Ideal MHD

Ideal MHD (magnetohydrodynamics) is a simplification of MHD which assumes no plasma resistivity. The definition of the electric field, $\mathbf{𝐄}$,

$\mathbf{𝐄}+\mathbf{𝐯}\times \mathbf{𝐁}=\eta \mathbf{𝐉}$

is simplified (setting resistivity $\eta$ to zero) to

$\mathbf{𝐄}=-\mathbf{𝐯}\times \mathbf{𝐁}$

for a fluid velocity $\mathbf{𝐯}$ and magnetic field $\mathbf{𝐁}$. This allows for simple representations of MHD equilibria.

Limitations

Ideal MHD cannot model physical phenomenon requiring resistivity. This imposes the 'frozen-in flux' condition where magnetic field lines are bound to fluid elements. This prevents modelling of, for example, magnetic reconnection events.