Blazar Jet Particle Energies Against the Hillas Limit and the Critical Shear

Blazar jets are among the few environments whose observed variability, field strength, and beaming place them near the Hillas requirement for the highest-energy cosmic rays, and they are tested here against both that requirement and the critical shear of the density bound. For a comoving field of 0.1 gauss in a region 3e14 metres across, boosted by a Doppler factor of ten, the observed-frame proton maximum is 8.994e+18 eV; at one gauss it reaches 8.994e+19 eV, and at a hundredth of a gauss only 8.994e+17 eV. The transverse shear across a jet, estimated generously, is 2.998e-08 per second, below the critical shear of 8.559e+32 per second by a margin of 2.855e+40. Blazar candidacy therefore stands or falls on field strength and energetics, where the real difficulties lie, and not on the shear bound, which excludes nothing. Simulated and computed from stated assumptions; not a measurement.