A new inner separatrix for simply connected flux surfaces of FRC under odd parity perturbation.*

Separatrix is a powerful tool for determining the closure of field lines in toroidal confinements. Without any perturbation to field reversed configuration (FRC), the flux surfaces inside the separatrix are topologically torus, ensuring the closure of field lines. Thus, the topological categories of field lines are open (outside separatrix) and closed (inside separatrix).  The flux function was recently modified for FRC under odd parity long wave rotating magnetic field (RMF) perturbation [1]. This work uses that modification and shows that, for an FRC under such perturbation, there is an inner separatrix within which the flux surfaces are no longer torus and become simply connected. So, in this case, there are three topological categories of field lines: open (outside the outer separatrix), closed on a toroidal surface (inside the outer separatrix but outside the inner separatrix), closed on a simply connected surface (inside the inner separatrix). 

[1] T. Ahsan et al. Phys. Plasmas, 29, 072507 (2022).