Lightning in Cosmic Ray Sources Shapes Their Spectra

The Loaded Layer-Cake Model provides a quantitative framework for understanding cosmic ray spectra through time-dependent acceleration, diffusion, and spallation processes within supernova shocks, wind shock shells, and OB-Superbubble regions. After integration, the model yields a series of mathematical expressions, which are applied to AMS-02 cosmic ray data to provide fits. In the interaction zone, a Kolmogorov spectrum of magnetic field irregularities shapes the rigidity-dependent variation in cosmic ray spectra, resulting in a local spectral slope change of $-1/3$. In the bubble zone, lightning-induced magnetic wave-fields excited by electric discharges influence the spectra, leading to a slope change of $-5/3$. Additionally, at rigidities greater than $135~\mathrm{GV}$, a global fit shows a common spectral slope of $-2.65 \pm 0.02$ for primaries, depicting behavior of the acceleration zone. The model accommodates AMS-02 data for $ Z = 1-14$ and $Z = 26$ elements and has been extended to nickel. Within the framework of the model, the fit coefficients provide a foundation for interpreting cosmic ray behavior across the entire spectrum of each element. Fitting results for the expanded dataset demonstrate that the spectral slopes capture the induced variations. Nonetheless, challenges with the current model, such as parameter degeneracy, are analyzed and discussed. To address these limitations, future refinements are proposed to improve the model’s accuracy and its ability to characterize cosmic ray propagation and interactions. Furthermore, a plausible OB association, Scorpio -- Centaurus is discussed as a source.