Because of the possibilities of fluid and electromagnetic force interactions, there is a broader range of possible fluid waves in plasma with applied magnetic fields (Cowling, 1957; Spitzer, 1962; Jeffrey, 1966). By introducing compressibility into the equations, we take a step to allow this coupling to become evident in the analysis. As above, we take the basic set of equations and generally follow the procedures of Boyd and Sanderson (1969):

Continuity:

$\frac{\partial \rho}{\partial t}+\nabla \xb7\left(\rho \overrightarrow{v}\right)=0;$

Momentum:

$\rho \frac{D\overrightarrow{v}}{Dt}=-\nabla p+\overrightarrow{J}\times \overrightarrow{B};$

Maxwell:

$\nabla \times \overrightarrow{B}=\mu \overrightarrow{J},$

and:

$\nabla \times \overrightarrow{E}=-\frac{\partial \overrightarrow{B}}{\partial t};$

Ohm's law:

$\frac{\overrightarrow{J}}{\sigma}=\overrightarrow{E}+\overrightarrow{v}\times \overrightarrow{B}.$

The set of equations ...

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