Poloidal Beta

The ratio of plasma pressure to the pressure of the poloidal magnetic field, a key equilibrium and stability parameter.

Definition

Poloidal beta is beta_p = 2 mu0

/ B_p^2, where

is the volume-averaged plasma pressure and B_p is the poloidal magnetic field, typically evaluated at the plasma edge. Whereas the total beta compares pressure to the full magnetic pressure, poloidal beta isolates the poloidal field produced by the plasma current, making it the natural measure for current-driven equilibrium effects.

Equilibrium Meaning

Poloidal beta controls the outward Shafranov shift of the plasma column and the diamagnetic or paramagnetic character of the equilibrium. At high beta_p the plasma pressure pushes flux surfaces outward and the plasma becomes diamagnetic. Poloidal beta also sets the bootstrap current fraction, which scales roughly with beta_p times the square root of the inverse aspect ratio, so high beta_p is desirable for self-driven steady-state operation.

Relation to Other Parameters

Total beta, toroidal beta, and poloidal beta are related through the field decomposition B^2 = B_t^2 + B_p^2. Because B_p is much smaller than the toroidal field in a conventional tokamak, poloidal beta can substantially exceed unity even when total beta is a few percent. In spherical tokamaks the poloidal field is relatively larger, changing this balance.

Relevance

High poloidal beta is a signature of advanced, bootstrap-dominated scenarios but is also associated with equilibrium limits and increased Shafranov shift. For the Hyperion breeder concept, beta_p is an output of the equilibrium reconstruction and a driver of bootstrap-current estimates in design-stage modeling; the machine is not yet built.