Collisionality nu-star
The dimensionless ratio that places a plasma in the banana, plateau, or Pfirsch-Schluter transport regime.
Definition
The normalized collisionality nu-star is the ratio of the effective collision frequency for de-trapping to the bounce frequency of a trapped particle. Equivalently it is the number of times a trapped particle would be scattered out of its banana orbit during one bounce period. A common form is nu-star = nu_eff q R / (epsilon^{3/2} v_th), where nu_eff is the pitch-angle scattering rate, q the safety factor, R the major radius, epsilon the inverse aspect ratio, and v_th the thermal speed.
Regime Boundaries
- nu-star much less than one: banana regime; trapped orbits survive many bounces; diffusivity peaks.
- nu-star of order one to epsilon^{-3/2}: plateau regime; diffusivity independent of collision frequency.
- nu-star much greater than one: Pfirsch-Schluter regime; collisional parallel return currents dominate.
Why It Is Dimensionless
Collisionality is one of the small set of dimensionless parameters (with normalized gyroradius rho-star and beta) that determine plasma behavior independent of absolute size. Two devices with matched nu-star, rho-star, beta, and shape are expected to exhibit the same normalized transport. This underpins the dimensionless-scaling approach to projecting confinement from present experiments to future devices.
Relevance
Because the bootstrap current fraction and neoclassical transport both depend on nu-star, it is a primary design parameter. A reactor-grade core is deep in the banana regime, giving high bootstrap fraction but also the largest neoclassical transport enhancement. For the Hyperion breeder concept, the nu-star profile is an input to neoclassical and confinement modeling; the device is a simulation study, not built hardware.