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A flux rope is a domain of concentration of the magnetic field $\textbf{B}$.Insofar as $\textbf{B}$ outside such a domain is considered as vanishinglysmall, a flux rope can be described as the core of a singularity of the outervector potential $\textbf{A}$, whose topological invariant is the magnetic fluxthrough the rope. By 'topological' it is meant that$\oint_C\textbf{A}\cdot\mathrm d\textbf{s}$ measures along any loop $C$surrounding the flux rope the same constant flux $\Phi$. The electric currentintensity is another invariant of the theory, but non-topological. We showthat, in this theoretical framework, the linear force-free field (LFFF)Lundquist model and the non-linear (NLFFF) Gold-Hoyle model of a flux ropeexhibit stable solutions distributed over quantized strata of increasingenergies (an infinite number of strata in the first case, only one stratum inthe second case); each stratum is made of a continuous set of stable states.The lowest LFFF stratum and the unique NLFFF stratum come numerically close oneto the other, and match with a reasonable accuracy the data collected byspacecrafts travelling across magnetic clouds. The other LFFF strata do notmatch these data at all. It is not possible at this stage to claim which modelfits better the magnetic cloud data. We also analyze in some detail the mergingof tubes belonging to the same stratum, with conservation of the magnetichelicity, and the transition of a tube from one stratum to another one, whichdoes not conserve magnetic helicity.

Flux Ropes as Singularities of the Vector Potential