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<!DOCTYPE html><html lang="en-GB"><head><title>Neutronics Workshop</title><meta property="og:title" content="Neutronics Workshop"><meta name="author" content="Jonathan Shimwell"><meta property="article:author" content="Jonathan Shimwell"><meta name="description" content="Presentation slides for the fusion energy neutronics workshop"><meta property="og:description" content="Presentation slides for the fusion energy neutronics workshop"><meta name="keywords" content="fusion,neutronics,neutron,photon,radiation,simulation,openmc,dagmc"><meta charset="UTF-8"><meta name="viewport" content="width=device-width,height=device-height,initial-scale=1.0"><meta name="apple-mobile-web-app-capable" content="yes"><meta http-equiv="X-UA-Compatible" content="ie=edge"><meta property="og:type" content="website"><meta name="twitter:card" content="summary"><style>@media screen{body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>button,body[data-bespoke-view=next] 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/*!
* Marp default theme.
*
* @theme default
* @author Yuki Hattori
*
* @auto-scaling true
* @size 16:9 1280px 720px
* @size 4:3 960px 720px
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footer{bottom:21px}div#\:\$p>svg>foreignObject>section{--h1-color:#246;--header-footer-color:hsla(0,0%,40%,.75);--heading-strong-color:#48c;--paginate-color:#777;align-items:stretch;display:flex;flex-flow:column nowrap;font-size:29px;height:720px;justify-content:center;padding:78.5px;width:1280px}div#\:\$p>svg>foreignObject>section{--marpit-root-font-size:29px}div#\:\$p>svg>foreignObject>section:where(.invert){--h1-color:#cee7ff;--header-footer-color:hsla(0,0%,60%,.75);--heading-strong-color:#7bf;--paginate-color:#999}div#\:\$p>svg>foreignObject>section>:last-child,div#\:\$p>svg>foreignObject>section[data-footer]>:nth-last-child(2){margin-bottom:0}div#\:\$p>svg>foreignObject>section>:first-child,div#\:\$p>svg>foreignObject>section>header:first-child+*{margin-top:0}div#\:\$p>svg>foreignObject>section:after{bottom:21px;color:var(--paginate-color);font-size:24px;padding:0;position:absolute;right:30px}div#\:\$p>svg>foreignObject>section:after{--marpit-root-font-size:24px}div#\:\$p>svg>foreignObject>section[data-color] :is(h1,marp-h1),div#\:\$p>svg>foreignObject>section[data-color] :is(h2,marp-h2),div#\:\$p>svg>foreignObject>section[data-color] 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class="bespoke-marp-osc"><button data-bespoke-marp-osc="prev" tabindex="-1" title="Previous slide">Previous slide</button><span data-bespoke-marp-osc="page"></span><button data-bespoke-marp-osc="next" tabindex="-1" title="Next slide">Next slide</button><button data-bespoke-marp-osc="fullscreen" tabindex="-1" title="Toggle fullscreen (f)">Toggle fullscreen</button><button data-bespoke-marp-osc="presenter" tabindex="-1" title="Open presenter view (p)">Open presenter view</button></div><div id=":$p"><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="1" data-paginate="true" data-background-color="#fff" data-style=".columns {
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<h1 id="fusion-neutronics-workshop">Fusion Neutronics Workshop</h1>
<p><img src="images/cover.png" alt="Neutron" /></p>
</section>
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<h1 id="why-is-neutronics-useful">Why is neutronics useful</h1>
<ul>
<li><strong>Radioactivity</strong> - Neutrons activate material, making it radioactive leading to handling and waste storage requirements.</li>
<li><strong>Hazardous</strong> - Neutrons are Hazardous to health and shielded will be needed to protect the workforce.</li>
<li><em><strong>Produce fuel</strong></em> - Neutrons will be needed to convert lithium into tritium to fuel the reactor.</li>
<li><em><strong>Electricity</strong></em> - 80% of the energy release by each DT reaction is transferred to the neutron.</li>
<li><em><strong>Structural integrity</strong></em> - Neutrons cause damage to materials such as embrittlement, swelling, change conductivity …</li>
<li><em><strong>Diagnose</strong></em> - Neutrons are an important method of measuring a variety of plasma parameters (e.g. Q value).</li>
</ul>
</section>
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<h1 id="topics-covered-half-day-course">Topics Covered Half Day Course</h1>
<ul>
<li>
