[en] A relativistically intense ultra-short pulse (∼10 femto seconds) laser pulse can produce large flux of X-rays through the interaction with electrons that are driven by its intense electromagnetic fields. In the case of the high-Z matter irradiation of intense laser, X-ray with long tail is generated through the complex processes, polarization and atomic process, although two main fast processes, the Larmor radiation and Bremsstrahlung, are among the most significant mechanisms for X-ray emission from short pulse laser irradiation on low-Z matter in the relativistic regime of intensity. We evaluate the power, energy spectrum, brilliance, polarization, and time structure of these ultra-short X-rays. We suggest a few methods that significantly enhance the power of Larmor X-rays. Because of its peakedness of energy spectrum of Larmor X-rays, the Larmor X-rays have important applications, light source of hollow atom X-ray Laser and ultra-fast spectroscopy. (author)