The rapid destruction of toroidal magnetic surfaces

An ideal magnetic evolution can cause the development of an exponentially large variation between the distance of closest approach and greatest separation between neighboring pairs of magnetic field lines.  When this occurs, a fast magnetic reconnection naturally arises on the evolution time scale of magnetic field times a factor that depends only logarithmically on the strength of the non-ideal effects.  An obvious example arises when the magnetic evolution is driven by footpoint motion, as in the solar corona.  A similar effect can be responsible for the sudden loss of magnetic surfaces during a tokamak disruption.  In almost all magnetic surfaces in toroidal geometry, a magnetic field line never closes on itself as it is followed in the toroidal angle φ, and the line comes arbitrarily close to every point in the surface.  When an arbitrary pair of magnetic field lines are separated by an infinitesimal distance δ₀ in a surface at φ=0, then their separation can be written as δ₀ exp(Υ(φ)).  The Lyapunov exponent, which is Υ/φ as φ→∞, vanishes, but that does not preclude the variation in their exponentiation, Υ_v ≡ Υ_max - Υ_{_min}, from having an arbitrarily large value.  When Υ_v  is sufficiently large in a region of magnetic surfaces, rapid reconnection becomes inevitable.