Laser-driven ions have compelling properties and their potential use for medical applications has attracted a huge global interest. One of the major challenges of these applications is generating beams of the required energies. To date, there has been no systematic study of the effect of laser intensity on the generation of laser-driven ions from ultrathin foils during relativistic transparency. Here we present a scaling for ion energies with respect to the on-target laser intensity and in considering target thickness we find an optimum thickness closely related to the experimentally observed relativistic transparency. A steep linear scaling with the normalized laser amplitude a0 has been measured and verified with PIC simulations. In contrast to TNSA, this scaling is much steeper and has been measured for ions with Z > 1. Following our results, ion energies exceeding 100MeV/amu are already accessible with currently available laser systems enabling realization of numerous advanced applications
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