<content> <p>NEUTRON TRANSPORT INPUT TO YIELD CALCULATIONS</p> </content>

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NUCLEAR FISSION YIELD CALCULATIONS

TSTART 1 time :

ALPHA AND LAMDA MODEL

CHOOSE TAMPER MATERIAL; "DU" OR "WC"

Tamper WC :

TAMPER RADIUS: \[REGION[d7c409e0cd5945509a1e123c97ddb16f]]\

R.T 21.21 cm * :

DEFINE SOME UNITS

AMU 1.66 1027 -^* kg * :

1 eV * 1.602 1019 -^* J *

1 MeV * 1.602 1013 -^* J *

Avogadro's Number

N.A 6.022 1023^* 1 mol / *

Ton.TNT 4.2 109^* J * :

KT 1000 Ton.TNT * :

CORE DEFINITION

HEU 235U PERCENT: \[REGION[ee5d80608d224c02b46b1fbc905fb865]]\

HEU% 80 :

HEUMASS 65.8 kg * :

M.core HEUMASS HEU% 100 / * : 52.640 kg *

GRAM MOLECULAR WEIGHT OF 235U: \[REGION[030ac39937c445e5971bc1bfa63e3a99]]\

U235.gmw 235 g * :

MolesU235.kg kg U235.gmw / : mol 4.255 1 mol / *

NumberAtomsU235.kg MolesU235.kg N.A * : 2.563 1024^* 1 mol / *

DATA MANHATTAN DATA Sheet1 A1:E5 importData.XLSX :

ρ DATA 22 el g cm 3^/ * : g cm 3^/ 18.710

DATA ELEMENT r (gm/cm3) lf (cm) lt (cm) n U235 1.871 101^* 1.689 101^* 3.596 2.637 Pu239 1.560 101^* 1.414 101^* 4.108 3.172 DU 1.895 101^* 0.000 4.342 0.000 WC 1.480 101^* 0.000 3.159 0.000 55 mat

ρ.DU DATA 42 el g cm 3^/ * : g cm 3^/ 18.950

ρ.WC DATA 52 el g cm 3^/ * : g cm 3^/ 14.800

λ.f DATA 23 el g cm 3^/ * : g cm 3^/ 1.689 101^*

λ.TampDU DATA 44 el g cm 3^/ * : g cm 3^/ 4.342

ν DATA 25 el : 2.637

λ.t DATA 24 el g cm 3^/ * : g cm 3^/ 3.596

λ.TampWC DATA 54 el g cm 3^/ * : g cm 3^/ 3.159

NOW DEFINE λs IN TERMS OF NUCLEAR CROSS SECTION AND NUCLEI NUMBER DENSITY

A 235.04 g mol / * :

n ρ N.A * A / : cm 3 -^4.794 1022^*

σ.f 1.235 barn * :

λ.f 1 n σ.f * / : 0.169 m *

σ.el 4.566 barn * :

σ.t σ.f σ.el + :

λ.t 1 n σ.t * / : 3.596 102 -^* m *

A.WC 195.85 g mol / * :

n.WC ρ.WC N.A * A.WC / : cm 3 -^4.551 1022^*

σ.elWC 6.857 barn * :

λ.TampWC 1 n.WC σ.elWC * / : 0.032 m *

M.core 52.640 kg *

R.c 3 M.core * 4 π * ρ * / 3 nthroot : cm 8.76

M.Tamper 43 / π * ρ.WC * R.T 3^R.c 3^- (* : 549.88 kg *

NOW LET THE RADII OF THE CORE AND TAMPER EXPAND BY Δr

maxk 50 :

k 1 maxk range :

Δr 0.01 cm * :

Rexp R.c k 1 - (Δr * + :

Rexp max cm 9.25

RTexp R.T k Δr * + :

RTexp max cm 21.71

ρexp 3 M.core * 4 π * / Rexp (3 -^* vectorize :

nexp ρexp N.A * A / :

ρTexp 3 M.Tamper * 4 π * RTexp 3^Rexp 3^- (* / vectorize :

nTexp ρTexp N.A * A.WC / :

λf 1 σ.f nexp * / vectorize :

λt 1 σ.t nexp * / vectorize :

λT 1 σ.elWC nTexp * / vectorize :

Λ λT λt / vectorize :

λT max λT min / 1.06

α f1 e 23 α * λT λf * / sqrt * R.c R.T - (*^vectorize :

α f2 3 ν α - 1 - (* λf λt * / sqrt R.c * 3 ν α - 1 - (* λf λt * / sqrt R.c * cot * 1 - Λ 3 α * λT λf * / sqrt R.c * 1 - (* - R.T 23 / λT * 3 α * λT λf * / sqrt R.T * 1 - (* + / vectorize :

α f3 3 ν α - 1 - (* λf λt * / sqrt R.c * 3 ν α - 1 - (* λf λt * / sqrt R.c * cot * 1 - Λ 3 α * λT λf * / sqrt R.c * 1 + (* + R.T 23 / λT * 3 α * λT λf * / sqrt R.T * 1 + (* - / vectorize :

α F α f1 α f2 * α f3 - vectorize :

Ans α F α solve 2 el vectorize :

α Ans :

r Rexp :

slope α maxk el α 1 el - r maxk el cm / r 1 el cm / - / : 0.372 -

αfit slope r r 1 el - cm / (* α 1 el + :

alpha α 1 el slope 21 mat :

alpha 0.485 0.372 - 21 mat

x r cm / :

