Shielda: Debye Shielding
Electromagnetism & Plasma arc, page 82 of 193. Back to The Pixelated Physics Universe
Who they are
Shielda glows with charge, but a swarm of opposite charges mutes her beyond arm's length.
Shielda 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
Put a charge in a plasma and opposite charges crowd round it, hiding it from far away. Its potential falls off exponentially over the Debye length. A gas counts as a plasma only if it is much bigger than the Debye length and holds many particles in a Debye sphere. Peter Debye and Erich Hückel worked out the same screening in salt solutions in 1923.
$$ \begin{gathered} \lambda_D = \sqrt{\frac{\varepsilon_0 k_B T_e}{n_e e^{2}}} \\ \phi(r) = \frac{q\,e^{-r/\lambda_D}}{4\pi\varepsilon_0 r} \\ N_D = \frac{4}{3}\pi n_e \lambda_D^{3} \gg 1 \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\lambda_D$ | Debye length | m |
| $\varepsilon_0$ | vacuum permittivity, 8.854 187 8 × 10⁻¹² F/m | F/m |
| $k_B$ | Boltzmann constant, 1.380 649 × 10⁻²³ J/K (exact) | J/K |
| $T_e$ | electron temperature (1 eV ≈ 11 604.5 K) | K |
| $n_e$ | electron number density | m⁻³ |
| $e$ | elementary charge, 1.602 176 634 × 10⁻¹⁹ C (exact) | C |
| $\phi$ | electric potential | V |
| $q$ | test charge | C |
| $r$ | distance from the charge | m |
| $N_D$ | number of electrons in a Debye sphere | 1 |
Sources
- Chen (2016) Introduction to Plasma Physics and Controlled Fusion, 3rd ed., Springer, sec. 1.4
- Bittencourt (2004) Fundamentals of Plasma Physics, 3rd ed., Springer, ch. 1
Crossovers
Shielda meets Plasma Drift (Ionized Gas / Plasma). Plasma Drift is a gas of free charges. Shielda is what those charges do to any one of them: they gather round it and screen its field beyond the Debye length.
Shielda meets Islandine (Coulomb Blockade). Shielda hides charge in a plasma by crowding opposite charges round it. Islandine's island is too small to hide anything: adding a single electron changes its energy by e²/2C, enough to block the next one.
Wear the lore
- Shielda – Debye Shielding Physics T-Shirt
- Related infographic poster: The Bennett Pinch – Plate 079 Physics Poster
Concept keywords: Debye Shielding, Shielda, Electromagnetism & Plasma, physics lore, Pixelated Physics