RAD-19

CSDA range snapshot

R ≈ E / S̄. Continuous-slowing-down range from a mean stopping power.

Reading speed

DosimetryCSDA

Governing equation

R\approx E/\bar S

$E \in \left[0.1, 250\right]$

where

E: Energy (MeV)
\bar S: Mean stopping (MeV/cm)
R: CSDA range (cm)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

R\approx E/\bar S

$E \in \left[0.1, 250\right]$

$E = 0.1$ $R = 0.02$

Along the curve

②

Domain of the variable — blue

E_{\min} = 0.1,\quad E_{\max} = 250

$E \in \left[0.1, 250\right]$

$E = 0.1$ $E = 0.1$

Along the curve

③

Response curve — green

R\approx E/\bar S

$E \in \left[0.1, 250\right]$

$E = 0.1$ $R = 0.02$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R}{\mathrm{d}E}

$E \in \left[0.1, 250\right]$

$E = 1.672$ $R^{\prime} = 0.2$

Along the curve

Lecture brief

Historical brief

Beer attenuation, Compton (1923), Klein–Nishina, Bragg–Gray cavity and KERMA are the transport of photons and charged particles in matter. The sheets compute fluence, kerma and stopping. This sheet (RAD-19 — CSDA range snapshot) is the form associated with CSDA. Working symbols: $E$ , $\bar S$ $\rightarrow$ $R$ . True CSDA is ∫ dE / S(E). Straggling spreads a Bragg peak around this mean.

Purpose

Purpose: compute

R

from

E

\bar S

in Radiation physics via

R\approx E/\bar S

R ≈ E / S̄. Continuous-slowing-down range from a mean stopping power. Use it when a real radiation physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E = 10.000\,\mathrm{MeV}

\bar S = 5.000\,\mathrm{MeV/cm}

, the governing relation

R\approx E/\bar S

yields

R = 2.000\,\mathrm{cm}

. A particle, a fading energy, a stop. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Energy E10 MeVMean stopping \bar S5 MeV/cm

Outputs

CSDA range R2.000 cm

Reading speed

Watch on YouTube

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Narration of this film

A particle, a fading energy, a stop.

True CSDA is ∫ dE / S(E). Straggling spreads a Bragg peak around this mean.

Reading speed

Watch on YouTube