  Numerical simulations of the helical ($m\!=\!1$) kink instability of an
arched, line-tied flux rope demonstrate that the helical deformation enforces
reconnection between the legs of the rope if modes with two helical turns are
dominant as a result of high initial twist in the range $\Phi\gtrsim6\pi$. Such
reconnection is complex, involving also the ambient field. In addition to
breaking up the original rope, it can form a new, low-lying, less twisted flux
rope. The new flux rope is pushed downward by the reconnection outflow, which
typically forces it to break as well by reconnecting with the ambient field.
The top part of the original rope, largely rooted in the sources of the ambient
flux after the break-up, can fully erupt or be halted at low heights, producing
a "failed eruption." The helical current sheet associated with the instability
is squeezed between the approaching legs, temporarily forming a double current
sheet. The leg-leg reconnection proceeds at a high rate, producing sufficiently
strong electric fields that it would be able to accelerate particles. It may
also form plasmoids, or plasmoid-like structures, which trap energetic
particles and propagate out of the reconnection region up to the top of the
erupting flux rope along the helical current sheet. The kinking of a highly
twisted flux rope involving leg-leg reconnection can explain key features of an
eruptive but partially occulted solar flare on 18 April 2001, which ejected a
relatively compact hard X-ray and microwave source and was associated with a
fast coronal mass ejection.
