The energy of positive ions accelerated in laser-matter interaction experiments can be significantly increased by providing a plurality of laser pulses, e.g., through the process of splitting the incoming laser pulse, to form multiple laser-matter interaction stages. From a thermodynamic point of view, the splitting procedure can be viewed as an effective way of increasing the efficiency of energy transfer from the laser light to positive ions, which energy peaks for processes having the least amount of entropy gain. A 100% increase in the energy efficiency is achieved for a six-stage laser positive ion accelerator compared to a single-stage laser positive ion accelerator.