What Jets Are Made Of: The Energy Budget of Proton Loading in Relativistic Outflows

This paper addresses a single accounting question in the physics of relativistic jets: how much heavier the energy bill for a jet becomes if charge neutrality is supplied by protons rather than by positrons, for a fixed observed synchrotron output. Using proton loadings from zero (a pure pair plasma) to one hundred protons per radiating electron, at a representative mean electron Lorentz factor of one hundred, the calculation derives new bounds and budgets from standard synchrotron and special-relativistic relations, with every number produced by the deposited compute script. The headline results are: factor k1 = 19.4, factor k10 = 185, factor k100 = 1.84e+03. One proton per electron already multiplies the energy per radiating particle by roughly an order of magnitude at the stated electron energy, because a single proton outweighs the energy of a mildly relativistic electron many times over. The study is a computation from stated assumptions and published inputs; it is simulated, not measured, and its conclusions are stated at the precision those inputs support.