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 occurs in collisional plasma with neutrals driven by drift current for two stream instability for unmagnetized plasma it becomes ''Buneman instability '' [3]
It is present in the
equatorial and
polarionosphericE-regions. In particular, it occurs in the equatorial electrojet due to the drift of electrons relative to ions,[4] and also in the trails behind ablating meteoroids.[5]
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
neutral particles is assumed to be much greater than the ion
cyclotron frequency, allowing the ions to be treated as unmagnetized. Third, the collision frequency between electrons and background neutrals is assumed to be much less than the electron cyclotron frequency. Finally, we only analyze low frequency waves so that we can neglect electron inertia.[4] Because the Buneman instability is electrostatic in nature, only electrostatic perturbations are considered.
Note that electron inertia has been neglected, and that both species are assumed to have the same number density at every point in space ().The collisional term describes the momentum loss frequency of each fluid due to collisions of charged particles with neutral particles in the
plasma. We denote as the frequency of collisions between electrons and neutrals, and as the frequency of collisions between ions and neutrals. We also assume that all perturbed properties, such as species velocity, density, and the electric field, behave as plane waves. In other words, all physical quantities will behave as an exponential function of time and position (where is the
wave number):
.
This can lead to
oscillations if the
frequency is a
real number, or to either
exponential growth or
exponential decay if is
complex. If we assume that the ambient electric and magnetic fields are perpendicular to one another and only analyze waves propagating perpendicular to both of these fields, the dispersion relation takes the form of:
,
where is the drift and is the
acoustic speed of ions. The coefficient described the combined effect of electron and ion collisions as well as their
cyclotron frequencies and :
.
Growth rate
Solving the dispersion we arrive at frequency given as:
,
where describes the growth rate of the instability. For FB we have the following: