Debye Length Calculator

Calculator Inputs

Choose a plasma or electrolyte model, enter known values, then submit to see the Debye length above this form.

Calculation model

Relative permittivity εr

Potential amplitude φ0

Electron temperature

Ion temperature

Electron density

Ion density

Ion charge state Z

Solution temperature

Cation concentration

Anion concentration

Cation valence z+

Anion valence z−

Plot range in λD

Plot points

Tip: use εr ≈ 1 for vacuum plasmas and around 78.5 for water near room temperature.

Example Data Table

These worked examples are illustrative and are computed using the same formulas implemented in the calculator.

Case	Model	Representative Inputs	Computed Debye Length
Glow discharge plasma	Plasma	Te = 3 eV, Ti = 0.03 eV, ne = ni = 1×10¹⁶ m⁻³, Z = 1, εr = 1	12.8121 µm
Dense laboratory plasma	Plasma	Te = 10 eV, Ti = 0.1 eV, ne = ni = 1×10¹⁸ m⁻³, Z = 1, εr = 1	2.3392 µm
Water with 0.01 M 1:1 salt	Electrolyte	T = 25 °C, cation = 0.01 mol/L, anion = 0.01 mol/L, z+ = 1, z− = 1, εr = 78.5	3.0421 nm

Formula Used

Plasma form

λe = √(ε kB Te / (ne e²))

λi = √(ε kB Ti / (ni Z² e²))

1 / λD² = 1 / λe² + 1 / λi²

Electrolyte form

λD = √(ε kB T / (e² Σ ni zi²))

ε = εr ε0

I = 0.5 Σ ci zi² for ionic strength in molar units.

Higher temperature generally increases Debye length, while higher charge density or higher valence reduces it by strengthening electrostatic screening.

How to Use This Calculator

Select Plasma for electron-ion systems or Electrolyte for ionic solutions.
Enter the relevant temperatures, densities, concentrations, valences, and relative permittivity.
Set the graph range in multiples of Debye length and choose the number of plot points.
Click Calculate Debye Length to place the results above the form.
Use the CSV and PDF buttons to save the current output and review the chart offline.

FAQs

1) What is Debye length?

Debye length is the characteristic distance over which electric fields are screened in a plasma or ionic medium. Beyond this distance, charge disturbances weaken rapidly.

2) Why does higher density reduce Debye length?

More charged particles are available to rearrange around a disturbance. That stronger collective response screens electric fields faster, so the shielding distance becomes shorter.

3) Why does temperature increase Debye length?

Hotter particles have greater thermal motion and resist tight electrostatic clustering. That spreads the screening cloud farther outward and increases the characteristic shielding distance.

4) What is the difference between electron and ion Debye lengths?

Electron and ion terms reflect separate species responses. Electrons usually react faster, but ions can still shorten the combined shielding length when their density and charge contribution are significant.

5) Can this calculator be used for electrolytes?

Yes. Switch to the electrolyte model and enter ionic concentrations, valences, temperature, and relative permittivity. The calculator then uses the ionic screening relation instead of plasma densities.

6) Which units should I choose?

Use whichever units match your source data. The calculator converts eV, kelvin, Celsius, m⁻³, cm⁻³, mol/L, mol/m³, and mmol/L into consistent internal SI values.

7) What does the plot represent?

The graph shows an exponentially screened potential profile, φ(r) = φ₀e^−r/λD. It helps visualize how quickly the disturbance decays as distance increases.

8) How can I validate my result?

Check that temperatures, densities, concentrations, valences, and εr are physically reasonable. Then compare your Debye length with expected scale ranges from literature or trusted laboratory references.