Plasma Collision Frequency Calculator
Find a plasma's electron collision frequency, the rate of Coulomb collisions that underlies resistivity and transport.
💥 What is the Plasma Collision Frequency Calculator?
This plasma collision frequency calculator finds how often electrons undergo effective Coulomb collisions with ions in a plasma. Enter the electron density and temperature, and it returns the collision frequency, the mean time between collisions, and the underlying Coulomb logarithm.
Electron collision frequency, νe = 2.91×10⁻⁶ ne[cm⁻³] lnΛ Te[eV]^(−3/2), is the standard NRL Plasma Formulary result that combines the effect of many small-angle Coulomb scatterings into a single effective collision rate. It falls off steeply with temperature, exactly the physics behind why hot plasmas conduct electricity so well.
Despite sounding like a small number, this collision rate underlies essentially all classical plasma transport, resistivity, thermal conductivity, and diffusion. Yet on the faster timescales relevant to waves and instabilities (like the GHz-scale cyclotron frequency), a hot fusion plasma behaves as nearly collisionless, which is why kinetic theory works so well for describing fast plasma dynamics.
This calculator is useful for plasma physics and fusion engineering students studying transport theory, and anyone curious how "collisional" a real plasma actually is on different timescales.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Tokamak fusion plasma core
Example 2 - Solar corona
Example 3 - Cool, tenuous plasma
❓ Frequently Asked Questions
🔗 Related Calculators
What is plasma collision frequency?
Plasma collision frequency (specifically the electron collision frequency here) is the effective rate at which electrons undergo cumulative 90-degree deflections from Coulomb collisions with ions, combining the effect of the many small-angle scatterings captured by the Coulomb logarithm into a single characteristic rate.
What is the formula for electron collision frequency?
νe = 2.91×10⁻⁶ × ne[cm⁻³] × lnΛ × Te[eV]^(−3/2) per second, a standard closed-form result from the NRL Plasma Formulary, where lnΛ is the Coulomb logarithm and Te is the electron temperature in electronvolts.
Why does collision frequency fall so steeply with temperature?
Faster (hotter) electrons spend less time near each ion and are deflected less by each encounter, so the effective collision rate drops as Te^(-3/2), the same physics behind the Te^(-3/2) scaling of Spitzer resistivity. This is why hot fusion plasmas become dramatically better electrical conductors as they heat up.
How is collision frequency related to Spitzer resistivity?
Both quantities come from the same underlying electron-ion Coulomb scattering physics and share the same Coulomb logarithm and Te^(-3/2) scaling. Collision frequency describes the rate of momentum-randomizing collisions directly, while the related <a href="/science/plasma-physics/spitzer-resistivity-and-conductivity-calculator/">Spitzer Resistivity Calculator</a> translates that same physics into an electrical resistivity.
Why are fusion plasmas often described as 'collisionless'?
Although a tokamak-core electron does collide thousands of times per second, this collision rate is extremely slow compared to other relevant timescales, like the cyclotron frequency (tens of GHz) or the time it takes a particle to transit the device. On these faster timescales, individual particles behave almost as if collisions were absent, which is why kinetic (collisionless) plasma theory works so well for describing fast wave and instability physics.
What is the mean time between collisions?
The mean time between collisions, τ = 1/νe, is simply the reciprocal of the collision frequency, representing the average time an electron travels between effective large-angle deflections. For a hot tokamak plasma this can be a fraction of a millisecond, while for a cooler, denser plasma it can be much shorter.
Does collision frequency depend on the ion charge state?
This basic formula depends only on electron density and temperature, the standard simplified case for a singly-charged (Z=1) plasma. More detailed NRL formulary expressions include an explicit ion charge factor for multiply-charged ion plasmas, which increases the collision rate roughly in proportion to Z.
How does collision frequency compare between a tokamak and the solar corona?
A tokamak's much higher density gives it a substantially higher collision frequency than the tenuous, similarly hot solar corona, even though both are considered 'hot' plasmas. This illustrates how density, not just temperature, strongly controls how collisional a plasma actually is.
What role does collision frequency play in plasma transport?
Collision frequency sets the timescale for how quickly a plasma relaxes toward local thermodynamic equilibrium and directly controls classical (collisional) transport coefficients like resistivity, thermal conductivity, and diffusion. Understanding it is the starting point for essentially all classical plasma transport theory.
Why does this calculator compute the Coulomb logarithm internally?
The Coulomb logarithm only depends on the same electron density and temperature already entered here, so this calculator computes it automatically using the same standard NRL formula as the dedicated <a href="/science/plasma-physics/coulomb-logarithm-calculator/">Coulomb Logarithm Calculator</a>, avoiding a separate lookup step.