NEUTRON TRANSPORT INPUT TO YIELD CALCULATIONS

901f033a-1911-48e2-9f3d-f8ca0d1ba70d 46 NEUTRON TRANSPORT INPUT TO YIELD CALCULATIONS Reg Curry This snippet is intended for input to a yield calculation in SMATH. It reads an EXCEL file of important nuclear parameters, so the SMATH yield calculation file must be in a folder with the EXCEL file. The snippet calculates the neutron growth factor, alpha, and the neutron fission mean free path, lambda-f. It fits both with a linear fit. The slopes and intercepts for alpha and lambda are then used in the yield calculator for input to the coupled differential equations for the yield calculation. neutron, core, tamper, growth rate, mean free path 2 4 true false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

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^/ #

DATA #

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

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

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

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

ν DATA 25 el : #

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

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

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 -^#

σ.f 1.235 barn * :

λ.f 1 n σ.f * / : #

σ.el 4.566 barn * :

σ.t σ.f σ.el + :

λ.t 1 n σ.t * / : #

A.WC 195.85 g mol / * :

n.WC ρ.WC N.A * A.WC / : cm 3 -^#

σ.elWC 6.857 barn * :

λ.TampWC 1 n.WC σ.elWC * / : #

M.core 52.640 kg *

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

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

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 #

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 / #

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 / - / : #

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

alpha α 1 el slope 21 mat :

alpha #

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 #

x #

αfit #

λf cm #

lambda λf 1 el cm / λslope 21 mat :

lambda #

plot x α augment :

Fit x αfit augment :

Lambda x λf cm / augment :

λFit x λfit augment :

plot Fit 2 1 sys

plot #

Fit #

Lambda λFit 2 1 sys

Lambda #

λFit #