# Triangularity

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 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.

The upper triangularity is then defined as follows:

${\displaystyle \delta _{upper}=(R_{geo}-R_{upper})/a}$

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 ${\displaystyle R}$ than the center of the plasma), which makes H-mode difficult or impossible to access but improves performance of the L-mode.[3]