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I'm relatively lay in astrophysics. Could the origin not be galactic magnetic field lines between Earth and the galactic nucleus? Like the magnetic mirror between Earth and the Sun but much larger.

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To our best understanding, particles of such high energy do not originate in our own galaxy. We don't have a good understanding of what exact process might be putting this much energy into a single particle, but the commonly accepted acceleration mechanisms of, eg., supernovae don't reach anywhere near these energies.

GP also said "nearby source (in astrophysical terms)" which in this case is code for "could be over 100 million light years".

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