The kinetic pressure exerted by hot fusion plasma — the force that the magnetic field must contain, and the key driver of fusion power output.
Plasma pressure is the kinetic pressure exerted by the thermal motion of the charged particles in a fusion plasma. For a plasma with electron density ne, electron temperature Te, ion density ni, and ion temperature Ti, the total pressure is p = neTe + niTi (in SI units, with temperatures converted via kB). In a typical D-T reactor plasma at n = 1020 m−3 and T = 15 keV, the plasma pressure reaches several atmospheres — comparable to the pressure in a car tyre, but at hundreds of millions of degrees.[1]
The ratio of plasma pressure to magnetic pressure is called beta (β), defined as β = 2μ0p / B2, where B is the magnetic field strength. Beta is a dimensionless figure of merit for magnetic confinement: a higher beta means more fusion power is produced for a given magnetic field strength, directly reducing the cost and engineering difficulty of the magnets. Conventional tokamaks typically operate at β = 2–5%, while spherical tokamaks have demonstrated β values above 40%.[2]
There is an upper limit to the plasma pressure that a given magnetic configuration can stably confine. In tokamaks, this is described by the Troyon beta limit: βmax (%) = βN × Ip / (aB), where βN is the normalised beta (typically limited to 2.5–3.5 for stable operation), Ip is the plasma current, a is the minor radius, and B is the toroidal field. Exceeding this limit triggers MHD instabilities — particularly pressure-driven ballooning modes and kink modes — that can rapidly degrade confinement or cause disruptions.[3]
The radial distribution of plasma pressure, not just its volume average, strongly influences fusion performance. A peaked pressure profile with high central values maximises the fusion reaction rate in the hot core. However, overly peaked profiles can drive internal MHD instabilities such as sawteeth and neoclassical tearing modes. The pedestal pressure in H-mode plasmas sets a boundary condition that largely determines the core pressure and overall fusion power.[1]
The plasma pressure must be reacted by the magnetic field, and the magnetic pressure must in turn be supported by the magnet structure. In a reactor-scale device with B = 12 T, the magnetic pressure alone exceeds 500 atmospheres, imposing severe structural demands on the toroidal field coils and their support systems. The interplay between achievable plasma pressure, magnetic field strength, and structural engineering is one of the central design trade-offs in fusion reactor engineering.[2]