The Plasma Beta Parameter
The ratio of plasma pressure to magnetic pressure, the primary measure of magnetic confinement efficiency.
Definition
Plasma beta is beta = 2 mu0 p / B^2, the ratio of the thermal pressure p to the magnetic pressure B^2/(2 mu0). It quantifies how much plasma pressure a given magnetic field confines. High beta is economically and physically desirable because fusion power density rises with pressure squared while the cost and engineering burden rise with field strength, so more pressure per unit field is more effective confinement.
Variants
- Toroidal beta: uses the toroidal field, usually the vacuum field on axis.
- Poloidal beta: uses the poloidal field from the plasma current.
- Normalized beta (beta_N): beta divided by the ratio I/(a B), giving a shape- and current-independent stability figure of merit used in the Troyon limit.
Stability Ceiling
Beta cannot be raised without bound: pressure-driven MHD instabilities set a maximum. The Troyon scaling caps normalized beta at roughly a few, and neoclassical tearing modes often intervene below the ideal limit. The achievable beta is therefore a compromise between pressure drive and stability, and pushing it is a main objective of advanced scenarios.
Relevance
Spherical tokamaks are notable for achieving high beta because their geometry provides strong magnetic well and shaping. The Hyperion breeder concept is a spherical tokamak whose design-stage equilibria target high beta consistent with stability limits; the on-axis field near 8 T and peak field of 16.84 T frame the magnetic pressure against which beta is measured. All values here are simulation-stage design points, not measured results.