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NUC-26

Delayed-neutron reactivity

ρ = (k−1)/k, $ = ρ/β. Dollars of reactivity in units of the delayed fraction β.

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NuclearDelayed neutrons

Governing equation

ρ=(k−1)/k,$=ρ/β\rho=(k-1)/k,\quad \$=\rho/\beta

k∈[0.9,1.1]k \in \left[0.9, 1.1\right]

where

k
Multiplication k (—)
\beta
Delayed fraction (—)
\rho
Reactivity (pcm)
\$
Dollars ($)

The figure, part by part

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NUC-26 · reactor
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①

Governing law — red

ρ=(k−1)/k,$=ρ/β\rho=(k-1)/k,\quad \$=\rho/\beta

k∈[0.9,1.1]k \in \left[0.9, 1.1\right]

k=0.9k = 0.9ρ=−17.09\rho = -17.09

②

Domain of the variable — blue

kmin⁡=0.9,kmax⁡=1.1k_{\min} = 0.9,\quad k_{\max} = 1.1

k∈[0.9,1.1]k \in \left[0.9, 1.1\right]

k=0.9k = 0.9k=0.9k = 0.9

③

Response curve — green

ρ=(k−1)/k,$=ρ/β\rho=(k-1)/k,\quad \$=\rho/\beta

k∈[0.9,1.1]k \in \left[0.9, 1.1\right]

k=0.9k = 0.9ρ=−17.09\rho = -17.09

④

Rate of change — amber

dρdk\frac{\mathrm{d}\rho}{\mathrm{d}k}

k∈[0.9,1.1]k \in \left[0.9, 1.1\right]

k=0.901k = 0.901ρ′=189.4\rho^{\prime} = 189.4

Lecture brief

Historical brief

Rutherford, Chadwick, the semi-empirical mass formula, fission (Hahn–Strassmann 1938) and fusion Q-values, then Compton and Bethe–Bloch stopping, are the nuclear toolkit. Decay, binding and dose start here. This sheet (NUC-26 — Delayed-neutron reactivity) is the form associated with Delayed neutrons. Working symbols: kk, β\beta →\rightarrow ρ\rho, \$. Prompt critical is ρ = β. Delayed neutrons make reactors controllable.

Purpose

Purpose: compute ρ\rho, \fromfromk,,\betainNuclearphysicsviain Nuclear physics via\rho=(k-1)/k,\quad \=\rho/\beta $ρ=(k−1)/k,ρ = (k−1)/k, = ρ/β. Dollars of reactivity in units of the delayed fraction β. Use it when a real nuclear physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given k=1.001 —k = 1.001\,\mathrm{—}, β=0.006 —\beta = 0.006\,\mathrm{—}, the governing relation ρ=(k−1)/k,$=ρ/β\rho=(k-1)/k,\quad \$=\rho/\beta yields ρ=99.9 pcm\rho = 99.9\,\mathrm{pcm}, \ = 0.154\,\mathrm{}$. A k needle, a β band, a dollar mark. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • Reactivity \rho99.9 pcm
  • Dollars \$0.154 $
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NUC-26 · reactor
00:0 / 00:08

Narration of this film

A k needle, a β band, a dollar mark.

Prompt critical is ρ = β. Delayed neutrons make reactors controllable.

Reading speed

Watch on YouTube