ec6a5240-2dd1-4cf7-80a1-f9fac8d81035 7 RegRetired 2 5 false false false 0 3 decimal

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

ALPHA AND LAMDA MODEL

DEFINE SOME UNITS

CHOOSE TAMPER MATERIAL; "DU" OR "WC"

Tamper DU :

M.Tamper 231.0 kg * :

CHOOSE CORE MATERIAL: "U" OR "Pu"

CORE Pu :

M.Core 6.3 kg * :

COMPRESSION RATIO: \[REGION[9aa76a8d31f14602b1b72effb33e911a]]\

CR 2.5 :

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% 100 :

HEUMASS M.Core :

M.core HEUMASS HEU% 100 / * : 6.300 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 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 DATA 22 el g cm 3^/ * : g cm 3^/ 18.710

λ.f DATA 23 el g cm 3^/ * : g cm 3^/ 16.890

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

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

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

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

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

ρ.pu DATA 32 el g cm 3^/ * : g cm 3^/ 15.600

λ.puf DATA 33 el g cm 3^/ * : g cm 3^/ 14.140

λ.put DATA 34 el g cm 3^/ * : g cm 3^/ 4.108

ν DATA 25 el : 2.637

ν.pu DATA 35 el : 3.172

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 + :

σ.t barn 5.801

λ.t 1 n σ.t * / : cm 3.596

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 * / : cm 3.205

A.DU 238.05 g mol / * :

n.DU ρ.DU N.A * A.DU / : cm 3 -^4.79 1022^*

σ.elDU 4.804 barn * :

λ.TampDU 1 n.DU σ.elDU * / : cm 4.34

σ.put σ.puel σ.puf + :

A.pu 239.05 g mol / * :

σ.puel 4.394 barn * :

σ.puf 1.80 barn * :

ν CORE U ≡ ν ν.pu if :

ρ.core CORE U ≡ ρ ρ.pu if :

ρ.tamper Tamper WC ≡ ρ.WC ρ.DU if :

R.c 3 M.core * 4 π * ρ.core * / 3 nthroot : cm 4.585

R.T 3 M.Tamper * 4 π * ρ.tamper * / R.c 3^+ 3 nthroot : cm 14.433

ρ.core g cm 3^/ 15.600

ρ.tamper g cm 3^/ 18.950

M.core 6.300 kg *

M.Tamper 231.000 kg *

NOW LET THE RADII OF THE CORE AND TAMPER EXPAND BY Δr \[REGION[40f85b2fef844511aa77e4d06a791dd3]]\

maxk 10 :

RMAX 1.1 R.c * :

Δr RMAX R.c - maxk 1 - / : 0.0005 m *

TO OBTAIN A SOLUTION, MUST CHOOSE A REASONABLE MAX(Rexp) AND THEN COMPUTE

THE CORRECT ∆r TO ACHIVE THE MAXIMUM CORE EXPANSION RADIUS. OTHERWISE, THE

SOLUTION MAY NEVER BE ACHIEVED.

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k 1 maxk range :

Rexp R.c k 1 - (Δr * + :

Rexp max cm 5.04

RTexp R.T k Δr * + :

RTexp max cm 14.94

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

nexp CORE U ≡ ρexp N.A * A / ρexp N.A * A.pu / if :

σt CORE U ≡ σ.t σ.put if :

σf CORE U ≡ σ.f σ.puf if :

ρexp 1 el g cm 3^/ 15.600

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

nTexp Tamper WC ≡ ρTexp N.A * A.WC / ρTexp N.A * A.DU / if :

σ.tamper Tamper WC ≡ σ.elWC σ.elDU if :

σ.tamper barn 4.804

ρTexp 1 el g cm 3^/ 18.744

λf 1 σf nexp * / vectorize :

λt 1 σt nexp * / vectorize :

λT 1 σ.tamper nTexp * / vectorize :

Λ λT λt / vectorize :

λT max λT min / 1.090

Rexp Rexp CR 3 nthroot / :

RTexp RTexp CR 3 nthroot / :

λT λT CR / :

λf λf CR / :

λt λt CR / :

α f1 e 23 α * λT λf * / sqrt * Rexp RTexp - (*^vectorize :

α f2 3 ν α - 1 - (* λf λt * / sqrt Rexp * 3 ν α - 1 - (* λf λt * / sqrt Rexp * cot * 1 - Λ 3 α * λT λf * / sqrt Rexp * 1 - (* - RTexp 23 / λT * 3 α * λT λf * / sqrt RTexp * 1 - (* + / vectorize :

α f3 3 ν α - 1 - (* λf λt * / sqrt Rexp * 3 ν α - 1 - (* λf λt * / sqrt Rexp * cot * 1 - Λ 3 α * λT λf * / sqrt Rexp * 1 + (* + RTexp 23 / λT * 3 α * λT λf * / sqrt RTexp * 1 + (* - / vectorize :

I DON'T UNDERSTAND THE NEED FOR THE INDEX 2 IN THE solve function.

α F α f1 α f2 * α f3 - vectorize :

Ans α F α solve 2 el vectorize :

Sol α F α solve vectorize :

α Ans :

r Rexp :

slope α maxk el α 1 el - r maxk el cm / r 1 el cm / - / : 0.726 -

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

alpha α 1 el slope 21 mat :

alpha 0.793 0.726 - 21 mat

x r cm / :

Sol 0 0.79 21 mat 0 0.76 21 mat 0 0.73 1.8 31 mat 0 0.71 21 mat 0 0.68 21 mat 0 0.65 21 mat 0 0.62 21 mat 0 0.6 21 mat 0 0.57 21 mat 0 0.55 21 mat 101 mat

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 0.793 0.764 0.735 0.706 0.678 0.651 0.624 0.598 0.573 91 mat

x 3.379 3.416 3.454 3.491 3.529 3.566 3.604 3.641 3.679 91 mat

αfit 0.793 0.766 0.738 0.711 0.684 0.657 0.629 0.602 0.575 91 mat

λf cm 5.65 5.85 6.04 6.24 6.44 6.65 6.86 7.08 7.30 91 mat

lambda λf 1 el m / λslope 21 mat :

lambda 0.057 5.540 21 mat

plot x α augment :

Fit x αfit augment :

Lambda x λf cm / augment :

λFit x λfit augment :

λf cm / max 7.526

α max 0.793

x max 3.72

λf cm / min 5.655

α min 0.548

x min 3.38

plot Fit 2 1 sys

CR 2.5

Lambda λFit 2 1 sys