Formula used
Plasma (single species): λD = √( ε kB T / ( n (z e)² ) )
Plasma (multi‑species): 1/λD² = Σ [ ns (zs e)² / ( ε kB Ts ) ]
Electrolyte (ionic strength): λD = √( ε kB T / ( 2 NA e² I ) ), where I = 0.5 Σ cᵢ zᵢ².
ε is absolute permittivity in F/m. T is in kelvin. n is in m⁻³. c is in mol/m³.
How to use this calculator
- Select the model that matches your system.
- Enter relative permittivity εr or absolute ε in F/m.
- Set temperature in K, °C, or eV as needed.
- For plasma models, enter number density and charge number.
- For electrolyte, enter ion concentrations and valences.
- Press calculate to see results above the form.
- Use the download buttons to export CSV or PDF.
Example data table
| Scenario | Model | Key inputs | Output λD |
|---|---|---|---|
| Room‑temperature salt solution | Electrolyte | εr=78.5, T=300 K, 0.10 M Na⁺, 0.10 M Cl⁻ | ≈ 0.96 nm |
| Low‑density plasma | Plasma (single) | εr=1, T=2 eV, n=1×10¹⁶ m⁻³, z=−1 | ≈ 0.10 mm |
| Two‑species plasma | Plasma (multi) | εr=1, n₁=1×10¹⁸ m⁻³ z₁=−1 T₁=300 K; n₂=1×10¹⁸ m⁻³ z₂=+1 T₂=300 K | ≈ 0.12 µm |
Example outputs are approximate and depend on constants and rounding.
Debye length guide
1) What the number represents
The Debye length (λD) is the characteristic distance over which electric fields are screened in a plasma or an ionic solution. Beyond roughly a few λD, charge imbalances are strongly reduced and the medium appears quasi‑neutral.
2) Two common definitions
In plasmas, a widely used form is λD=√(εkBT/(nq²)), where n is number density and q is particle charge. In electrolytes, the Debye–Hückel form uses ionic strength I and gives λD=√(εkBT/(2NAe²I)).
3) How temperature changes screening
Because λD scales with √T, hotter systems screen more weakly. Doubling temperature increases λD by about 41%. For example, raising an electron temperature from 2 eV to 8 eV increases λD by a factor of 2.
4) Density and ionic strength effects
Higher charge density strengthens screening. In a single‑species plasma, λD scales as 1/√n. Increasing n from 10¹⁶ to 10¹⁸ m⁻³ shortens λD by 10×. In electrolytes, λD scales as 1/√I; ten‑times higher ionic strength reduces λD by about 3.16×.
5) Typical magnitudes you may see
At 300 K in water (εr≈78.5), a 0.10 M 1:1 salt has λD≈0.96 nm (about a billionth of a meter). A 1 mM solution is much less screened, with λD near 9.6 nm. A low‑density plasma with n≈10¹⁶ m⁻³ and T≈2 eV can have λD near 0.10 mm, which is visible with a ruler.
6) Choosing the permittivity
Permittivity matters linearly inside the square‑root. Using εr=1 for vacuum is correct for many dilute plasmas, while liquids can be far higher (water near 80 at room temperature). If you enter absolute ε, ensure it is in F/m; otherwise results will be off by orders of magnitude.
7) Multi‑species screening in plasmas
When multiple species contribute, the effective screening strength adds: 1/λD²=Σ nsqs²/(εkBTs). Cold, dense species dominate because n/T is large. The multi‑species option in this calculator implements this sum directly.
8) Interpreting results and limits
λD is a scale, not a boundary. Sheath thicknesses near surfaces can be several λD, and strongly coupled plasmas may violate ideal assumptions. As a quick check, the number of particles in a Debye sphere should be large; if it is not, kinetic or correlation effects may matter.
FAQs
1) What is the Debye length used for?
It estimates how quickly electric potentials decay in a charged medium. Engineers use it to size plasma sheaths, judge quasi‑neutrality, and compare screening in electrolytes, colloids, and semiconductor depletion regions.
2) Which model should I choose: plasma or electrolyte?
Use plasma models when you know number density n (m⁻³) and particle charge. Use electrolyte when you know ion concentrations (mol/L or mol/m³). If you have multiple plasma species with different T, choose multi‑species.
3) Why does the calculator ask for permittivity?
Screening depends on the material’s ability to polarize. Vacuum uses εr=1, while liquids like water are much higher. Enter εr or absolute ε in F/m, but do not mix them.
4) How do I convert mol/L to mol/m³?
Multiply mol/L by 1000 to get mol/m³. For example, 0.10 mol/L equals 100 mol/m³. The electrolyte section can accept either unit and converts internally.
5) Can the Debye length be negative?
No. It is a distance scale and should be positive. If inputs create a non‑physical situation (negative temperature, zero density, or zero ionic strength), the calculator will warn you and stop the computation.
6) What does a smaller Debye length mean?
It means stronger screening: electric fields are neutralized over shorter distances. This typically happens with higher density, higher ionic strength, or lower temperature, depending on the system.
7) Is Debye length the same as screening length in all cases?
It matches ideal, weakly coupled theory. In strongly coupled plasmas, very concentrated electrolytes, or near interfaces, correlations and finite‑size effects can change the effective screening. Treat λD as a first‑order estimate.