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Plasma Drift

Ionized Gas / Plasma Physics

\[\omega_p = \sqrt{\frac{n_e e^{2}}{\varepsilon_0 m_e}}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Heat a gas far enough and its atoms come apart. Plasma is ionized gas: free electrons and ions, found in stars, lightning and neon signs. Meet Plasma Drift, named for the E × B drift: in crossed electric and magnetic fields, electrons and ions circle in opposite directions yet drift together, the same way at the same speed, v = E/B. Plasma Drift wears it in pixel art on a unisex tee. The physics panel below has the equation, every symbol and the sources.

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

參考尺度：M 碼寬 20 in（50.80 cm），約為 3.143 × 1034 個普朗克長度（lP = 1.616255 × 10−35 m）。用捲尺量更快。

Measurements in inches, ±1.5 in tolerance.

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The physics

In a plasma, electrons that are pushed aside spring back and oscillate at the plasma frequency, which depends only on how dense they are. Charges also screen each other beyond the Debye length, and in crossed electric and magnetic fields the whole plasma drifts sideways at E/B.

Plasma Drift is a gas that stopped being polite.

Heat a gas enough, or hit it with enough radiation, and electrons come loose from their atoms. What remains is a mixture of free electrons and positive ions, and it behaves unlike any neutral gas, because every charged particle feels the others at a distance through electric and magnetic fields. Irving Langmuir named it plasma in 1928.

Its signature, the first formula on this page, is a collective oscillation. Nudge the electrons sideways and the ions, thousands of times heavier, stay put. The exposed charge pulls the electrons back, they overshoot, and the whole cloud rings at the plasma frequency, set only by how many free electrons there are per cubic metre. In Earth's ionosphere that frequency is a few megahertz. Radio waves below it cannot pass through and are turned back toward the ground, which is how shortwave broadcasts reach around the planet. Waves well above it pass out to space, which is why satellites talk to you at gigahertz.

The second formula is the Debye length: the distance over which a plasma hides any stray charge you put into it, by gathering a cloud of the opposite sign around it. A few Debye lengths away, the charge is invisible.

The third is the drift in Drift. Put a charged particle in crossed electric and magnetic fields and it does not simply fall along the electric field. It circles, and the circle creeps sideways at a speed E/B, at right angles to both fields. The answer contains neither the charge nor the mass. Electrons and ions, opposite in sign and thousands of times different in weight, drift together, in the same direction, at the same speed.

Drift does not go where you push. They go sideways, with everyone.

Equations

\[\omega_p = \sqrt{\frac{n_e e^{2}}{\varepsilon_0 m_e}}\]
\[\lambda_D = \sqrt{\frac{\varepsilon_0 k_B T_e}{n_e e^{2}}}\]
\[\vec v_E = \frac{\vec E \times \vec B}{B^{2}}\]
SymbolMeaningUnit
\(\omega_p\) electron plasma frequency \(\mathrm{rad/s}\)
\(n_e\) electron number density \(\mathrm{m⁻³}\)
\(e\) elementary charge \(\mathrm{C}\)
\(\varepsilon_0\) vacuum permittivity \(\mathrm{F/m}\)
\(m_e\) electron mass \(\mathrm{kg}\)
\(\lambda_D\) Debye length \(\mathrm{m}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(T_e\) electron temperature \(\mathrm{K}\)
\(\vec v_E\) E×B drift velocity \(\mathrm{m/s}\)
\(\vec E\) electric field \(\mathrm{V/m}\)
\(\vec B\) magnetic field \(\mathrm{T}\)

Sources

  1. Langmuir (1928) Oscillations in Ionized Gases, PNAS 14, 627
  2. Encyclopaedia Britannica — Plasma (state of matter)
  3. NIST CODATA 2022 — elementary charge e
  4. NIST CODATA 2022 — vacuum electric permittivity ε0
  5. NIST CODATA 2022 — electron mass energy equivalent in MeV

Source Tonks, L.; Langmuir, I. (1929). Oscillations in Ionized Gases. Physical Review 33, 195–210.doi.org/10.1103/physrev.33.195

Field notes

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