{"id":13466,"date":"2017-01-01T20:10:04","date_gmt":"2017-01-01T20:10:04","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=13466"},"modified":"2022-10-19T11:07:52","modified_gmt":"2022-10-19T11:07:52","slug":"self-shielding","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/self-shielding\/","title":{"rendered":"Self-shielding"},"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\">It was written, in some cases, the amount of absorption reactions is dramatically reduced despite the <strong>unchanged microscopic cross-section<\/strong> of the material. This phenomenon is commonly known as <strong>the resonance self-shielding<\/strong> and also <strong>contributes to reactor stability<\/strong>. There are two types of self-shielding.<\/div><\/div>\n<ul>\n<li><strong>Energy Self-shielding.<\/strong><\/li>\n<li><strong>Spatial Self-shielding.<\/strong><\/li>\n<\/ul>\n<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>Radiative capture cross-sections of 238U and 240Pu<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Doppler-Broadening-240Pu-238U.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13462\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Doppler-Broadening-240Pu-238U.png\" alt=\"Doppler coefficient - fuel burnup\" width=\"804\" height=\"527\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Doppler-Broadening-240Pu-238U.png 804w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/Doppler-Broadening-240Pu-238U-300x197.png 300w\" sizes=\"(max-width: 804px) 100vw, 804px\" \/><\/a><\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Energy Self-shielding<\/h2>\n<p>In each <a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\">nuclear reactor<\/a>, there is a <strong>characteristic neutron energy spectrum<\/strong> that, in the case of thermal reactors, also covers <a title=\"Neutron Capture Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/neutron-capture-cross-section\/\">the resonance region<\/a> of various materials (<a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup>238<\/sup>U<\/a> is important in this phenomenon). The vicinity of the <a title=\"What is Nuclear Resonance \u2013 Compound Nucleus\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/compound-nucleus-reactions\/what-is-nuclear-resonance-compound-nucleus\/\">resonance<\/a> causes an<strong> increase in the neutron absorption probability<\/strong>\u00a0when a <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a> has <strong>energy near a resonance<\/strong>. This reduces the effective absorption per nucleus due to the <strong>depression of the energy-dependent flux \u03a6(E)<\/strong> near the resonance compared to a flat flux. At energies just below the resonance, where <strong>\u03c3<sub>a<\/sub> (E)<\/strong> becomes small again, the neutron flux reaches almost the same value above the resonance. This reduction in the energy-dependent neutron flux near the resonance energy is known as <strong>energy self-shielding<\/strong>.<\/p>\n<figure id=\"attachment_13383\" aria-describedby=\"caption-attachment-13383\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-cross-section.png\"><img loading=\"lazy\" class=\"wp-image-13383 size-medium\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-cross-section-300x240.png\" alt=\"\" width=\"300\" height=\"240\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-cross-section-300x240.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-cross-section-177x142.png 177w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-cross-section-147x118.png 147w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-cross-section.png 649w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-13383\" class=\"wp-caption-text\">Energy-dependent neutron flux versus uranium density at 6.67eV resonance of 238U.<\/figcaption><\/figure>\n<figure id=\"attachment_13382\" aria-describedby=\"caption-attachment-13382\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-238-uranium.png\"><img loading=\"lazy\" class=\"wp-image-13382 size-medium\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-238-uranium-300x227.png\" alt=\"\" width=\"300\" height=\"227\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-238-uranium-300x227.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-238-uranium.png 666w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-13382\" class=\"wp-caption-text\">Energy-dependent neutron flux versus fuel temperature at 6.67eV resonance of 238U.<\/figcaption><\/figure>\n<h2>Spatial Self-shielding<\/h2>\n<p>The basic fuel element of light water reactors is a <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">fuel rod<\/a> that contains <strong>fuel pellets<\/strong> made of <strong>uranium dioxide<\/strong>. For example, an 1100 MWe (3300 MWth) <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor core<\/a> may contain <strong>157 fuel assemblies<\/strong> composed of over <strong>45,000 fuel rods<\/strong> and <strong>15 million fuel pellets<\/strong>. The <a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">neutron moderator<\/a> surrounds these fuel rods. The <strong>spatial self-shielding<\/strong> is a phenomenon primarily connected with this <strong>heterogeneity of the reactor core<\/strong>.<\/p>\n<p>The fission neutrons are <strong>born in the fuel<\/strong>, but they are primarily <strong>moderated (slowed down) in the moderator<\/strong>. Thermal and epithermal neutrons return into the fuel to be absorbed and to cause further fission. With energy, self-shielding neutrons are <strong>more likely absorbed<\/strong> by the nuclei <strong>near the fuel surface<\/strong>. In this case, the <strong>surface layers<\/strong> of the fuel geometrically <strong>shield the inner layers<\/strong> from neutron flux, leading to a relatively lower neutron flux inside the fuel rod. For neutron energies near resonances (energy self-shielding), the depression of the energy-dependent flux is dramatic.