It is argued that the key task in understanding magnetic fields in the cosmos is to comprehend the origin of their order or coherence over large length scales in galaxies. Obtaining magnetic fields can be done in stars, whose lifetime is usually 1010 rotations, while galactic disks have approximately 20 to 50 rotations in their lifetime since the last major merger, which established the present day gaseous disk. Disorder in the galactic magnetic fields is injected on the disk time scale of about 30 million years, about a tenth of the rotation period, so after one half rotation already it should become completely disordered. Therefore whatever mechanism Nature is using, it must compete with such a short time scale, to keep order in its house. This is the focal quest.

Assuming that particles can be accelerated to high energies via diffusive shock acceleration process at the accretion shocks formed by the infalling flow toward the clusters of galaxies, we have calculated the expected spectrum of high-energy protons from the cosmological ensemble of the cluster accretion shocks. The model with Jokipii diffusion limit could explain the observed cosmic ray spectrum near 10 19eV with reasonable parameters and models if about 10-4 of the infalling kinetic energy can be injected into the intergalactic space as the high energy particles.