Ellipticity

The ellipticity (also referred to as elongation) refers to the shape of the poloidal cross section of the Last Closed Flux surface or separatrix of a tokamak.

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).

Assuming:

• R_max is the maximum value of R along the LCFS or separatrix.
• R_min is the minimum value of R along the LCFS or separatrix.
• Z_max is the maximum value of Z along the LCFS or separatrix.
• Z_min is the minimum value of Z along the LCFS or separatrix.
• a is the minor radius of the plasma, defined as (R_max - R_min)/2.

The ellipticity is then defined as follows:

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

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. Because of vertical stability constraints, $\kappa$ is usually limited to a value close to about 1.8.

See also

• Triangularity
• Toroidal coordinates
• Effective plasma radius