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A separatrix is a boundary between domains with distinct dynamical behaviour (phase curves) in a dynamical system.  
In the fusion context, the term refers to the trajectories of the magnetic field lines and is used to describe:
- In the case of a divertor configuration in tokamaks, or a similar situation in other devices: the boundary between closed and open field lines, separating the toroidally confined region from the region where field lines connect to material surfaces. In the case of a 'double null' configuration, two separatices can be distinguished: the main (primary) and secondary separatrix. Only the main separatrix truly separates the regions of closed and open field lines.
- The boundary between the inside of a magnetic island and the surrounding region.
In the case of plasmas that are limited by material objects (limiters or walls), the use of the term separatrix to describe the boundary between the confined plasma and the external part of the plasma that connects to the wall (the Scrape-Off Layer, SOL) is not correct. In this case, the boundary should be referred to as the Last Closed Magnetic Surface (LCMS) or Last Closed Flux Surface (LCFS).