We derived the coronal magnetic field, plasma density, and temperature from the observation of polarization and intensity of radio thermal free-free emission using the Nobeyama Radioheliograph (NoRH) and extreme ultraviolet (EUV) observations. We observed a post-flare loop on the west limb 11 April 2013. The line-of-sight magnetic field was derived from the circularly polarized free-free emission observed by NoRH.The emission measure and temperature were derived from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO). The derived temperature was used to estimate the emission measure from the NoRH radio free-free emission observations. The derived density from NoRH was larger than that determined using AIA, which can be explained by the fact that the low temperature plasma is not within the temperature coverage of the AIA filters used in this study. We also discuss the other observation of the post-flare loops by the EUV Imager onboard the Solar Terrestrial Relations Observatory (STEREO), which can be used in future studies to reconstruct the coronal magnetic field strength. The derived plasma parameters and magnetic field were used to derive the plasma beta, which is a ratio between the magnetic pressure and the plasma pressure. The derived plasma beta is about 5.7 10 to 7.6 10 at the loop top region.

We estimated the accuracy of coronal magnetic fields derived from radio observations by comparing them to potential field calculations and the differential emission measure measurements using EUV observations. We derived line-of-sight components of the coronal magnetic field from polarization observations of the thermal bremsstrahlung in the NOAA active region 11150, observed around 3:00 UT on 2011 February 3 using the Nobeyama Radioheliograph at 17 GHz. Because the thermal bremsstrahlung intensity at 17 GHz includes both chromospheric and coronal components, we extracted only the coronal component by measuring the coronal emission measure in EUV observations. In addition, we derived only the radio polarization component of the corona by selecting the region of coronal loops and weak magnetic field strength in the chromosphere along the line of sight. The upper limits of the coronal longitudinal magnetic fields were determined as 100-210 G. We also calculated the coronal longitudinal magnetic fields from the potential field extrapolation using the photospheric magnetic field obtained from the Helioseismic and Magnetic Imager. However, the calculated potential fields were certainly smaller than the observed coronal longitudinal magnetic field. This discrepancy between the potential and the observed magnetic field strengths can be explained consistently by two reasons:(1) the underestimation of the coronal emission measure resulting from the limitation of the temperature range of the EUV observations, and (2) the underestimation of the coronal magnetic field resulting from the potential field assumption.

We investigate the upper chromosphere and the transition region of the sunspot umbra using the radio brightness temperature at 34 GHz (corresponding to 8.8-mm observations) as observed by the Nobeyama Radioheliograph (NoRH). Radio free-free emission in the longer millimeter range is generated around the transition region, and its brightness temperature yields the region's temperature and density distribution. We use the NoRH data at 34 GHz by applying the Steer-CLEAN image synthesis. These data and the analysis method enable us to investigate the chromospheric structures in the longer millimeter range with high spatial resolution and sufficient visibilities. We also perform simultaneous observations of one sunspot using the NoRH and the Nobeyama 45-m telescope operating at 115 GHz. We determine that 115-GHz emission mainly originates from the lower chromosphere while 34-GHz emission mainly originates from the upper chromosphere and transition region. These observational results are consistent with the radio emission characteristics estimated from the current atmospheric models of the chromosphere. On the other hand, the observed brightness temperature of the umbral region is almost the same as that of the quiet region. This result is inconsistent with the current sunspot models, which predict a considerably higher brightness