λslope λf maxk el cm / λf 1 el cm / - r maxk el cm / r 1 el cm / - / :

λfit λslope r r 1 el - cm / (* λf 1 el cm / + :

α 0.485 0.481 0.477 0.473 0.469 0.466 0.462 0.458 0.454 0.450 0.447 0.443 0.439 0.435 0.432 151 mat

x 8.758 8.768 8.778 8.788 8.798 8.808 8.818 8.828 8.838 8.848 8.858 8.868 8.878 8.888 141 mat

αfit 0.485 0.481 0.477 0.474 0.470 0.466 0.462 0.459 0.455 0.451 0.447 0.444 0.440 0.436 141 mat

λf cm 16.89 16.95 17.01 17.06 17.12 17.18 17.24 17.30 17.36 17.42 17.48 17.54 17.59 17.65 141 mat

lambda λf 1 el cm / λslope 21 mat :

lambda 16.891 6.116 21 mat

plot x α augment :

Fit x αfit augment :

Lambda x λf cm / augment :

λFit x λfit augment :

plot Fit 2 1 sys

plot 8.758 0.485 8.768 0.481 8.778 0.477 8.788 0.473 8.798 0.469 8.808 0.466 8.818 0.462 8.828 0.458 8.838 0.454 8.848 0.450 8.858 0.447 8.868 0.443 8.878 0.439 8.888 0.435 8.898 0.432 8.908 0.428 8.918 0.424 172 mat

Fit 8.758 0.485 8.768 0.481 8.778 0.477 8.788 0.474 8.798 0.470 8.808 0.466 8.818 0.462 8.828 0.459 8.838 0.455 8.848 0.451 8.858 0.447 8.868 0.444 8.878 0.440 8.888 0.436 8.898 0.433 8.908 0.429 8.918 0.425 172 mat

Lambda λFit 2 1 sys

Lambda 8.758 16.891 8.768 16.949 8.778 17.007 8.788 17.065 8.798 17.123 8.808 17.182 8.818 17.240 8.828 17.299 8.838 17.358 8.848 17.417 8.858 17.476 8.868 17.535 8.878 17.595 8.888 17.654 8.898 17.714 8.908 17.774 8.918 17.834 172 mat

λFit 8.758 16.891 8.768 16.952 8.778 17.013 8.788 17.074 8.798 17.135 8.808 17.197 8.818 17.258 8.828 17.319 8.838 17.380 8.848 17.441 8.858 17.502 8.868 17.564 8.878 17.625 8.888 17.686 8.898 17.747 8.908 17.808 8.918 17.869 172 mat

M.core 52.64 kg *

M.Tamper 549.88 kg *

Tamper WC

Δr 1.00 104 -^* m *

E.f 180 MeV * :

M.total M.core M.Tamper + :

M.total 602.52 kg *

N.o 1 cm 3 -^* :

γ 13 / :

E 1 el 1010 -^KT * :

r 1 el R.c :

u 1 el 0 m s / * :

V.core 1 el 43 / π * r 1 el 3^* : cm 3^2813.47 11 mat

LambdaFit λf 1 el m / λslope 21 mat : 0.17 6.12 21 mat

NeutronFissionEnergy 2 MeV * :

m.n 1.67493 1027 -^* kg *

Nvel 2 NeutronFissionEnergy * m.n / sqrt :

τ 1 el LambdaFit 1 el m * Nvel / : 8.64 109 -^* s * 11 mat

mint 0.1 μs * :

npoints 10 :

Δt τ 1 el α 1 el / 40 / : μs 4.45 104 -^*

τ 1 el α 1 el / μs 1.782 102 -^*

j 1 npoints range :

t j el mint j Δt * + :

t max μs 0.10

r j el r 1 el Δr j * + :

r 1 el 0.09 m *

r max 0.09 m *

α j el alpha 2 el r j el r 1 el - cm / (* alpha 1 el + :

alpha 1 el 0.485

FITλ j el LambdaFit 2 el r j el r 1 el - (* LambdaFit 1 el m * + :

j 2 npoints range r j el r j 1 - el v j 1 - el Δt * + eval : αf j el alpha 2 el r j el r 1 el - cm / (* alpha 1 el + eval : τ j el LambdaFit 2 el r j el r 1 el - (* LambdaFit 1 el m * + Nvel / eval : v j el v j 1 - el 4 π * r j 1 - el (2^* γ * E j 1 - el * V.core j 1 - el M.total * / Δt * + eval : V.core j el 43 / π * r j 1 - el (3^* eval : E j el E j 1 - el N.o V.core j 1 - el * E.f * τ j 1 - el / (e αf j 1 - el τ j 1 - el / (t j 1 - el *^* Δt * + eval : 61 line for

α 1 el 0.48

αf 1 el α 1 el :

Yield t μs / E KT / augment :

Ngrowth t μs / αf augment :

Yield 0.1004 1.0000 1010 -^* 0.1009 1.0000 1010 -^* 0.1013 1.0000 1010 -^* 0.1018 1.0000 1010 -^* 0.1022 1.0000 1010 -^* 0.1027 1.0000 1010 -^* 0.1031 1.0000 1010 -^* 0.1036 1.0000 1010 -^* 82 mat

Ngrowth 0.10 0.48 0.10 0.48 0.10 0.48 0.10 0.48 0.10 0.48 0.10 0.48 0.10 0.48 0.10 0.48 0.10 0.48 0.10 0.48 102 mat

1 time TSTART - 14.77 s *