Super-luminous ionization front achieved by using axicon as focus lens is proposed to improve the transition-Cherenkov radiation of terahertz emitted from a femtosecond laser filament in air. Benefitted from the better coherent superposition of radiation electric field generated by dipole-like electron current behind the ionization front, the terahertz radiation in far zone is enhanced by one order when the velocity of ionization front exceeds the light speed. Moreover, the radiation spectrum extends toward high frequency and covers the entire terahertz gap.
