The compactnesses of proton processes for a δ-function proton injection as a function of the energy γ₀. Full line is for proton synchrotron, dashed line for photopair, and dotted line for photopion. For this process the sum of photon and electron injection resulting from neutral and charged pion decay is plotted. The other parameters are R = 3 × 10¹⁶ cm, B = 1 G, ℓ_p = 0.4, and t_p,esc = t_cr.