Nuclear Fusion Physics and Technology/Magnetohydrodynamics

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Definition: Minimal MHD density equation[edit]

Minimal MHD density equation is equation

 \frac{\partial \varrho}{\partial t} + \text{div} \varrho \vec{u} = 0

Definition: Magnetic viskozity[edit]

Magnetic viskozity  \eta \in \mathbb{C} is defined as

 \eta = \frac{1}{\sigma \mu}

where  \sigma is conductivity and  \mu permeability.

Definition: Minimal MHD magnetic equation[edit]

Minimal MHD magnetic equation is equation

 \frac{\partial \vec{B}}{\partial t} = \eta \Delta \vec{B} + \text{rot} ( \vec{u} \times \vec{B})

Definition: Minimal MHD speed equation[edit]

Minimal MHD speed equation is equation

 \varrho \frac{\partial \vec{u}}{\partial t} + \varrho ( \vec{u} \cdot \nabla ) \vec{u} = - \nabla p + \eta \Delta \vec{u} + ( \xi + \frac{\eta}{3} ) \nabla ( \text{div} \vec{u} ) + \vec{j} \times \vec{B}

where  \eta, \xi are viskosity coefficients,  \varrho is particle density.