An analytical approach to evaluate magnetic field closure and topological changes in FRC devices.*

We describe mathematical methods, one based on analyzing the topology of modified non-linear flux function (MFF),

to evaluate whether odd-parity perturbations affect the local closure of magnetic field lines in FRCs. Using the MFF

methodology, quantitative formulas are derived that provide the shift of the field minimum and the threshold for field-

line opening, a discontinuous change in field topology.