Wave Propagation In M. F. D.

Abstract

The basic equations of Magnetofluiddynamics are :

$$ {\rm{\rho }}\frac{{\text{d}}}{{{\text{dt}}}}{\rm{\overrightarrow v}}\,\,\,{\rm{ = }}\,\,\,\,\frac{{\text{1}}}{{\text{c}}}{\rm{\overrightarrow j \times \overrightarrow B}}\,\,{\rm{ - }}\,\,\,{\rm{grad}}\,{\text{p}}$$

((1))

$$ \frac{{\text{1}}}{{\rm{\sigma }}}{\rm{\overrightarrow j}}\,\,{\rm{ = }}\,\,{\rm{\overrightarrow E}}\,\,{\rm{ + }}\,\,\frac{{\text{1}}}{{\text{c}}}\,{\rm{\overrightarrow v \times \overrightarrow B}}$$

((2))

$$ \begin{array}{*{20}c}{\frac{\partial }{{\partial {\text{t}}}}{\rm{\rho }}\,\,{\rm{ = }}\,\,\,{\rm{ - }}\,\,{\rm{div}}\,{\rm{\rho }}\,{\rm{\overrightarrow v}}\,\,{\rm{;}}} \hfill & {\frac{{\text{d}}}{{{\rm{dt}}}}\left( {{\rm{p\rho }}^{{\rm{ - \gamma }}} } \right)\,\,\, = \,\,\,0} \hfill \\ \end{array}$$

((3))

$$ \frac{1}{{\text{c}}}\frac{\partial }{{\partial {\text{t}}}}\,{\rm{\overrightarrow B}}\,\,{\rm{ = }}\,\,{\rm{ - }}\,\,{\rm{curl}}\,\,{\rm{\overrightarrow E}}$$

((4))

$$ \frac{{{\rm{4\pi }}}}{{\text{c}}}{\rm{\overrightarrow j}}\,\,{\rm{ = }}\,\,{\rm{curl}}\,\,{\rm{\overrightarrow B}}\,\,{\rm{.}}$$

((5))

They contain 14 scalar variables : 4 vector ${\rm{\overrightarrow v}}\,\,{\rm{,}}\,\,{\rm{\overrightarrow j}}\,\,{\rm{,}}\,\,{\rm{\overrightarrow E}}\,\,{\rm{,}}\,\,{\rm{\overrightarrow B}}$ i. e. velocity, current density, electric and magnetic field, and 2 scalars p ,ρ i. e. pressure and mass density, ( σ is the electric conductivity, γ the ratio of the specific heats, and c the velocity of light; heat conduction and viscosity is neglected).