⚛️ Debye Screening — Plasma Physics

A central positive charge in a plasma is surrounded by a cloud of mobile electrons that screen its electric field. The potential decays as φ(r) = (q/4πε₀r)·e^−r/λ_D rather than the bare Coulomb law. Adjust temperature T and density n to see how the Debye length λ_D changes.

Adjust temperature and density to see how the Debye length changes · P pause/play · R reset

Plasma Parameters

Temperature T 10 000 K Electron density n 1×10¹⁸ m⁻³ Charge magnitude Q +1 e

Live Stats

Debye length λ_D —

φ at r = λ_D —

φ_Coulomb at λ_D —

Screening ratio —

Electrons —

Display

Show potential field

Show Debye circle

Legend
🔴 Central positive ion
🔵 Negative electrons (mobile)
🟡 Positive background ions (fixed)
Heatmap: warm = high φ, cool = screened

What is Debye Screening?

In a plasma — an ionised gas of electrons and ions — free electrons redistribute themselves around any excess charge to shield it from the rest of the plasma. The resulting potential is the Yukawa / screened-Coulomb potential:

φ(r) = (q / 4πε₀r) · exp(−r / λ_D)

The Debye length λ_D sets the scale of screening:

λ_D = √(ε₀ k_B T / n e²)

Beyond ~3 λ_D the potential is reduced to less than 5 % of the bare Coulomb value. This is why plasmas are quasi-neutral on scales larger than λ_D: any local charge imbalance is neutralised within a Debye sphere.

Key Dependencies

Higher temperature → electrons have more kinetic energy → screening cloud spreads out → larger λ_D.
Higher density → more electrons available to screen → tighter cloud → smaller λ_D.

Real-world examples

Solar wind plasma: λ_D ≈ 10 m. Fusion tokamak plasma: λ_D ≈ 70 µm. Ionosphere: λ_D ≈ 1 cm. Understanding Debye screening is essential for modelling spacecraft charging, ion thrusters, and magnetic confinement fusion.