Pressure Balance and Plasma Diamagnetism

How a plasma reduces the internal magnetic field to make room for its own pressure.

A plasma is diamagnetic

A confined plasma carries currents that reduce the magnetic field inside it, so the total pressure, plasma plus magnetic, stays balanced. In the simplest one-dimensional case, perpendicular pressure balance reads:

p + B^2 / (2 mu0) = constant

Where the plasma pressure p is high, the magnetic pressure B^2/2mu0 is correspondingly lower. The plasma excludes some field, exactly like a diamagnetic material, which is why the effect is called plasma diamagnetism.

The diamagnetic current

The current responsible is the diamagnetic current, which flows perpendicular to both the field and the pressure gradient: J_dia = (B x grad p)/B^2. It is not the motion of individual guiding centers but arises from the gradient in gyrating-particle density, a subtle but real fluid current that supports the pressure.

Diamagnetic drift and waves

• The diamagnetic drift is the fluid velocity associated with the pressure gradient
• Diamagnetic frequency effects stabilize some modes and set drift-wave frequencies
• The diamagnetic loop measures stored energy by sensing the excluded flux

Measuring beta

The reduction of field inside the plasma is measured externally by the diamagnetic loop, giving the poloidal beta and hence the stored thermal energy. This is one of the primary diagnostics of plasma performance.

Design context

How much field the plasma can exclude, while remaining stable, is exactly what the beta limit governs. High-beta devices like the spherical-tokamak Hyperion breeder are strongly diamagnetic, which is efficient use of the field but places them near the pressure-driven stability boundaries analyzed by ballooning and Troyon theory.