  The coronal magnetic configuration of an active region typically evolves
quietly during few days before becoming suddenly eruptive and launching a
coronal mass ejection (CME). The precise origin of the eruption is still
debated. Among several mechanisms, it has been proposed that a loss of
equilibrium, or an ideal magneto-hydrodynamic (MHD) instability such as the
torus instability, could be responsible for the sudden eruptivity. Distinct
approaches have also been formulated for limit cases having circular or
translation symmetry. We revisit the previous theoretical approaches, setting
them in the same analytical framework. The coronal field results from the
contribution of a non-neutralized current channel added to a background
magnetic field, which in our model is the potential field generated by two
photospheric flux concentrations. The evolution on short Alfvenic time scale is
governed by ideal MHD. We show analytically first that the loss of equilibrium
and the stability analysis are two different views of the same physical
mechanism. Second, we identify that the same physics is involved in the
instability of circular and straight current channels. Indeed, they are just
two particular limiting case of more general current paths. A global
instability of the magnetic configuration is present when the current channel
is located at a coronal height, h, large enough so that the decay index of the
potential field, (d ln |Bp|) / (d ln h) is larger than a critical value. At the
limit of very thin current channels, previous analysis found a critical decay
index of 1.5 and 1 for circular and straight current channels, respectively.
However, with current channels being deformable and as thick as expected in the
corona, we show that this critical index has similar values for circular and
straight current channels, typically in the range [1.1,1.3].
