Abstract
The laser-ion acceleration from the ultra-short and ultra-intense laser-matter interactions attracts more and more interest nowadays. When a laser pulse interacts with a target, relativistic electrons are generated in a period of few femtoseconds and driven away by the ponderomotive force, then a huge charge-separation field forms. In general cases, the ion acceleration is determined by this charge-separation field and the scale length of the plasma density. A general time-dependent solution is obtained to describe laser-plasma isothermal expansions into a vacuum, which is the fundamental theory of the laser-ion acceleration. It is adequate for non-quasi-neutral plasmas and different types of the scale length of the density gradient. The previous solutions are some special cases of our general solution. It is found that there exist both a compression layer of the ion velocity distribution and a potential well for some initial conditions. However, many unaccounted idiographic solutions, which may be used to reveal new mechanisms of ion acceleration, may be deduced from our general solutions.
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