<p>Neutron and Photon interaction cross sections</p>
</li>
<li>
<p>Material creation</p>
</li>
<li>
<p>Particle sources</p>
</li>
<li>
<p>Constructive Solid Geometry (CSG)</p>
</li>
<li>
<p>Tallies (heat, tritium breeding ratio, damage, flux)</p>
</li>
<li>
<p>Neutron activation</p>
</li>
</ul>
</section>
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<h1 id="getting-started">Getting started</h1>
<ul>
<li>
<p><img class="emoji" draggable="false" alt="🐋" src="https://cdn.jsdelivr.net/gh/jdecked/[email protected]/assets/svg/1f40b.svg" data-marp-twemoji=""/> Install Docker</p>
</li>
<li>
<p><img class="emoji" draggable="false" alt="🔽" src="https://cdn.jsdelivr.net/gh/jdecked/[email protected]/assets/svg/1f53d.svg" data-marp-twemoji=""/> Download the docker image</p>
</li>
<li>
<p><img class="emoji" draggable="false" alt="🏃" src="https://cdn.jsdelivr.net/gh/jdecked/[email protected]/assets/svg/1f3c3.svg" data-marp-twemoji=""/>Run the docker image</p>
</li>
<li>
<p><img class="emoji" draggable="false" alt="🔗" src="https://cdn.jsdelivr.net/gh/jdecked/[email protected]/assets/svg/1f517.svg" data-marp-twemoji=""/> Navigate to the URL in the terminal</p>
</li>
</ul>
<p>Detailed instructions are on <a href="https://github.com/fusion-energy/neutronics-workshop/tree/main#local-installation"><u>GitHub</u></a></p>
</section>
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<h1 id="containers">Containers</h1>
<div class="columns" style="font-size: 30px;">
<div>
<p>Install single package (Docker) and avoid installing a few hundred packages.</p>
<ul>
<li>Portable</li>
<li>Reproducible</li>
<li>Security</li>
<li>Isolation</li>
<li>Deployable</li>
</ul>
</div>
<div>
<p><img src="https://imgs.xkcd.com/comics/python_environment.png" alt="xkcd" /><br />
image source xkcd.com</p>
</div>
<div>
</section>
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<h1 id="tasks">Tasks</h1>
<div class="columns" style="font-size: 30px;">
<div>
<ul>
<li>
<p>Collection of Jupyter notebooks</p>
</li>
<li>
<p>Separate task folder for each topic</p>
</li>
<li>
<p>Learning outcomes for each task</p>
</li>
<li>
<p>Simulation outputs include:</p>
<ul>
<li>numbers</li>
<li>graphs</li>
<li>images</li>
<li>3D visualization.</li>
</ul>
</li>
</ul>
</div>
<div>
<p><img src="images/jupyter.png" alt="" /></p>
</div>
<div>
</section>
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<h1 id="openmc">OpenMC</h1>
<div class="columns">
<div>
<ul>
<li>Increasing adoption in fusion</li>
<li><a href="https://openmc.discourse.group/">Supportive community</a></li>
<li><a href="https://github.com/openmc-dev/openmc/">GitHub repository</a></li>
<li>Permissive license (MIT)</li>
<li>Python API, C++ backend</li>
<li><a href="https://doi.org/10.1016/j.anucene.2014.07.048">Scales to 100,000+ cores</a></li>
<li>CPU and GPU version</li>
<li><a href="https://docs.openmc.org/en/stable/">Online documentation</a></li>
<li><a href="https://github.com/fusion-energy/neutronics-workshop">Excellent fusion specific workshops</a></li>
</ul>
</div>
<div>
<p><a href="https://star-history.com/#openmc-dev/openmc&Date"><img src="images/stars.png" alt="" style="width:900px;" /></a></p>
</div>
<div>
</section>
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<h1 id="getting-started-1">Getting started</h1>
<div class="columns" style="font-size: 30px;">
<div>
<ol>
<li>
<p>Run the docker image<br />
<code>docker run -p 8888:8888 ghcr.io/fusion-energy/neutronics-workshop</code></p>
</li>
<li>
<p>Double click on the <code>half-day-workshop</code> folder circled in red.</p>
</li>
</ol>
</div>
<div>
<p><img src="images/get_started.png" alt="" /></p>
</div>
<div>
</section>
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<h1 id="timetable">Timetable</h1>
<div class="columns" style="font-size: 20px;">
<div>
<ul>
<li>9.00 Introduction presentation</li>
<li>9.10 Plotting cross sections
<ul>
<li>task_01_isotope_xs_plot</li>
<li>task_02_element_xs_plot</li>
<li>task_03_material_xs_plot</li>
</ul>
</li>
<li>9.40 Making materials
<ul>
<li>task_04_example_materials_from_isotopes</li>
<li>task_05_example_materials_from_elements</li>
</ul>
</li>
<li>9.55 Geometry
<ul>
<li>task_06_simple_csg_geometry</li>
</ul>
</li>
<li>10.15 Break <img class="emoji" draggable="false" alt="☕" src="https://cdn.jsdelivr.net/gh/jdecked/[email protected]/assets/svg/2615.svg" data-marp-twemoji=""/></li>
<li>10.30 Plotting particles
