title=\"Neutron Absorption\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/\">neutron absorption<\/a> changes with core temperature. Both processes have the same direction. As the temperature of the core increases, <strong>the diffusion coefficient<\/strong> (<strong>D = 1\/3.\u03a3<sub>tr<\/sub><\/strong>) increases, and the absorption cross-section decreases, which causes the increase in the thermal neutron leakage. This physical process is a part of the <strong>moderator temperature coefficient (MTC).<\/strong><\/p>\n<p><strong>The fast neutron leakage<\/strong> is also dependent on the core temperature (or moderator temperature). <strong>The moderator temperature<\/strong> influences <a title=\"Macroscopic Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/macroscopic-cross-section\/\">macroscopic cross-sections<\/a> for <a title=\"Neutron Elastic Scattering\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/\">elastic scattering reaction<\/a> (<strong>\u03a3<sub>s<\/sub>=\u03c3<sub>s<\/sub>.N<sub>H<sub>2<\/sub>O<\/sub><\/strong>) due to the <strong>thermal expansion<\/strong> of water.\u00a0As the temperature of the core increases, the <strong>fast neutron leakage increases<\/strong>. This physical process is a part of the\u00a0<strong>moderator temperature coefficient<\/strong> (MTC). It is responsible for an increase in <a title=\"Neutron Flux Density \u2013 Neutron Intensity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-neutron-intensity\/\">neutron flux<\/a> measured by neutron detectors situated around the <a title=\"Reactor Pressure Vessel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/reactor-pressure-vessel\/\">reactor vessel<\/a>.<\/p>\n<p><strong>In power reactors<\/strong>, <strong>the total non-leakage probability<\/strong> also significantly changes with <strong>fuel burnup<\/strong>. This dependency is not associated\u00a0with any of the parameters like the diffusion coefficient or the geometrical buckling. In power reactors, the total non-leakage probability strongly depends on the certain <strong>fuel loading pattern,<\/strong> and the reload strategy. Neutron leakage is one of the key parameters in the<strong> neutron and fuel economy<\/strong>.<\/p>\n<p>To enhance the neutron and fuel economy, core designers design the <strong>low leakage loading patterns<\/strong>, in which fresh fuel assemblies are not situated in the peripheral positions of the <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor core<\/a>. The peripheral positions are loaded with the fuel with the highest fuel burnup. Compared to the average assemblies, these \u201chigh\u201d burnup assemblies have inherently lower relative power (due to the lower <strong>k<sub>inf<\/sub><\/strong> and the fact they feel the presence of a non-multiplying environment). In short, this parameter is significantly dependent on a certain loading pattern. During fuel burnup, the neutron leakage usually increases, especially in low leakage loading patterns. This process is caused by reducing the differences in <strong>k<sub>inf<\/sub><\/strong> between fresh fuel assemblies and peripheral high-burnup assemblies.<\/div><\/div><\/div>\n<h2>Neutron Reflectors &#8211; Leakage Reduction<\/h2>\n<figure id=\"attachment_15417\" aria-describedby=\"caption-attachment-15417\" style=\"width: 230px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Heavy-Reflector-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-15417\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Heavy-Reflector-min-240x300.png\" alt=\"heavy reflector\" width=\"240\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Heavy-Reflector-min-240x300.png 240w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Heavy-Reflector-min.png 800w\" sizes=\"(max-width: 240px) 100vw, 240px\" \/><\/a><figcaption id=\"caption-attachment-15417\" class=\"wp-caption-text\">Visualization of a heavy reflector. It is only an illustrative example.<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">It is well known that each <\/span><a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\"><span style=\"font-weight: 400;\">reactor core<\/span><\/a><span style=\"font-weight: 400;\"> is surrounded by a <a title=\"Neutron Reflector\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/\"><strong>neutron reflector<\/strong><\/a> or <a title=\"Core Baffle\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/core-baffle\/\"><strong>reactor core baffle<\/strong><\/a>. The reflector reduces the non-uniformity of the power distribution in the peripheral fuel assemblies, reduces neutron leakage, and reduces a coolant flow bypass of the core. The neutron reflector is a non-multiplying medium, whereas the reactor core is a multiplying medium.<\/span><\/p>\n<p>Except for research reactors, practically all power reactor cores are designed to minimize <strong>neutron leakage<\/strong>. <a title=\"Neutron Reflector\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/\"><strong>Neutron reflectors<\/strong><\/a> surround reactor cores to minimize leakage. The neutron reflector scatters back (or reflects) into the core many neutrons that would otherwise escape. By <strong>reducing neutron leakage<\/strong>, the reflector increases <a title=\"Six Factor Formula \u2013 Effective Multiplication Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/six-factor-formula-effective-multiplication-factor\/\">k<sub>eff<\/sub> <\/a>and reduces the amount of fuel necessary to maintain the reactor <a title=\"Critical Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactor-criticality\/critical-reactor\/\">critical<\/a> for a long period. In LWRs, the neutron reflector is installed for the following purposes:<\/p>\n<ul>\n<li>The<a title=\"Neutron Flux Density \u2013 Neutron Intensity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-neutron-intensity\/\"> neutron flux<\/a> distribution is \u201c<strong>flattened<\/strong>\u201d, i.e., the ratio of the average flux to the maximum flux is increased. Therefore reflectors <strong>reduce the non-uniformity<\/strong> of the power distribution.<\/li>\n<li>Because of the higher flux at the edge of the core, there is much <strong>better utilization<\/strong> in the peripheral fuel assemblies. In the outer regions of the core, this fuel now contributes much more to the total power production.<\/li>\n<li>The neutron reflector scatters back (or reflects) into the core many neutrons that would otherwise escape. The neutrons reflected into the core are available for a <a title=\"Nuclear Fission Chain Reaction\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/\">chain reaction<\/a>. This means that the <strong>minimum critical size<\/strong> of the reactor is reduced. Alternatively, if the core size is maintained, the reflector makes additional <a title=\"Reactivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity\/\">reactivity<\/a> available for higher fuel burnup. The decrease in the critical size of the core required is known as <strong>reflector savings<\/strong>.<\/li>\n<li>Neutron reflectors reduce neutron leakage, i.e., to reduce the neutron fluence on a reactor pressure vessel.<\/li>\n<li>Neutron reflectors reduce a coolant flow bypass of a core.<\/li>\n<li>Neutron reflectors serve as a thermal and radiation shield of a reactor core.<\/li>\n<\/ul>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Nuclear and Reactor Physics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics.\u00a0Clarendon Press; 1 edition, 1991, ISBN:\u00a0978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics.\u00a0Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory.\u00a0DOE Fundamentals Handbook,\u00a0Volume 1 and 2.\u00a0January\u00a01993.<\/li>\n<\/ol>\n<p><strong><\/strong><strong>Advanced Reactor Physics:<\/strong><\/p>\n<ol>\n<li>K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/li>\n<li>K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.<\/li>\n<li><span style=\"font-weight: 400;\">D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.\u00a0<\/span><\/li>\n<li>E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Diffusion Theory<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In an infinite multiplication system, the leakage of the system is logically neglected. But all multiplying systems, all realistic reactor cores are finite multiplying systems, and the leakage may not be neglected. In general, neutrons may leak out of the system during: During the slowing down process, some of the neutrons leak out of the &#8230; <a title=\"Neutron Leakage\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/neutron-leakage\/\" aria-label=\"More on Neutron Leakage\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":15150,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/15560"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=15560"}],"version-history":[{"count":3,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/15560\/revisions"}],"predecessor-version":[{"id":33675,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/15560\/revisions\/33675"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/15150"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=15560"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}