Introduction to Plasmas and Plasma Dynamics

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Basic Equations of Continuum Plasma Dynamics

Mass conservation:

$\frac{\partial ρ}{\partial t} + \nabla \cdot (ρ \vec{v}) = 0;$

Momentum conservation:

$ρ \frac{D \vec{v}}{D t} = - \nabla p + \vec{J} \times \vec{B};$

Energy conservation:

$ρ \frac{D e_{i n t}}{D t} = - p (\nabla \cdot \vec{v}) + \frac{J^{2}}{σ};$

Ohm's law:

$\vec{J} = σ (\vec{E} + \vec{v} \times \vec{B});$

Ampere's law:

$\nabla \times \vec{H} = \vec{J}, \vec{H} = \frac{\vec{B}}{μ};$

Faraday's law:

$\nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t} .$

The variables ...

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