<ul>
<li>task_07_point_source_plots</li>
<li>task_08_ring_source</li>
<li>task_09_plasma_source_plots</li>
</ul>
</li>
</ul>
</div>
<div>
<ul>
<li>11.05 Tritium Breeding Ratio (TBR)
<ul>
<li>task_10_example_tritium_production</li>
</ul>
</li>
<li>11.15 Damage (DPA)
<ul>
<li>task_11_find_dpa</li>
</ul>
</li>
<li>11:30 Break <img class="emoji" draggable="false" alt="☕" src="https://cdn.jsdelivr.net/gh/jdecked/[email protected]/assets/svg/2615.svg" data-marp-twemoji=""/></li>
<li>11:45 neutron photon spectra
<ul>
<li>task_12_example_neutron_spectra_on_cell</li>
<li>task_13_example_photon_spectra</li>
</ul>
</li>
<li>12.15 mesh tallies
<ul>
<li>task_14_example_2d_regular_mesh_tallies</li>
</ul>
</li>
<li>12.30 activation
<ul>
<li>task_15_full_pulse_schedule</li>
</ul>
</li>
<li>12.45 Putting it all together
<ul>
<li>task_16_optimal_design</li>
</ul>
</li>
</ul>
</div>
</div>
</section>
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<h1 id="microscopic-cross-sections">Microscopic Cross Sections</h1>
<ul>
<li>
<p>Probability of interaction is characterised by the microscopic cross-section (σ). It is the effective size of the nucleus.</p>
</li>
<li>
<p>Cross section data is key to the neutronics workflow and provide us with the likelihood of a particular interaction.</p>
</li>
<li>
<p>Cross sections can be measured experimentally with monoenergetic neutrons.</p>
</li>
</ul>
</section>
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<h1 id="experimental-data">Experimental data</h1>
<div class="columns" style="font-size: 30px;">
<div>
<p>Availability of experimental data varies for different reactions and different isotopes.</p>
<p>Typically the experimental data is then interpreted to create evaluation libraries, such as ENDF, JEFF, JENDL, CENDL.</p>
</div>
<div>
<p><a href="https://nds.iaea.org/dataexplorer/"><img src="images/exfor_be_n_2n.png" alt="" /></a></p>
<p>Source <a href="https://nds.iaea.org/dataexplorer/?target_elem=Au&target_mass=197&reaction=n%2Cg">IAEA nuclear data services</a></p>
</div>
<div>
</section>
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<h1 id="cross-section-reactions">Cross section reactions</h1>
<p>Cross section evaluations exist for:</p>
<ul>
<li>different nuclides</li>
<li>different interactions.</li>
</ul>
<p>A list of reactions available in OpenMC is <a href="https://docs.openmc.org/en/stable/usersguide/tallies.html#id2"><u>here</u></a></p>
<p>For example:</p>
<ul>
<li>Be9(n,2n)2He would be a neutron interaction with beryllium 9 which results in 2 neutrons and 2 helium nuclei.</li>
<li>Li6(n,Xt) would be a neutron interaction with lithium 6 nuclei which results in a tritium and X is a wildcard.</li>
</ul>
</section>
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<h1 id="reaction-rate">Reaction rate</h1>
<ul>
<li>The reaction rate (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.048ex;" xmlns="http://www.w3.org/2000/svg" width="3.434ex" height="1.593ex" role="img" focusable="false" viewBox="0 -683 1518 704"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></g><g data-mml-node="mi" transform="translate(759,0)"><path data-c="1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></g></g></g></svg></mjx-container>) can be found by knowing the number of neutrons per unit volume (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg></mjx-container>), the velocity of neutrons (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.097ex" height="1.027ex" role="img" focusable="false" viewBox="0 -443 485 454"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g></g></g></svg></mjx-container>), the material density (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="1.138ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 503 636"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g></g></g></svg></mjx-container>), Avogadro's number (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.355ex;" xmlns="http://www.w3.org/2000/svg" width="2.851ex" height="1.901ex" role="img" focusable="false" viewBox="0 -683 1260.1 840.1"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D441" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"></path></g><g data-mml-node="TeXAtom" transform="translate(836,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g></g></g></g></g></svg></mjx-container>), the microscopic cross section at the neutron energy (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.357ex;" xmlns="http://www.w3.org/2000/svg" width="2.225ex" height="1.332ex" role="img" focusable="false" viewBox="0 -431 983.5 588.8"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z"></path></g><g data-mml-node="TeXAtom" transform="translate(604,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g></g></g></g></g></svg></mjx-container>) and the atomic weight of the material (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="2.378ex" height="1.545ex" role="img" focusable="false" viewBox="0 -683 1051 683"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D440" d="M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path></g></g></g></svg></mjx-container>).</li>
<li>This reduces down to the neutron flux (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="1.348ex" height="2.034ex" role="img" focusable="false" viewBox="0 -694 596 899"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D719" d="M409 688Q413 694 421 694H429H442Q448 688 448 686Q448 679 418 563Q411 535 404 504T392 458L388 442Q388 441 397 441T429 435T477 418Q521 397 550 357T579 260T548 151T471 65T374 11T279 -10H275L251 -105Q245 -128 238 -160Q230 -192 227 -198T215 -205H209Q189 -205 189 -198Q189 -193 211 -103L234 -11Q234 -10 226 -10Q221 -10 206 -8T161 6T107 36T62 89T43 171Q43 231 76 284T157 370T254 422T342 441Q347 441 348 445L378 567Q409 686 409 688ZM122 150Q122 116 134 91T167 53T203 35T237 27H244L337 404Q333 404 326 403T297 395T255 379T211 350T170 304Q152 276 137 237Q122 191 122 150ZM500 282Q500 320 484 347T444 385T405 400T381 404H378L332 217L284 29Q284 27 285 27Q293 27 317 33T357 47Q400 66 431 100T475 170T494 234T500 282Z"></path></g></g></g></svg></mjx-container>), nuclide number density (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.355ex;" xmlns="http://www.w3.org/2000/svg" width="2.836ex" height="1.901ex" role="img" focusable="false" viewBox="0 -683 1253.7 840.1"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D441" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"></path></g><g data-mml-node="TeXAtom" transform="translate(836,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g></g></g></g></g></svg></mjx-container>) and microscopic cross section\sigma_{e}.</li>
<li>This can be reduced one more stage by making use of the Macroscopic cross section (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.357ex;" xmlns="http://www.w3.org/2000/svg" width="2.567ex" height="1.902ex" role="img" focusable="false" viewBox="0 -683 1134.5 840.8"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="3A3" d="M666 247Q664 244 652 126T638 4V0H351Q131 0 95 0T57 5V6Q54 12 57 17L73 36Q89 54 121 90T182 159L305 299L56 644L55 658Q55 677 60 681Q63 683 351 683H638V679Q640 674 652 564T666 447V443H626V447Q618 505 604 543T559 605Q529 626 478 631T333 637H294H189L293 494Q314 465 345 422Q400 346 400 340Q400 338 399 337L154 57Q407 57 428 58Q476 60 508 68T551 83T575 103Q595 125 608 162T624 225L626 251H666V247Z"></path></g><g data-mml-node="TeXAtom" transform="translate(755,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g></g></g></g></g></svg></mjx-container>).</li>
</ul>
<p><mjx-container class="MathJax" jax="SVG" display="true" style="margin: 0;"><svg style="vertical-align: -1.552ex; display: block; width: 100%; height: auto; max-height: 4.627ex;" xmlns="http://www.w3.org/2000/svg" width="32.507ex" height="4.627ex" role="img" focusable="false" viewBox="0 -1359 14368 2045"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 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<h1 id="now-complete-tasks-1-2-and-3-in-the-half-day-workshop">Now complete tasks 1, 2 and 3 in the half day workshop</h1>
</section>
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<h1 id="making-materials">Making materials</h1>
<div class="columns" style="font-size: 30px;">
<div>
<p>Neutronics codes require the isotopes and the number density.</p>
<p>This can be provided with different combinations of density units, isotope/element concentration and weight or atom fractions.</p>
</div>
<div>
<p><img src="images/nuc_chart.png" alt="" /></p>
</div>
<div>
</section>
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<h1 id="making-materials---nuclides">Making materials - nuclides</h1>
<p>Simple material construction from nuclides.</p>
<pre is="marp-pre" data-auto-scaling="downscale-only"><code class="language-python">mat2 = openmc.Material()
