Time-dependent energetic laser-ion acceleration by strong charge   separation field
  The laser-ion acceleration in the ultra-short and ultra-intense laser-matter interactions attracts more and more interest nowadays. Since electrons gain relativistic energy from laser pulse in a period of several femtoseconds and driven away by the ponderomotive force of laser pulse, a huge charge-separation field pulse is generated. In general cases, the ion acceleration is determined by this charge-separation field. A novel general time-dependent solution for laser-plasma isothermal expansions into a vacuum with different types of the scale length of the density gradient which correspond to different charge separation forms is obtained. The previous solutions are some special cases of our general solution. A series of new solutions have been proposed and may be used to predict new mechanisms of ion acceleration. However, many unaccounted idiographic solutions that may be used to reveal new acceleration mode of ions such as shock wave acceleration, may be deduced from our general solutions. 
Yongsheng Huang, Yuanjie Bi, Naiyan Wang, Xiuzhang Tang, Zhe Gao