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

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.

See also

• Triangularity
• Toroidal coordinates
• Effective plasma radius