The frequency at which plasma oscillations occur. A plasma oscillation is the most fundamental collective effect exhibited by a plasma (a quasineutral ensemble of charged particles- see also plasma physics).
In equilibrium, the electric fields of the electrons and ions cancel each other out. However, due to the thermal motion of the particles, this field free equilibrium cannot be maintained. In order to explain the concept of plasma oscillations, it is useful to consider the motion of the center of masses of the electrons and of the ions (rather than the motion of all the individual particles). If the center of mass of the electrons is now displaced from that of the ions, an electric field is set up (as the charges no longer cancel) which acts to attract the electrons and ions back together. This acts as a restoring force and sets up a simple harmonic motion of the electrons about the center of mass of the ions. This amounts to a continual conversion of electrostatic energy to kinetic energy and back again. This process takes place at the electron plasma frequency ωpe given as follows in mks units
ωpe= sqrt((ne*e^2)/(εo*me)) rad s-1
is the electron density, e is the electric charge
is the permittivity
of free space and me
is the mass
of an electron. Since all terms are constants apart from the electron density we may write
ωpe= 56.4 sqrt(ne) rad s-1
Note that this is an angular frequency
. Converted to a straightforward frequency one has
fpe=ωpe/2*π= 8.98sqrt(ne) Hz
In the same way, the ions can oscillate about the electron center of mass
. Simply substitute the ion mass and density into the equations above to get the ion plasma frequency.
fpi=ωpi/2*π= 0.21sqrt(ni/A) Hz
where A is the atomic weight
of the ion.
'Tokamaks' by John Wesson