In the paper the spectral temporal evolution of a steeply rising submillimeter (THz) burst occurred on 2003 November 2 was investigated in detail for the first time. Observations show that the flux density of the THz spectrum increased steeply with frequency above 200GHz. Their average rising rates reached a value of 235 sfu/GHz (corresponding spectral index α of 4.8) during the burst. The flux densities reached about 4,000 and 70,000 sfu at 212 and 405 GHz at maximum phase, respectively. The emissions at 405 GHz maintained continuous high level that they exceed largely the peak values of the microwave (MW) spectra during the main phase. Our studies suggest that only energetic electrons with a low-energy cutoff of ∼1 MeV and number density of ∼10 6 -10 8 cm −3 can produce such strong and steeply rising THz component via gyrosynchrotron (GS) radiation based on numerical simulations of burst spectra in the nonuniform magnetic field case. The electron number density N, derived from our numerical fits to the THz temporal evolution spectra, increased substantially from 8 × 10 6 to 4 × 10 8 cm −3 , i.e., N value increased 50 times during the rise phase. During the decay phase it decreased to 7 × 10 7 cm −3 , i.e., decreased about five times from the maximum phase. The total electron number decreased an order of magnitude from the maximum phase to the decay phase. Nevertheless the variation amplitude of N is only about one time in the MW emission source during this burst, and the total electron number did not decrease but increased by about 20% during the decay phase. Interestingly, we find that the THz source radius decreased by about 24% while the MW source one, on the contrary, increased by 28% during the decay phase.

In the paper we investigate three novel rising submillimeter (THz) bursts occurred sequentially in a super-Active Region NOAA 10486. The average rising rate of the flux den- while it only requires a low-energy cutoff of 30 keV for the two slowly rising THz bursts, via gyrosynchrotron (GS) radiation based on our numerical simulations of burst spectra in the magnetic dipole field case. The electron density variation is much larger in the THz source than that in microwave (MW) one. It is interesting that the THz source radius decreased by 20-50% during the decay phase for the three events, but the MW one increased by 28% for the 2003 November 2 event. In the paper we will present a calculation formula of energy released by ultrarelativistic electrons, accounting the relativistic correction for the first time.We find that the energy released by energetic electrons in the THz source exceeds that in microwave one due to the strong GS radiation loss at THz range, although the modeled THz source area is 3-4 orders smaller than the modeled MW one. The total energies released by energetic electrons via the GS radiation in radio sources are estimated, respectively, to be 5.2 × 10 33 , 3.9 × 10 33 and 3.7 × 10 32 erg for the October 28, November 2 and 4 bursts, which are 131, 76 and 4 times as large as the thermal energies of 2.9 × 10 31 , 2.1 × 10 31 and 5.2 × 10 31 erg estimated from the soft x-ray GOES observations.