Figure 1 shows the relationship between source size and magnetic field that would be given by an equality in relation (3) for a particle of energy 100 EeV/($Z\beta_{acc})$. For comparison I have marked rough coordinates for some energetic phenomena that are thought likely to produce cosmic rays in some form. By the arguments given, only points above the line are viable candidates to produce 100 EeV CRs. This excludes supernova remnants or winds from starburst galaxies, for example. They simply do not have the combined size and magnetic field to produce UHECRs.

There are further basic filters that must be applied to phenomena passing this first test, starting with limitations from energy losses within the accelerator. In particular the energy loss times must obviously exceed the maximum of the acceleration time and the escape time from the accelerator. The two energy loss processes that most commonly limit acceleration to the highest energies are synchrotron emission and photon scattering. Inverse Compton scattering (elastic photon scattering) looks much like synchrotron emission, so is usually included in that context. Synchrotron/Compton energy losses scale as $E^2$, so become smoothly more important as the energy increases. The energy loss rate from inelastic collisions rises sharply 