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The energetics, spectrum, and composition of cosmic rays with energies belowabout $10^{15}$ eV are fairly well explained by models involving supernovashocks. In contrast, no widely accepted theory exists for the origin ofultra-high energy cosmic rays (UHECRs), which have energies above $10^{15}$ eV.Instead of proposing a specific model, here we place strong constraints on anymodel of UHECRs involving isolated neutron stars (no companions). We considerthe total power requirements and show that the only viable power sourceassociated with isolated neutron stars is rotation. Mechanisms based onaccretion from the interstellar medium fall short of the necessary powerdespite the most optimistic assumptions. Power considerations also demonstratethat not enough rotational energy is tapped by a "propeller"-like accelerationof interstellar matter. The most promising source of energy is rotationalspindown via magnetic braking. We examine microphysical energy loss processesnear magnetized neutron stars and conclude that the most likely site foryielding UHECRs from isolated neutron stars is near or beyond the lightcylinder.Comment: 12 pages, LaTex (aaspp4.sty), 1 figure, appears here as published in  The Astrophysical Journal; compared to previous version, this has minor  writing changes, numerical estimates slightly changed in Sections 3.1, 3.2,  4.3.3, revision of numbers in Section 4.3.

Constraints on the Production of Ultra–High‐Energy Cosmic Rays by Isolated Neutron Stars