Calculated proton spectra under different assumptions. Left panel: proton spectra at the radical distance r = 10 pc from the hypothetical CR source with various injection spectral indices, in which s = 1.0 (dashed line), 2.0 (solid line), 3.0 (dotted line), and 4.0 (dash-dotted line), assuming a diffusion coefficient parameter χ = 1.0. Right panel: proton spectra with injection spectral index s = 2.0 under various assumptions of diffusion coefficients (solid lines for χ = 1.0, dashed lines for χ = 0.1, and dotted lines for χ = 0.01) at different radial distances, where r = 1 pc (red), 10pc (black), or 100 pc (blue). In both panels, Q∕d² = 1 × 10³⁸ erg s⁻¹ kpc⁻² and n = 1 cm⁻³ are assumed, and the gray lines represents the fit of the CR proton intensity from Phan et al. (2018) based on the measured fluxes of local CRs reported by Voyager 1 (Cummings et al. 2016) and AMS-02 (Aguilar et al. 2015a).