Magnetogasdynamics and Electromagnetogasdynamics

  • Shih-I Pai


In this chapter, we consider the plasma as a single fluid. The fundamental equations are given in chapter II, § 8. They are as follows:
$$p={{R}_{p}}\rho T$$
$$\frac{\partial \rho }{\partial t}+\frac{\partial }{\partial {{x}^{i}}}(\rho {{u}^{i}})=0$$
$$\rho \frac{D{{u}^{i}}}{Dt}=-\frac{\partial pt}{\partial {{x}^{i}}}+\frac{\partial {{\tau }^{ij}}}{\partial {{x}^{j}}}+{{F}_{{{e}^{i}}}}+{{F}_{{{g}^{i}}}}$$
$$\frac{\partial \rho \overline{em}}{\partial t}+\frac{\partial \rho \overline{em}{{u}^{j}}}{\partial {{x}^{j}}}=-\frac{\partial {{u}^{j}}pt}{\partial {{x}^{j}}}+\frac{\partial {{u}^{i}}{{\tau }^{ij}}}{\partial {{x}^{j}}}+{{E}^{j}}{{J}^{j}}+\frac{\partial {{Q}^{j}}}{\partial {{x}^{j}}}$$
$$\nabla \times \overrightarrow{H}=\overrightarrow{J}+\frac{\partial \varepsilon \overrightarrow{E}}{\partial t}$$
$$\nabla \times \overrightarrow{E}=-\frac{\partial {{\mu }_{e}}\overrightarrow{H}}{\partial t}$$
$$\frac{\partial {{\rho }_{e}}}{\partial t}+\frac{\partial {{J}^{j}}}{\partial {{x}^{j}}}=0$$
$${{J}^{i}}={{i}^{i}}+{{\rho }_{e}}{{u}^{i}}=\sigma [{{E}^{i}}+{{\mu }_{e}}(\overrightarrow{u}\times {{\overrightarrow{H}}^{i}})]+{{\rho }_{e}}{{u}^{i}}$$
$$\nabla \cdot \overrightarrow{H}=0$$
$$\nabla \cdot \overrightarrow{E}=\frac{1}{\varepsilon }\rho e$$
where the unknowns to be investigated are u i , p, ρ, T,E i , H i , ρ e and J i . Equations (4.9) and (4.10) are not independent equations which may be derived from equations (4.5), (4.6) and (4.7) (cf. chapter III, § 5); but they are important relations, hence we list them here for reference.


Magnetic Field Mach Number External Electric Field Fundamental Equation Compressible Fluid 
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© Springer-Verlag GmbH Wien 1962

Authors and Affiliations

  • Shih-I Pai
    • 1
  1. 1.Institute for Fluid Dynamics and Applied MathematicsUniversity of MarylandCollege ParkUSA

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