The Banana Regime

Low-collisionality neoclassical transport set by the wide banana orbits of trapped particles.

Trapped Particles

In a torus the magnetic field is stronger on the inboard side, so a particle with small enough parallel velocity is reflected by the magnetic mirror before reaching the high-field side. Such particles are trapped and bounce back and forth in the low-field outboard region. Projected onto a poloidal cross-section, their guiding-center orbit traces a crescent, the banana orbit, whose radial width greatly exceeds the gyroradius.

Transport Scaling

The trapped fraction is of order the square root of the inverse aspect ratio, sqrt(epsilon) with epsilon = r/R. Random-walking with a step equal to the banana width and an effective de-trapping collision frequency (larger than the bare collision frequency because a small pitch-angle scatter suffices to de-trap) gives a diffusivity enhanced over classical by roughly epsilon^{-3/2} q^2. This is the largest neoclassical enhancement of the three regimes.

Validity

The banana regime requires that a trapped particle complete many bounce orbits before being de-trapped, meaning the normalized collisionality nu-star is much less than one. This holds in the hot, low-density core of a good-confinement plasma. As collisionality rises toward the edge the plasma passes through the plateau regime and then into the Pfirsch-Schluter regime.

Relevance

Banana-orbit physics also determines the trapped fraction that drives the bootstrap current, so the banana regime is doubly important: it sets both the core neoclassical transport floor and the self-generated current. Spherical tokamaks such as the Hyperion concept have large inverse aspect ratio and thus large trapped fractions, amplifying both effects in design-stage modeling.