  The stability of the magnetic field in the solar corona is important for
understanding the causes of solar eruptions. Although various scenarios have
been suggested to date, the tether-cutting reconnection scenario proposed by
Moore et al.(2001) is one of the widely accepted models to explain the onset
process of solar eruptions. Although the tether-cutting reconnection scenario
proposed that sigmoidal field formed by the internal reconnection is the
magnetic field in pre-eruptive state, the stability of the sigmoidal field has
not yet been investigated quantitatively. In this paper, in order to elucidate
the stability problem of pre-eruptive state, we developed a simple numerical
analysis, in which the sigmoidal field is modeled by a double arc electric
current loop and its stability is analyzed. As a result, we found that the
double arc loop is more easily destabilized than the axisymmetric torus, and it
becomes unstable even if the external field does not decay with altitude, which
is in contrast to the axisymmetric torus instability. This suggests that the
tether-cutting reconnection may well work as the onset mechanism of solar
eruptions, and if so the critical condition for eruption under certain geometry
may be determined by a new type of instability rather than the torus
instability. Based on them, we propose a new type of instability called double
arc instability (DAI). We discuss the critical conditions for DAI and derive a
new parameter $\kappa$ defined as the product of the magnetic twist and the
normalized flux of tether-cutting reconnection.
