The debye length is the screening distance of the moving charge carriers that screen electric field. It is also known as the debye sphere. In this calculator, the debye length of an electron is calculated using boltzmann constant, permeability of vacuum, electron temperature, electron density and electronic charge.The debye length is the screening distance of the moving charge carriers that screen electric field. It is also known as the debye sphere. In this calculator, the debye length of an electron is calculated using boltzmann constant, permeability of vacuum, electron temperature, electron density and electronic charge.

Debye length Calculator

Electron Debye Length Calculator
Permittivity Of Vacuum
Boltzmann Constant
Electron Temperature
Electron Number Density
Electronic Charge
Debye Length: {{debyeLengthResult() | number:3}}

How ito use Electron Debye Length Calculator?

Step 1 - Enter the Electron Temperature

Step 2 - Enter the Electron Number Density

Step 3 - Calculate Debye length

Debye Length Formula:

λDe = ((εo*kB*Te) / (ne*e2))1/2

Where,

λDe = Electron Debye Length

εo = Permittivity Of Vacuum

kB = Boltzmann Constant

Te = Electron Temperature

ne = Electron Number Density

e= Electronic charge

Frequently Asked Questions

What is Debye length and why is it critical in plasma physics?

Debye length (λD) is the characteristic distance scale over which electric fields are screened in plasmas by surrounding charges. Beyond the Debye length, electric fields are largely canceled by charge redistribution. This parameter is fundamental to plasma behavior, determining whether a plasma is quasi-neutral, how collective effects dominate over binary collisions, and controlling phenomena like plasma oscillations and wave propagation. Regions smaller than λD show non-collective behavior.

How does electron density affect Debye length?

Debye length is inversely proportional to the square root of electron density (n^-1/2). Higher electron densities mean more charges available to screen electric fields, reducing the screening distance. In dense plasmas, Debye length becomes very small, while in rarefied plasmas it becomes very large. This inverse relationship is critical for understanding plasma behavior across different regimes.

How does temperature affect plasma screening and Debye length?

Debye length increases with electron temperature (proportional to T^1/2). Higher temperatures increase thermal energy and electron mobility, requiring larger distances for charge screening to become effective. This is why hot plasmas (like those in fusion devices) have larger Debye lengths than cold plasmas, affecting plasma stability and confinement requirements.

When do plasma approximations break down?

Plasma theory assumes the Debye length is much smaller than the system size and larger than atomic dimensions. When λD approaches atomic spacing, quantum effects become important. When λD exceeds system dimensions, the quasineutrality assumption fails and individual particle effects dominate. These limits define the valid regime for classical plasma physics.

Debye length and plasma frequency are complementary descriptions of plasma behavior. Plasma frequency (ωp) describes oscillation timescales, while Debye length describes spatial scales. Waves with frequencies above ωp propagate through the plasma, while lower frequencies are screened. The relationship k_D ≈ ωp/v_th connects these scales through thermal velocity.

Physical Basis & References

This calculator applies Debye-Hückel screening theory:

$$\lambda_D = \sqrt{\frac{\varepsilon_0 k_B T_e}{n_e e^2}}$$

Key Physics Principles:

  • Debye Screening - Charge redistribution creates exponential decay of electric potential
  • Quasineutrality - Plasma maintains approximate charge neutrality at scales » λD
  • Debye Sphere - Sphere of radius λD contains characteristic number of particles for screening
  • Thermal Velocity - Electron temperature determines charge mobility and screening effectiveness

Key Assumptions:

  • Electrons are in thermal equilibrium (Boltzmann distribution)
  • Coulomb interaction is the dominant force
  • Density is uniform (mean-field approximation)
  • Temperature » ionization energy (fully ionized plasma)
  • System size » Debye length

Typical Range of Values:

  • Debye length: 10 μm (dense laboratory plasma) to 1000 km (space plasma)
  • Electron temperature: 1 eV to 100 keV
  • Electron density: 10^6 to 10^20 m⁻³
  • Debye number: 1 to 10⁹ particles in Debye sphere

Further Reading:

  • Chen, F.F. (2016). Introduction to Plasma Physics and Controlled Fusion, 3rd Edition. Springer.
  • Debye, P. & Hückel, E. (1923). “Zur Theorie der Elektrolyte”, Physikalische Zeitschrift.
  • Plasma Science and Fusion Energy Research - Princeton Plasma Physics Laboratory

Conclusion

I hope you find above Debye length calculator helpful to calculate debye length. Use below recommended articles of debye screening length.

  1. Debye Number Calculator
  2. Debye Screening Effective Potential Calculator

Read more about other Physics Calculator on below links