Debye Length Calculator

Formula

The formula to calculate the Debye Length (λD) is:

\[ \lambda_D = \sqrt{ \frac{\epsilon_0 \cdot k_B \cdot T_e}{n_e \cdot q_e^2} } \]

Where:

\( \lambda_D \) is the Debye Length
\( \epsilon_0 \) is the Permittivity of Free Space
\( k_B \) is the Boltzmann Constant
\( q_e \) is the Charge of an Electron
\( T_e \) is the Electron Temperature
\( n_e \) is the Density of Electrons

Debye Length Definition

A Debye length is a measure of a charge carrier’s net electrostatic effect in a solution and how far that effect persists. This is an important metric in plasma physics.

Example Calculation

Let's consider an example:

Electron Temperature (Te): 10000 K
Density of Electrons (ne): 1e18 m^-3

Using the formula to calculate the Debye Length:

\[ \lambda_D = \sqrt{ \frac{8.854187817 \times 10^{-12} \cdot 1.380649 \times 10^{-23} \cdot 10000}{1 \times 10^{18} \cdot (1.602176634 \times 10^{-19})^2} } \approx 6.9 \times 10^{-6} \, \text{meters} \]

This demonstrates that with an electron temperature of 10000 K and a density of electrons of 1e18 m^-3, the Debye length would be approximately 6.9e-6 meters.