Triangularity

The triangularity refers to the shape of the poloidal cross section of the Last Closed Flux surface (LCFS) or separatrix of a tokamak. Assuming[1]:

  • Rmax is the maximum value of R along the LCFS or separatrix.
  • Rmin is the minimum value of R along the LCFS or separatrix.
  • Rgeo is the geometric major radius, defined as (Rmax + Rmin)/2.
  • a is the minor radius of the plasma, defined as (Rmax - Rmin)/2.
  • Rupper is the major radius of the highest vertical point of the LCFS or separatrix.
  • Rlower is the major radius of the lowest vertical point of the LCFS or separatrix.
Sketch of tokamak geometry, including separatrix
Illustration of the m=1,2,3, and 4 perturbations to a tokamak plasma cross section. Triangularity is the m=3 perturbation.

The upper triangularity is then defined as follows:

and similar for δlower. The overall triangularity is defined as the mean of δupper and δlower.

Triangularity, especially the triangularity opposite the dominant X-point (so upper triangularity for a lower null plasma), influences the stability and character of the pedestal and ELMs.[2]

Some devices (TCV and DIII-D) can form plasma cross sections with negative triangularity (the X-points are pushed to larger than the center of the plasma), which makes H-mode difficult or impossible to access but improves performance of the L-mode.[3]

See also

References