Optimized ion spectra for ultra-uniform and high-efficiency heat transfer into dense matter

Achieving ultra-uniform and high-efficiency heat transfer into dense matter using energetic ion beams has remained a long-standing challenge due to the strong energy dependence of ion stopping power. Here, we introduce a generalizable computational framework for determining the optimal ion energy spectrum required to achieve highly uniform and efficient heat transfer into solid-density samples. Using Monte Carlo simulations, we evaluate stopping-power profiles for monoenergetic ion beams and apply a non-negative least-squares method to inversely reconstruct the optimal spectrum. As a case study, we apply this framework to carbon ions transferring heat into a 1-cm-thick solid-density aluminum sample. Our results reveal that a super-exponential energy distribution peaking near 1 GeV achieves over 99% heat transfer efficiency with exceptional spatial uniformity, while even a simpler spectrum with a dominant 1 GeV peak maintains ≈95% efficiency. This framework provides a practical tool for engineering ion-beam-driven heat transfer processes in advanced material processing, nuclear technologies, and other applications requiring precise thermal control.