<\/p>\n<p><strong>The spatial and energy self-shielding<\/strong> that occurs primarily in heterogeneous reactor cores causes a <strong>significant increase in the resonance escape probability<\/strong> (\u201cp\u201d from the four-factor formula) compared to homogeneous cores. Without the spatial self-shielding provided by the separation of fuel and moderator, values of <strong>k<sub>eff<\/sub> = 1<\/strong> are possible with natural uranium fuel only if heavy water is used as the moderator.<\/p>\n<p><strong>Another example:<\/strong><\/p>\n<p>In the nuclear industry,<a title=\"Gadolinium\" href=\"http:\/\/sitepourvtc.com\/glossary\/gadolinium\/\"> gadolinium <\/a>is commonly used as a <strong>neutron absorber<\/strong> due to the very high neutron absorption cross-section of two isotopes <strong><sup>155<\/sup>Gd<\/strong> and<strong> <sup>157<\/sup>Gd<\/strong>. In fact, their absorption cross-sections are the highest among all stable isotopes. <strong><sup>155<\/sup>Gd<\/strong>\u00a0has <strong>61 000 barns<\/strong> for <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutrons<\/a> (for 0.025 eV neutron) and <strong><sup>157<\/sup>Gd<\/strong>\u00a0has even <strong>254 000 barns<\/strong>. Some power plants use gadolinium as a <strong>burnable absorber<\/strong> diluted in the <strong>fuel matrix<\/strong> in mixture Gd<sub>2<\/sub>O<sub>3<\/sub>\u00a0+ UO<sub>2<\/sub>. Such a high absorption cross-section of gadolinium causes the fuel rod to burn up<strong> layer by layer<\/strong> (from the surface to inner layers). At the beginning of the cycle, this fuel rod behaves like being from neutron black material. At the beginning of the cycle, the higher content (i.e., from 4% to 6% of Gd<sub>2<\/sub>O<sub>3<\/sub>) of gadolinium causes a minimal decrease in the overall compensation of the core reactivity. Only the higher amount of such rods with burnable absorbers results in the overall decrease in core reactivity. This is also an example of a very strong effect of self-shielding.<\/p>\n<h2>Self-shielding and Doppler Broadening<\/h2>\n<figure id=\"attachment_13381\" aria-describedby=\"caption-attachment-13381\" style=\"width: 1014px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min.png\"><img loading=\"lazy\" class=\"wp-image-13381 size-large\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min-1024x512.png\" alt=\"Self-shielding - neutron cross-section\" width=\"1024\" height=\"512\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min-1024x512.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min-300x150.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min.png 1200w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption id=\"caption-attachment-13381\" class=\"wp-caption-text\">An increase in temperature from T1 to T2 causes the broadening of spectral lines of resonances. Although the area under the resonance remains the same, the broadening of spectral lines causes an increase in neutron flux in the fuel \u03c6f(E), increasing the absorption as the temperature increases.<\/figcaption><\/figure>\n<p>There is a further phenomenon connected with <strong>spatial and energy self-shielding<\/strong>. The energy self-shielding is significantly <strong>affected by the material temperature<\/strong>. It is closely connected with the <a title=\"Doppler Broadening \u2013 Doppler Effect\" href=\"http:\/\/sitepourvtc.com\/glossary\/doppler-broadening\/\"><strong>Doppler broadening<\/strong><\/a> and the<strong> fuel temperature coefficient<\/strong> (also known as the <strong>Doppler coefficient<\/strong>). The material temperature affects the energy self-shielding through Doppler-broadening of the microscopic resonance cross-section. With an increase in fuel temperature, the<strong> thermal motion<\/strong> of target nuclei increases resulting in the <strong>broadening of spectral lines<\/strong> due to the Doppler effect. The wings of resonances are broadened while their peak magnitude decreases. The <strong>energy-dependent neutron flux<\/strong> closely follows the behavior of the changed resonances in a <strong>reverse manner<\/strong>, leading to a <strong>reduction in the self-shielding<\/strong> and an increase in the effective microscopic absorption cross-section. This, in turn, provides <strong>negative reactivity feedback<\/strong> against fuel temperature increase.<\/p>\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><span style=\"font-weight: 400;\">K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/span><\/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\">\n<h2>See previous:<\/h2>\n<a href=\"\" 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><\/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>Neutron Cross-section<a href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\" 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\">\n<h2>See next:<\/h2>\n<a href=\"\" 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><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Energy Self-shielding. Spatial Self-shielding. Energy Self-shielding In each nuclear reactor, there is a characteristic neutron energy spectrum that, in the case of thermal reactors, also covers the resonance region of various materials (238U is important in this phenomenon). The vicinity of the resonance causes an increase in the neutron absorption probability\u00a0when a neutron has energy &#8230; <a title=\"Self-shielding\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/self-shielding\/\" aria-label=\"More on Self-shielding\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":12656,"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\/13466"}],"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=13466"}],"version-history":[{"count":4,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/13466\/revisions"}],"predecessor-version":[{"id":32814,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/13466\/revisions\/32814"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/12656"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=13466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}