Normalized Gyroradius rho-star

The ratio of the ion gyroradius to the plasma size, the key parameter for scaling turbulent transport across devices.

Definition

The normalized gyroradius rho-star is the ion gyroradius rho_i divided by the plasma minor radius a: rho-star = rho_i / a. It measures how many gyroradii span the machine. Fusion plasmas have small rho-star, of order a few thousandths, meaning the turbulent eddies that set transport are tiny compared with the device, so the plasma contains many correlation lengths.

Why It Governs Transport

Turbulent transport theory predicts that the normalized heat diffusivity scales as a power of rho-star. In gyro-Bohm scaling the diffusivity is proportional to rho-star, so confinement improves as the machine grows and rho-star shrinks. In Bohm scaling the dependence is stronger. Which scaling holds is a central question because it determines how confidently confinement can be projected from small experiments to larger devices.

The Dimensionless Trio

Together with beta and collisionality nu-star, rho-star forms the set of dimensionless parameters that, along with geometry, are believed to fully determine normalized plasma behavior. Dimensionless-identity experiments match all three between different-sized devices to test transport scaling directly, isolating the rho-star dependence by holding beta and nu-star fixed.

Relevance

Because gyro-Bohm scaling rewards low rho-star, larger and higher-field devices are favored for good confinement. A useful way to read rho-star is as the inverse of the number of turbulent eddies that fit across the plasma, so shrinking it means each eddy transports a smaller fraction of the stored energy per step. Spherical tokamaks such as the Hyperion breeder concept achieve high field at compact size, and the resulting rho-star is an input to gyrokinetic transport projections. These are computational estimates; the machine is a simulation study, not built hardware.