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The cold-plasma equations describe waves, and other perturbations, which
propagate through a plasma *much faster* than a typical thermal velocity.
It is instructive to consider the relationship between the collective
motions described by the cold-plasma model and the motions of individual
particles that we studied in Sect. 2. The key observation is that in the
cold-plasma model all particles (of a given species) at a given position effectively move with the
same velocity. It follows that the fluid velocity is identical to the particle
velocity, and is, therefore, governed by the same equations.
However, the cold-plasma
model goes beyond the single-particle description because it determines the
electromagnetic fields *self-consistently* in terms of the
charge and current densities generated by the motions of the
constituent particles of the plasma.
What role, if any, does the geometry of the plasma equilibrium play in
determining the properties of plasma waves? Clearly, geometry plays a
key role for modes whose wave-lengths are comparable to the dimensions of
the plasma. However, we shall show that modes whose wave-lengths are
*much
smaller* than the plasma dimensions
have properties which are, in a local sense, *independent* of the
geometry. Thus, the local properties of small-wave-length oscillations are
*universal* in nature. To investigate these properties, we
may, to a first approximation, represent the plasma as a homogeneous
equilibrium (corresponding to the limit
, where
is the magnitude of the wave-vector, and is the characteristic
equilibrium length-scale).

** Next:** Plane Waves in a
** Up:** Waves in Cold Plasmas
** Previous:** Waves in Cold Plasmas
Richard Fitzpatrick
2011-03-31