Plasma Physics: The Fourth State of Matter

What turns a gas into plasma

When a gas is heated sufficiently or exposed to strong electric fields, electrons are stripped from atoms — a process called ionisation. The resulting mixture of positive ions and free electrons is called plasma. Unlike neutral gas, plasma is electrically conducting and responds to electromagnetic fields. Plasma is not simply "hot gas": what makes it special is its collective behaviour — the long-range Coulomb forces mean that disturbing one region affects all other regions simultaneously, so the whole plasma responds in concert. Degree of ionisation ranges enormously: a flame at 3000 K is only ~0.1% ionised, while a fusion reactor at 100–150 million K is fully ionised deuterium-tritium.

Debye shielding and the three plasma criteria

If a positive charge is placed in a plasma, nearby electrons are attracted and ions repelled, screening the charge beyond a characteristic distance called the Debye length:

λ_D = √(ε₀ k_B T_e / n_e e²)

Solar wind:    n_e = 10⁷ m⁻³,  T_e = 10⁵ K  →  λ_D ≈ 10 m
Tokamak edge:  n_e = 10¹⁹ m⁻³, T_e = 10⁶ K  →  λ_D ≈ 70 μm

For genuine plasma behaviour: L ≫ λ_D, N_D ≫ 1 (particles per Debye sphere), ω_p·τ ≫ 1

Plasma frequency: why the ionosphere blocks AM radio

Displace the electrons in a plasma and they feel a restoring force from the ions left behind, oscillating at the plasma frequency ω_p = √(n_e e² / ε₀ m_e). Electromagnetic waves with frequency below ω_p simply cannot propagate through the plasma — they are reflected. That single fact explains why AM radio (≈1 MHz, below the ionosphere's plasma frequency) bounces around the globe while FM and TV signals (far above ω_p) pass straight through into space. Plasmas also support Langmuir waves (electron oscillations, the basis of laser-wakefield particle acceleration), ion acoustic waves, and Alfvén waves that propagate along magnetic field lines at the Alfvén speed v_A = B/√(μ₀ρ) — critical to solar corona heating.

MHD: treating plasma as a conducting fluid

For large-scale, slow motions, plasma is treated as a single conducting fluid via magnetohydrodynamics (MHD) — a combination of fluid dynamics and Maxwell's electromagnetism. In the ideal limit (resistivity η → 0), the "frozen-in" theorem says magnetic field lines are locked to the plasma: if the plasma moves, the field lines move with it. Equilibrium requires the pressure gradient to balance the magnetic (Lorentz) force, ∇p = J×B — the fundamental equation behind every magnetic-confinement fusion design.

Fusion confinement: tokamaks and the Lawson criterion

Deuterium-tritium fusion needs 100-150 million K, too hot for any material wall, so magnetic fields confine the plasma instead. A tokamak combines a toroidal field from external coils with a poloidal field from the plasma's own current (~15 MA), winding helically to prevent drift instabilities — ITER uses 18 superconducting magnets at 11.8 T. A stellarator generates all its confining field from external coils alone, more stable but geometrically far more complex; Germany's Wendelstein 7-X has sustained plasma for 30 minutes continuously. For a reactor to produce net energy, the Lawson criterion n·T·τ_E > 3×10²¹ m⁻³·keV·s must be exceeded — in December 2022, the NIF became the first facility to reach fusion ignition (Q > 1), producing 3.15 MJ from 2.05 MJ of input laser energy using inertial confinement.

Everyday and cosmic plasmas

Plasma is everywhere once you know to look for it. Fluorescent lamps use a mercury vapour plasma discharge; Hall-effect thrusters accelerate xenon ion plasma to 20-80 km/s for a specific impulse of 1600-3000 s, versus ~450 s for chemical rockets. The aurora borealis forms when solar-wind charged particles travel along Earth's magnetic field lines into the polar atmosphere and excite oxygen and nitrogen atoms — green aurora comes from oxygen at 557.7 nm (100-150 km altitude), red from oxygen at 630 nm (>200 km), and blue-purple from nitrogen. Plasma etching, using reactive plasma chemistry, is essential for sub-10-nm transistor fabrication in modern chips.

Frequently asked questions

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Everything above runs in your browser — open Plasma — Ionized Gas and watch charged particles interact via Coulomb and Lorentz forces, then switch between Free, Z-Pinch and Torus confinement modes. Nothing is installed, nothing is uploaded.