Abstract
We analyze the 3-dimensional (3D) geometry of solar flares that show so-called interacting flare
loops in soft X-ray, hard X-ray, and radio emission, as previously identified by Hanaoka and
Nishio. The two flare loops that appear brightest after the flare are assumed to represent the
outcome of a quadrupolar magnetic reconnection process, during which the connectivity of magnetic
polarities is exchanged between the four loop footpoints. We fit a 10-parameter 3D-model to
Yohkoh SXT and HXT data of 10 solar flares and determine this way the pre-reconnection and
post-flare geometry of interacting flare loops. We apply a flare model of Melrose to calculate the
magnetic flux transfer and energy released when two current-carrying field lines reconnect to form
a new current-carrying system in a quadrupolar geometry. Some findings are: (1) The
pre-reconnection field lines always show a strong asymmetry in size, consistent with the
scenario of new-emerging small-scale loops that reconnect with pre-existing large-scale loops.
(2) The relative angle between reconnecting field lines is near-collinear in half of the
cases, and near-perpendicular in the other half, contrary to the anti-parallel configuration
suggested in the model of Heyvaerts et al. (3) The shear angle between interacting field lines
reduces by 10-50 deg after quadrupolar reconnection. (4) The small-scale flare loop experiences
a shrinkage by a factor of 1.31+0.44, which is consistent with the scaling law found from previous
electron time-of-flight measurements, suggesting that electron acceleration occurs near the cusp
of quadrupolar configurations. (5) The large-scale loop is found to dominate the total induction
between current-carrying loops, providing a simple estimate of the maximum magnetic energy
available for flare energy release due to current transfer, which scales as E=10(29.63) [r2/10(9)
cm] [I2/10(11) A](2) , (with r2 the curvature radius and I2 the current of the large-scale loop)
and is found to correlate with observed flare energies deduced from soft X-ray and hard X-ray
fluxes. Most of the energy is transferred to small-scale loops that have half of the large-scale
current I1=I2/2. (6) The quadrupolar reconnection geometry provides also a solution of ``Canfield's
dilemma" of the offset between the maximum of vertical currents and the HXR flare loop
footpoints.