Abstract：It is believed that solar flares are a result of release of free magnetic energy contained in electric currents (ECs) flowing in active regions (ARs). However, there are still debates whether the primary energy release and acceleration of electrons take place in coronal current sheets or in chromospheric footpoints of current-carrying magnetic flux tubes (loops).  

   We present results of an observational statistical study of relationship between hard X-ray (HXR; E_HXR≥50keV) footpoint sources detected by RHESSI and vertical photospheric ECs calculated using vector magnetograms obtained from the SDO/HMI data. A sample of more than 40 flares (from C3.0 to X3.1 class) observed on the solar disk by both instruments in 2010-2017 was analyzed. We discuss effects of sensitivity and angular resolution of RHESSI and SDO/HMI. In general, the results indicate that there is a link between the flare HXR footpoint sources and enhanced vertical ECs in the photosphere. However, the results do not support a concept of electron acceleration by the electric field excited in footpoints of current-carrying loops due to some (e.g. Rayleigh-Taylor) instabilities.

   Also, we present results of a detailed analysis of high-cadence 135-second SDO/HMI vector magnetograms for one confined flare, for which we found good time consistency between the dynamics of vertical ECs and flare energy release efficiency. We interpret the observational results within the tether-cutting magnetic reconnection in the highly-sheared low-lying loops above the polarity inversion line (PIL). Some analogies between the processes in the solar corona and the earth's magnetosphere are briefly discussed.