Tallywick: Thermionic Emission
Electromagnetism & Plasma arc, page 88 of 193. Back to The Pixelated Physics Universe
Who they are
Tallywick has one line, and says it often: “In the dark, something still clicks.”
Tallywick is a character of the Electromagnetism & Plasma arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Thermionic emission: J = A T² e−W/kT (Richardson–Dushman). It is why photomultipliers have dark counts and why they are cooled.
$$ \begin{gathered} J = A T^{2} e^{-W/kT} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $J$ | emitted current density | A/m^2 |
| $A$ | Richardson constant | A/(m^2·K^2) |
| $T$ | cathode temperature | K |
| $W$ | work function | J |
| $k$ | Boltzmann constant | J/K |
Sources
- S. Dushman, Phys. Rev. 21, 623 (1923)
- O. W. Richardson, Nobel Lecture (1929)
Crossovers
Tallywick meets Islandine (Coulomb Blockade). Islandine's blockade only holds while the charging energy e²/2C is far above k_BT. Tallywick's thermionic electrons show what happens when heat wins: electrons escape over a barrier at a rate set by an exponential in temperature.
Tallywick meets Ayrtha (Hertha Ayrton, the Electric Arc and Sand Ripples). Ayrtha's carbon arc runs hot enough that its electrodes emit electrons thermally. Tallywick's Richardson–Dushman law gives that emission current: J = AT²e^(−W/k_BT).
Wear the lore
Concept keywords: Thermionic Emission, Tallywick, Electromagnetism & Plasma, physics lore, Pixelated Physics