# Ideal MHD equilibrium equations

1. Feb 28, 2012

### vibe3

I have a question about the ideal equilibrium MHD equation:

$$\vec{J} \times \vec{B} = \nabla p$$

where $\vec{J}$ is the current, $\vec{B}$ is the magnetic field, and $p$ is the plasma pressure.

Does the magnetic field here represent the total magnetic field (any applied external fields plus fields due to the plasma currents?) Or does it represent only the plasma current fields?

I'm asking because one consequence of this equation is:

$$\vec{B} \cdot \nabla p = 0$$

But if you consider a system with an arbitrarily strong applied external field, and a low plasma density, this condition will certainly not be true. (ie: the small plasma currents will not be strong enough to change the external field enough to make this condition true)