The ratio of plasma kinetic pressure to magnetic pressure — a dimensionless figure of merit that governs the economic and physical viability of magnetically confined fusion devices.
where μ0 is the permeability of free space, n is the particle number density, kB is the Boltzmann constant, T is the plasma temperature, and B is the magnetic field strength. Beta is dimensionless, typically expressed as a percentage.[1]
Fusion power density scales as β2·B4, so a device at higher beta can achieve the same fusion power with a weaker magnet system. However, above a critical value, pressure-driven MHD instabilities disrupt confinement.[1]
In practice, conventional tokamaks operate at 3–8%. NSTX achieved βT > 35% transiently.[2]
Conventional tokamaks: 3–8%. Spherical tokamaks: 15–40%. Stellarators: 3–5%. Field-reversed configurations: β approaching unity (~0.9), the highest of any confined plasma.[1]
Since magnet cost scales with B2·V, a high-beta device can be physically smaller for the same fusion power. However, the advent of HTS magnets (fields >20 T) has altered the calculus: moderate beta at high B may be preferable to high beta at low B.[1]