# Plasma assumed as a perfect eletrical conductor?

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1. May 4, 2014

### Silversonic

(Wasn't sure on the right section for plasma physics, I apologise if this is wrong).

I'm reading up right now on a plasma surrounded by a tokamak wall, and the assumption of ideal magnetohydrodynamics - which assumes very little internal electrical resistivity and so the plasma can be assumed as a perfect electrical conductor.

http://en.wikipedia.org/wiki/Magnetohydrodynamics#Ideal_and_resistive_MHD

But aren't all electric fields inside a perfect conductor equal to zero? This seems to go without mention in both that wiki page and a number of textbooks I'm reading.

The tokamak walls themselves are assumed to be perfectly conducting too. From this, it's shown that the tangential component of the electrical field $E_t$ is continuous across the boundary and thus must also be zero.

But surely wouldn't this have been obvious? If the plasma is perfectly conducting then the electric field components are zero everywhere? Why would I need boundary conditions to show that?

I'm at a bit of a loss. The only thing I can think of is that the plasma is under the effect of varies magnetic fields created by external coils, which creates a plasma current along with helical fields. Is $E = 0$ for a perfect conductor under the assumption the conductor is under no external effects from outside sources?

2. May 4, 2014

### dauto

The electric field inside a conductor will be zero if the charges are static.

3. May 5, 2014

### Jano L.

There may be currents, but the electric charge distribution $\rho$ has to be static. Also magnetic field has to be static:
$$\partial_t \mathbf B = -\nabla \times\mathbf E$$
implies that time-dependent magnetic field will be accompanied by non-vanishing electric field.

4. May 5, 2014

### dauto

If there are currents than the charges are moving.

5. May 7, 2014

### Jano L.

Yes, but current does not necessarily mean charge distribution changes. In a perfect conductor (or superconductor), there may be current while electric field vanishes.