A plasma of hydrogen ions is trapped in a tokamak by balancing the pressure gradient and magnetic forces.

The equation of motion of a plasma is described by magnetohydrodynamics

ρ(d**v**/dt)= **jxB** - grad p

where ρ is the plasma

density,

**v** is the

velocity of the plasma

fluid,

**j** is the plasma current,

**B** is the magnetic field and

*p* is the pressure.

When the plasma is in equilibrium the velocity will be zero and the following equation results

**j**X**B** = grad p

This is the

fundamental equation of magnetic equilibrium.

It follows that

**B.** grad p = 0

**j.** grad p = 0

These two equations imply that the

magnetic surfaces are surfaces of constant pressure and that the plasma current is a flux surface quantity (i.e. a quantity which is a constant on a magnetic

flux surface).

The picture that emerges in a tokamak is of toroidally nested magnetic surfaces. As the minor radius of these surfaces tends to zero, the flux toroid becomes a line known as the magnetic axis.

In the simplest scenario, the surfaces are nested circles. Each successive circle is shifted slightly outwards due to the plasma pressure (i.e. the Shafranov shift). In fact, in most modern tokamaks, the magnetic flux surfaces are warped in shape (to optimise performance). The triangularity and elongation are two quantities used to define the surface shape.

External current coils are used to impose magnetic fields to keep the plasma in one place. Otherwise it will quickly hit the vessel wall and quench.