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ALPHA AND LAMDA MODEL

α & λ MODEL

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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:E6 importData.XLSX :

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 0.000 0.000 0.000 0.000 0.000 65 mat :

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 0.000 0.000 0.000 0.000 0.000 65 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 10 :

k 1 maxk range :

Δr 0.01 cm * :

Rexp R.c k Δr * + :

Rexp max cm 8.86

RTexp R.T k Δr * + :

RTexp max cm 21.31

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 / 1.01

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

λT λf λt R.c R.T Λ 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.c * 1 - (* + / vectorize :

λT λf λt R.c R.T Λ 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.c * 1 - (* - / vectorize :

λT λf λt R.c R.T Λ α F λT λf λt R.c R.T Λ α f1 λT λf λt R.c R.T Λ α f2 * λT λf λt R.c R.T Λ α f3 - vectorize :

Φ k el λT λf λt R.c R.T Λ α F k el m * :

α Plot Φ mat2sys.1 :

Ans Φ 0.1 1.5 Bisection vectorize :

x Plot

Ans 1.0002 0.9995 0.9988 0.9981 0.9975 0.9968 0.9962 0.9956 0.995 0.9943 101 mat

THE REED TRANSINDENTAL EQUATION TO SOLVE OF α