Solar observations in the infrared domain can bring important clues on the response of the low solar atmosphere to primary energy released during flares. At present the infrared continuum has been detected at 30 THz (10 $mu$m) in only a few flares. In this work we present a detailed multi-frequency analysis of SOL2012-03-13, including observations at radio millimeter and sub-millimeter wavelengths, in hard X-rays (HXR), gamma-rays (GR), H-alpha, and white-light. HXR/GR spectral analysis shows that the event is a GR line flare and allows estimating the numbers of and energy contents in electrons, protons and alpha particles produced during the flare. The energy spectrum of the electrons producing the HXR/GR continuum is consistent with a broken power-law with an energy break at ~800 keV. It is shown that the high-energy part (above ~800 keV) of this distribution is responsible for the high-frequency radio emission (> 20 GHz) detected during the flare. By comparing the 30 THz emission expected from semi-empirical and time-independent models of the quiet and flare atmospheres, we find that most (~80%) of the observed 30 THz radiation can be attributed to thermal free-free emission of an optically-thin source. Using the F2 flare atmospheric model this thin source is found to be at temperatures T~8000 K and is located well above the minimum temperature region. We argue that the chromospheric heating, which results in 80% of the 30 THz excess radiation, can be due to energy deposition by non-thermal flare accelerated electrons, protons and alpha particles. The remaining 20% of the 30 THz excess emission is found to be radiated from an optically-thick atmospheric layer at T~5000 K, below the temperature minimum region, where direct heating by non-thermal particles is insufficient to account for the observed infrared radiation.
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