# Ellipticity

Sketch of tokamak geometry
Illustration of the m=1,2,3, and 4 perturbations to a tokamak plasma cross section. Ellipticity/elongation is the m=2 perturbation (second from the left).

The ellipticity (also referred to as elongation[1]) refers to the shape of the poloidal cross section of the Last Closed Flux surface 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.
• Zmax is the maximum value of Z along the LCFS or separatrix.
• Zmin is the minimum value of Z along the LCFS or separatrix.
• a is the minor radius of the plasma, defined as (Rmax - Rmin)/2.

The ellipticity is then defined as follows:

${\displaystyle \kappa =(Z_{max}-Z_{min})/2a}$

Higher elongation is beneficial for fusion performance, but comes with increased vertical instability growth rate and thus increased risk of vertical displacement event (VDE) type disruptions.[2] Because of vertical stability constraints, ${\displaystyle \kappa }$ is usually limited to a value close to about 1.8.