Using RHESSI hard X-ray imaging spectroscopy observations , we analyze electron flux maps for a number of extended coronal loop flares .
For each event , we fit a collisional model with an extended acceleration region to the observed variation of loop length with electron energy E , resulting in estimates of the plasma density in , and longitudinal extent of , the acceleration region .
These quantities in turn allow inference of the number of particles within the acceleration region and hence the filling factor f – the ratio of the emitting volume to the volume that encompasses the emitting region ( s ) .
We obtain values of f that lie mostly between 0.1 and 1.0 ; the ( geometric ) mean value is f = 0.20 \times / \div 3.9 , somewhat less than , but nevertheless consistent with , unity .
Further , coupling information on the number of particles in the acceleration region with information on the total rate of acceleration of particles above a certain reference energy ( obtained from spatially-integrated hard X-ray data ) also allows inference of the specific acceleration rate ( electron s ^ { -1 } per ambient electron above the chosen reference energy ) .
We obtain a ( geometric ) mean value of the specific acceleration rate \eta ( 20 keV ) = ( 6.0 \times / \div 3.4 ) \times 10 ^ { -3 } electrons s ^ { -1 } per ambient electron ; this value has implications both for the global electrodynamics associated with replenishment of the acceleration region and for the nature of the particle acceleration process .