Experimental measurement of magnetic flux surfaces in Wendelstein 7-X.

In an ideal magnetic configuration, charged particles follow helical orbits around magnetic field lines and remain largely confined to nested magnetic surfaces. In reality, collisions, particle drifts and plasma turbulence cause their guiding centres to move gradually across these surfaces. As a result, particles and energy can slowly migrate towards the plasma edge and eventually be lost from confinement.

Cross-field transport can move particles either inward or outward, but the net effect is a gradual loss of particles and thermal energy from the confined plasma. Lost fuel particles can be replaced by fuelling, but the energy they carry must be supplied again by external heating or, in a burning plasma, by fusion self-heating. Excessive transport therefore reduces the energy confinement time and can prevent the plasma from maintaining fusion-relevant conditions.

Diffusion

The gradual motion of particles across magnetic surfaces is described as diffusion, while the broader movement of particles and energy through the plasma is known as transport. Understanding and reducing transport losses is one of the central challenges of magnetic-confinement fusion, because these losses directly determine how well the plasma can retain its heat and particles. Early stellarator designs were initially expected to show transport close to classical predictions based mainly on particle collisions. In practice, however, the measured losses were much larger than classical theory suggested.

More complete neoclassical theory later showed that toroidal geometry, trapped particles and magnetic drifts can increase transport above classical levels. Experiments also revealed additional anomalous transport associated with plasma turbulence. Historically, this was often compared with the empirical Bohm diffusion scaling, which describes cross-field transport much larger than classical collisional predictions.

The early Model B and Model C stellarators at Princeton suffered from much poorer confinement than expected, raising doubts about the practical usefulness of the concept. Improvements in magnetic configuration, heating and plasma control gradually reduced the losses, but for decades stellarators remained limited by relatively high neoclassical and turbulent transport. Their three-dimensional magnetic geometry required much more careful optimisation than was initially possible.

Only advances in plasma theory, numerical optimisation, computing and precision engineering made it possible to design and manufacture coils that produce carefully tailored three-dimensional magnetic fields. Modern optimised stellarators can greatly reduce neoclassical particle and energy losses and achieve fusion-relevant plasma temperatures. Turbulent transport, impurity control and fast-particle confinement nevertheless remain important areas of research. Modern stellarators are also designed to minimise bootstrap current, which could otherwise modify the carefully optimised magnetic configuration.