Plasma physics diamagnetic current

[vibe3]

I have a question about the diamagnetic current caused by plasma pressure gradients. Various plasma physics / MHD texts state that the current due to a plasma pressure gradient in a magnetic field is given by

$$\mathbf{J} = \frac{\mathbf{B} \times \nabla p}{B^2}$$

where $$p = nkT$$

My question is, if I start with an ambient field $$\mathbf{B_0}$$ and some density distribution $$n(\mathbf{r})$$, and I want to calculate this current, can I simply plug in $$B_0$$ into the equation? Because once the current is flowing, it will change the ambient field into: $$B = B_0 + B_1$$, where $$B_1$$ is some additional field due to the current.

How could one account for this and compute the current once steady state has been reached?

 

[BigJDubs]

The equation for the diamagnetic current assumes that the magnetic field is not changing due to the current, so this equation is only valid when the current is small enough that it does not significantly alter the ambient magnetic field. If you want to calculate the current after steady state has been reached, then you would need to solve a system of equations that includes Faraday's law of induction, which states that the rate of change of the magnetic field is related to the electric current density.