What Is the Debye Length & Plasma Frequency Calculator?
The Debye length λD is the scale over which mobile charge carriers screen out electric fields in an ionized gas.
For an ionized gas to be classified as a true plasma, the Debye length must be much smaller than the physical system size (L >> λD) and the Debye sphere must contain many particles (ND >> 1).
How Does the Debye Length & Plasma Frequency Calculator Work?
Fast-moving electrons cloud around positive ions, neutralizing electric potentials exponentially: Φ(r) ∝ exp(-r/λD)/r.
Displacing electrons creates a restoring Coulomb force that oscillates at the Langmuir plasma frequency fpe.
Debye Length & Plasma Frequency Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Models electrostatic Debye screening length and collective plasma electron oscillations.
How to Use the Debye Length & Plasma Frequency Calculator
- Input the plasma electron density in particles/m³.
- Enter the electron temperature in eV.
- Verify that ND >> 1 to confirm collective plasma behavior.
Step-by-Step Example Calculation
Tokamak Edge Plasma at 10 eV and 10¹⁹ m⁻³
Input Values:
Understanding Your Result
λD indicates the minimum spatial scale of macroscopic quasi-neutrality.
fpe indicates the cutoff frequency below which electromagnetic waves cannot propagate through the plasma.
Factors That Affect the Result
- Higher density reduces Debye length and raises plasma frequency.
- Higher temperature increases thermal agitation, widening the Debye screening cloud.
When Should You Use This Calculator?
- Magnetic fusion energy research and tokamak scrape-off layer design.
- Semiconductor plasma etching and ion propulsion thruster sizing.
Assumptions & Limitations
- Assumes Maxwellian electron distribution and cold, immobile background ions.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard plasma formulation based on Poisson-Boltzmann linearization.