Effective plasma radius

The definition of the effective plasma radius is non-trivial for stellarators, yet needed for comparing the measurements of diagnostics.

Various alternative definitions are possible. Assuming the existence of toroidally nested flux surfaces, the simplest procedure is to define the mean radius as a function of some flux quantity (i.e., any quantity that is constant on a flux surface). At TJ-II, magnetic equilibria can be obtained from the VMEC code. It returns ψ, the poloidal magnetic flux. The effective radius is defined by

$\rho _{\rm {eff}}={\sqrt {\psi _{N}}}$

where ψ_N is the normalized poloidal flux, such that it is 0 on the magnetic axis and 1 at the Last Closed Flux Surface (LCFS). Other definitions can be based on the volume V(ψ) enclosed in a flux surface, or the surface area S(ψ) of a flux surface.

An effective radius can also be defined for magnetic configurations with magnetic islands, although this requires applying some special treatment for points inside the islands. It may be argued that assigning an effective radius to spatial points inside a magnetic island is not very useful, since such points are topologically disconnected from the main plasma volume. Similarly, the definition of an effective radius in ergodic magnetic zones is ambiguous, since the concept of flux surface has no meaning inside an ergodic zone.