Nuclear Fusion Physics and Technology/Magnetohydrodynamics

Definition: Minimal MHD density equation

Minimal MHD density equation is equation

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

Definition: Magnetic viskozity

Magnetic viskozity $\eta \in ℂ$ is defined as

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

where $\sigma$ is conductivity and $\mu$ permeability.

Definition: Minimal MHD magnetic equation

Minimal MHD magnetic equation is equation

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

Definition: Minimal MHD speed equation

Minimal MHD speed equation is equation

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

where $\eta ,\xi$ are viskosity coefficients, $\varrho$ is particle density. Template:BookCat