Banana Orbits
The crescent-shaped guiding-center paths of trapped particles that dominate neoclassical transport.
Trapping in a torus
The magnetic field in a torus is stronger on the inboard (high-field) side than the outboard side. A particle with small enough parallel velocity mirrors before reaching the inboard side and is trapped, bouncing back and forth on the low-field side. Its guiding center, viewed in the poloidal cross-section, traces a crescent, the banana orbit.
Banana width
As the particle bounces, the grad-B and curvature drifts shift its orbit radially, so the banana has a finite width much larger than the gyroradius:
w_banana ~ q rho_i / sqrt(eps)where q is the safety factor, rho_i the ion gyroradius, and eps the inverse aspect ratio. This width is the effective step size for neoclassical transport, which is why neoclassical diffusion greatly exceeds classical diffusion.
The trapped fraction
- The fraction of trapped particles scales as sqrt(eps), large at low aspect ratio
- Trapped particles carry the bootstrap current through their momentum imbalance
- Collisions that scatter trapped particles set the banana-regime transport rate
Consequences
Banana orbits are the origin of neoclassical transport, the bootstrap current, and trapped-particle instabilities (such as the trapped-electron mode). They explain why low-aspect-ratio devices have both a large bootstrap fraction and wide orbits.
Spherical-tokamak relevance
In a spherical tokamak like the Hyperion breeder, the inverse aspect ratio eps is large, so the trapped fraction is high and banana orbits are wide. This boosts the bootstrap current (favorable) but also widens neoclassical orbits, so both effects are computed carefully from drift-kinetic theory in the design analysis.