Neoclassical Transport
Collisional transport enhanced by toroidal geometry and trapped-particle orbits, the irreducible floor beneath turbulent losses.
Beyond Classical Transport
Classical transport treats cross-field diffusion as a random walk of gyro-orbits scattered by collisions, giving a diffusivity of order the gyroradius squared times the collision frequency. In a torus this underestimates transport because the magnetic field is non-uniform: it is stronger on the inboard side. Particles drift off flux surfaces and some become trapped in the low-field region, and their wide banana-shaped orbits set the true collisional step size.
Three Collisionality Regimes
- Banana regime (low collisionality): trapped particles complete banana orbits between collisions; the diffusivity is enhanced over classical by roughly the aspect ratio to the power 3/2.
- Plateau regime (intermediate): the diffusivity is independent of collision frequency.
- Pfirsch-Schluter regime (high collisionality): particles are collisional over a connection length; transport is enhanced over classical by a factor of order q^2.
The Bootstrap Current
The most consequential neoclassical effect is not a loss but a current. Trapped-particle pressure gradients drive a self-generated toroidal current, the bootstrap current, proportional to the pressure gradient and to the fraction of trapped particles. It offsets externally driven current and is essential to steady-state tokamak scenarios, but its loss inside a magnetic island drives neoclassical tearing modes.
Relevance
Neoclassical theory sets the minimum achievable transport and predicts the bootstrap current that shapes the current profile. Spherical tokamaks like the Hyperion concept have large trapped fractions because of their low aspect ratio, raising both neoclassical transport and the bootstrap fraction. These are design-stage calculations for a machine in simulation.