The Farley–Buneman instability, or FB instability, is a microscopic plasma instability named after Donald T. Farley and Oscar Buneman. It is similar to the ionospheric Rayleigh-Taylor instability.
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It occurs in collisional plasma with neutral component, and is driven by drift currents. It can be thought of as a modified two-stream instability arising from the difference in drifts of electrons and ions exceeding the ion acoustic speed.
It is present in the equatorial and polar ionospheric E-regions. Since the FB fluctuations can scatter the electromagnetic waves, the instability can be used to diagnose the state of ionosphere by the use of electromagnetic pulses.
Conditions
To derive the dispersion relation below, we make the following assumptions. First, quasi-neutrality is assumed. This is appropriate if we restrict ourselves to wavelengths longer than the Debye length. Second, the collision frequency between ions and background neutrals is assumed to be much greater than the ion cyclotron frequency, allowing the ions to be treated as unmagnetized. Because the Buneman instability is electrostatic in nature, only electrostatic perturbations are considered.
Dispersion relation
We use linearized fluid equations (equation of motion, equation of continuity) for electrons and ions with Lorentz force and collisional term. This additional term describes the collisions of charged particles with neutral particles in the plasma by frequency of collisions. We denote
This can lead to oscillations if the frequency
where
Growth rate
Solving the dispersion we arrive at frequency given as:
where