RAD-06

Collisional stopping power

S_col = −dE/dx. Energy lost per path by a charged particle.

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DosimetryStopping power

Governing equation

S=-dE/dx

$dx \in \left[0.001, 20\right]$

where

dE: Energy lost (MeV)
dx: Path (cm)
S: Stopping power (MeV/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

S=-dE/dx

$dx \in \left[0.001, 20\right]$

$dx = 0.001$ $S = 2000$

Along the curve

②

Domain of the variable — blue

dx_{\min} = 0.001,\quad dx_{\max} = 20

$dx \in \left[0.001, 20\right]$

$dx = 0.001$ $dx = 0.001$

Along the curve

③

Response curve — green

S=-dE/dx

$dx \in \left[0.001, 20\right]$

$dx = 0.001$ $S = 2000$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S}{\mathrm{d}dx}

$dx \in \left[0.001, 20\right]$

$dx = 0.127$ $S^{\prime} = -7918.9$

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-06 — Collisional stopping power) is the form associated with Stopping power. Working symbols: $dE$ , $dx$ $\rightarrow$ $S$ . Mass stopping is S/ρ. Electrons need the restricted stopping with a δ-ray cutoff.

Purpose

Purpose: compute

S

from

dE

dx

in Radiation physics via

S=-dE/dx

S_col = −dE/dx. Energy lost per path by a charged particle. 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

dE = 2.000\,\mathrm{MeV}

dx = 0.500\,\mathrm{cm}

, the governing relation

S=-dE/dx

yields

S = 4.000\,\mathrm{MeV/cm}

. A track, a dE, a dx. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Energy lost dE2 MeVPath dx0.5 cm

Outputs

Stopping power S4.000 MeV/cm

Reading speed

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Narration of this film

A track, a dE, a dx.

Mass stopping is S/ρ. Electrons need the restricted stopping with a δ-ray cutoff.

Reading speed

Watch on YouTube