Advanced Method for Calculations of Core Burn-Up, Activation of Structural Materials, and Spallation Products Accumulation in Accelerator-Driven Systems

<table>Evolution of effective neutron multiplication factor <svg height="15.4" id="M147" style="vertical-align:-3.39064pt" version="1.1" viewbox="0 0 26.200001 15.4" width="26.200001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M764 650l-7 -26q-61 -10 -91.5 -22.5t-76.5 -48.5l-235 -184q104 -152 208 -276q31 -37 54.5 -48.5t68.5 -16.5l-7 -28h-156q-138 170 -213 284q-19 29 -33.5 35t-33.5 -7l-29 -173q-15 -75 -5.5 -90.5t74.5 -20.5l-5 -28h-260l7 28q58 5 74 21.5t30 89.5l70 378
q12 68 2 83t-72 22l6 28h257l-7 -28q-62 -7 -76 -21.5t-27 -83.5l-32 -172q29 11 78 46q112 84 217 179q18 16 23.5 25.5t-1 14.5t-26.5 8l-30 4l5 28h249z" id="x1D43E"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.25,15.187)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g><g transform="matrix(.012,-0,0,-.012,18.307,15.187)"><path d="M187 566v-116h189c1.33478 44.0001 4.00146 75.3334 8 94c5.33411 24.0005 14.0008 46.3339 26 67c28 48 75 72 141 72c30.0005 0 54.8339 -5.83331 74.5 -17.5c19.6691 -11.6667 29.5024 -26.5 29.5 -44.5c0 -11.3368 -4 -21.0035 -12 -29c-8 -8 -18 -12 -30 -12
c-16 0 -31 12 -45 36c-16.0016 26 -33.6682 39 -53 39c-37.3333 -0.000915527 -56 -29.6676 -56 -89v-116h115v-32h-115v-315c0 -37.3333 5 -61 15 -71c11.3333 -10.6667 37.3333 -16.3333 78 -17v-15h-245v15c28.6667 2 47 8.33333 55 19c8.66666 10.6667 13 34 13 70v314
h-188v-314c0 -38 3.66667 -61.6667 11 -71c6.66667 -8.66667 25.6667 -14.6667 57 -18v-15h-235v15c36.6667 2 59.3333 8 68 18c10 11.3333 15 35 15 71v314h-82v32h82c1.33344 43.3338 4.0001 74.3338 8 93c4.66666 22 13.6667 44.6667 27 68c28 48 75 72 141 72
c29.3333 0 52.8333 -5.83331 70.5 -17.5s26.5 -26.5 26.5 -44.5c0 -11.3368 -4 -21.0035 -12 -29c-8 -8 -18 -12 -30 -12c-8 0 -14.1667 2.16669 -18.5 6.5s-10.8333 14.1667 -19.5 29.5c-16 26 -33.6667 39 -53 39c-37.3335 -0.000915527 -56.0001 -29.6676 -56 -89z" id="xFB00"></path></g>
</svg> and external source neutron multiplication factor <svg height="15.4" id="M148" style="vertical-align:-3.39064pt" version="1.1" viewbox="0 0 27.6 15.4" width="27.6" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D43E"></use></g>
<g transform="matrix(.012,-0,0,-.012,13.25,15.187)"><path d="M319 325l-25 -7q-33 99 -103 99q-29 0 -47 -19.5t-18 -49.5t22 -49.5t62 -36.5q63 -26 95 -57t32 -79q0 -64 -50 -101t-115 -37q-35 0 -67.5 10.5t-46.5 23.5q-5 11 -11 51t-6 67l27 5q14 -53 46.5 -88.5t75.5 -35.5q29 0 50 19.5t21 50.5t-19.5 51.5t-59.5 39.5
q-28 12 -46 22.5t-38.5 27t-30.5 38.5t-10 49q0 54 42.5 92t109.5 38q48 0 88 -18q6 -15 13 -50.5t9 -55.5z" id="x73"></path></g><g transform="matrix(.012,-0,0,-.012,17.617,15.187)"><path d="M181 342h2q63 107 121 107q24 0 41 -16t17 -34q0 -34 -32 -49q-17 -7 -26 2q-21 20 -43 20q-20 0 -42 -22t-38 -63v-183q0 -50 12.5 -62t69.5 -16v-26h-230v26q47 5 58 17t11 61v207q0 49 -9 60.5t-53 16.5v23q74 12 141 40v-109z" id="x72"></path></g><g transform="matrix(.012,-0,0,-.012,21.888,15.187)"><use xlink:href="#x63"></use></g>
</svg>.</table>

Science and Technology of Nuclear Installations

fig4

Figure 4

Figure 4: Advanced Method for Calculations of Core Burn-Up, Activation of Structural Materials, and Spallation Products Accumulation in Accelerator-Driven Systems 

Figure 4 | Advanced Method for Calculations of Core Burn-Up, Activation of Structural Materials, and Spallation Products Accumulation in Accelerator-Driven Systems 