  [Abridged]We present analysis of a pair of unusually energetic coronal hard
X-ray (HXR) sources detected by RHESSI during the impulsive phase of an X3.9
class solar flare on 2003 November 3, which simultaneously shows two intense
footpoint (FP) sources. A distinct loop top (LT) coronal source is detected up
to ~150 keV and a second (upper) coronal source up to ~80 keV. These photon
energies are much higher than commonly observed in coronal sources and pose
grave modeling challenges. The LT source in general appears higher in altitude
with increasing energy and exhibits a more limited motion compared to the
expansion of the thermal loop. The high energy LT source shows an impulsive
time profile and its nonthermal power law spectrum exhibits soft-hard-soft
evolution during the impulsive phase, similar to the FP sources. The upper
coronal source exhibits an opposite spatial gradient and a similar spectral
slope compared to the LT source. These properties are consistent with the model
of stochastic acceleration of electrons by plasma waves or turbulence. However,
the LT and FP spectral index difference (varying from ~0-1) is much smaller
than commonly measured and than that expected from a simple stochastic
acceleration model. Additional confinement or trapping mechanisms of high
energy electrons in the corona are required. Comprehensive modeling including
both kinetic effects and the macroscopic flare structure may shed light on this
behavior. These results highlight the importance of imaging spectroscopic
observations of the LT and FP sources up to high energies in understanding
electron acceleration in solar flares. Finally, we show that the electrons
producing the upper coronal HXR source may very likely be responsible for the
type III radio bursts at the decimetric/metric wavelength observed during the
impulsive phase of this flare.
