Quasimonoenergetic proton beams have long been anticipated in laser-driven ion acceleration, particularly via multispecies targets in radiation pressure and target normal sheath acceleration, yet experimental results are far from expectations, and the underlying cause remains elusive. Here we reveal that even under ideal conditions, only a power-law energy spectrum $d{\mathcal{N}}_p/d{\mathcal{E}}_p\propto {\mathcal{E}}_p^{-\eta }$, rather than a quasimonoenergetic one, is predicted by theory when full spatial dynamics are considered, where ${\mathcal{N}}_p$, ${\mathcal{E}}_p$, and $\eta$ represent the proton number, energy, and power-law index, respectively. Our theory and three-dimensional particle-in-cell simulations demonstrate that the spectral shape and index $\eta$ are independent of the specific acceleration mechanism, but are correlated with the target composition and laser focal spot profile. This provides a plausible explanation for the power-law spectra observed in experiments across a wide range of laser and plasma parameters. Possible paths to breaking the universality and achieving quasimonoenergetic proton beams are discussed.

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• Laser driven ion acceleration
• Laser-plasma interactions
• Plasma acceleration & new acceleration techniques
• Plasma instabilities
• Radiation pressure acceleration
• Particle-in-cell methods