With the development of laser technology, laser-driven proton acceleration provides a new method for proton tumor therapy. However, it has not been applied in practice because of the wide and decreasing energy spectrum of laser-accelerated proton beams. In this paper, we propose an analytical model to reconstruct the spread-out Bragg peak (SOBP) using laser-accelerated proton beams. Firstly, we present a modified weighting formula for protons of different energies. Secondly, a theoretical model for the reconstruction of SOBPs with laser-accelerated proton beams has been built. It can quickly calculate the number of laser shots needed for each energy interval of the laser-accelerated protons. Finally, we show the 2D reconstruction results of SOBPs for laser-accelerated proton beams and the ideal situation. The final results show that our analytical model can give an SOBP reconstruction scheme that can be used for actual tumor therapy.
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