mat2.add_nuclide(<span class="hljs-string">'Li6'</span>, <span class="hljs-number">0.0759</span>*<span class="hljs-number">2</span>)
mat2.add_nuclide(<span class="hljs-string">'Li7'</span>, <span class="hljs-number">0.9241</span>*<span class="hljs-number">2</span>)
mat2.add_nuclide(<span class="hljs-string">'O16'</span>, <span class="hljs-number">0.9976206</span>)
mat2.add_nuclide(<span class="hljs-string">'O17'</span>, <span class="hljs-number">0.000379</span>)
mat2.add_nuclide(<span class="hljs-string">'O18'</span>, <span class="hljs-number">0.0020004</span>)
mat2.set_density(<span class="hljs-string">'g/cm3'</span>, <span class="hljs-number">2.01</span>)
</code></pre>
</section>
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<h1 id="making-materials---elements">Making materials - elements</h1>
<p>Simpler material construction from elements.</p>
<pre is="marp-pre" data-auto-scaling="downscale-only"><code class="language-python"><span class="hljs-keyword">import</span> openmc
mat1 = openmc.Material()
mat1.add_element(<span class="hljs-string">'H'</span>, <span class="hljs-number">2</span>)
mat1.add_element(<span class="hljs-string">'O'</span>, <span class="hljs-number">1</span>)
mat1.set_density(<span class="hljs-string">'g/cm3'</span>, <span class="hljs-number">2.01</span>)
</code></pre>
</section>
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<h1 id="making-materials---enrichment">Making materials - enrichment</h1>
<p>Simple enriched material construction from elements.</p>
<pre is="marp-pre" data-auto-scaling="downscale-only"><code class="language-python"><span class="hljs-keyword">import</span> openmc
mat1 = openmc.Material()
mat1.add_element(<span class="hljs-string">'Li'</span>, <span class="hljs-number">4</span>, enrichment_target=<span class="hljs-string">'Li6'</span>, enrichment=<span class="hljs-number">60</span>)
mat1.add_element(<span class="hljs-string">'Si'</span>, <span class="hljs-number">1</span>)
mat1.add_element(<span class="hljs-string">'O'</span>, <span class="hljs-number">4</span>)
mat1.set_density(<span class="hljs-string">'g/cm3'</span>, <span class="hljs-number">2.01</span>)
</code></pre>
</section>
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<h1 id="now-complete-tasks-4-and-5-in-the-half-day-workshop">Now complete tasks 4 and 5 in the half day workshop</h1>
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<h1 id="making-geometry">Making Geometry</h1>
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<p>The simplest geometry is a single surface and a cell defined as below (-) that surface.</p>
<pre is="marp-pre" data-auto-scaling="downscale-only"><code class="language-python"><span class="hljs-keyword">import</span> openmc
surface_sphere = openmc.Sphere(r=<span class="hljs-number">10.0</span>)
region_inside_sphere = -surface_sphere
cell_sphere = openmc.Cell(region=region_inside_sphere)
cell_sphere.fill = steel
</code></pre>
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<h1 id="making-geometry-1">Making Geometry</h1>
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<p>Cells can also be constrained by multiple surfaces. This example is above (+) one surface and (&) below (-) another</p>
<pre is="marp-pre" data-auto-scaling="downscale-only"><code class="language-python"><span class="hljs-keyword">import</span> openmc
surf_sphere1 = openmc.Sphere(r=<span class="hljs-number">10.0</span>)
surf_sphere2 = openmc.Sphere(r=<span class="hljs-number">20.0</span>)
between_spheres = +surf_sphere1 & -surf_sphere2
cell_between = openmc.Cell(region= between_spheres)
cell_sphere.fill = steel
</code></pre>
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<h1 id="edge-of-the-model">Edge of the model</h1>
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<p>The outer most surface of the model should have a <code>boundary_type</code> set to <code>"vacuum"</code> to indicate that neutrons should not be tracked beyond this surface.</p>
<pre is="marp-pre" data-auto-scaling="downscale-only"><code class="language-python"><span class="hljs-keyword">import</span> openmc
surf_sphere = openmc.Sphere(r=<span class="hljs-number">10.0</span>, boundary_type=<span class="hljs-string">"vacuum"</span>)
between_spheres = -surf_sphere
cell_between = openmc.Cell(region= between_spheres)
</code></pre>
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