# Ellipticity

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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]}:

*R*is the maximum value of_{max}*R*along the LCFS or separatrix.*R*is the minimum value of_{min}*R*along the LCFS or separatrix.*Z*is the maximum value of_{max}*Z*along the LCFS or separatrix.*Z*is the minimum value of_{min}*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:

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, is usually limited to a value close to about 1.8.

## See also

## References

- ↑
^{1.0}^{1.1}T.C. Luce, Plasma Phys. Control. Fusion**55**(2013) 095009 - ↑ D.A. Humphreys, et al.,
*Experimental vertical stability studies for ITER performance and design guidance*Nucl. Fusion**49**(2009) 115003