We propose a new hypothesis for the origin of the major part of non-solar h
adronic cosmic rays (CRs) at all energies: highly relativistic, narrowly co
llimated jets from the birth or collapse of neutron stars (NSs) in our Gala
xy accelerate ambient disk and halo matter to CR energies and disperse it i
n hot spots which they form when they stop in the Galactic halo. Such event
s are seen as cosmological gamma-ray bursts (GRBs) in other galaxies when t
heir beamed radiation happens to point towards Earth. This source of CRs is
located in the Galactic halo. It therefore explains the absence of the Gre
isen-Zatsepin-Kuz'min cutoff in the spectrum of the ultra-high energy CRs.
The position in energy of the "ankle" in the CR energy spectrum is shown to
arise in a natural way. Moreover, an origin of lower energy CRs in the Gal
actic halo naturally accounts for the high degree of isotropy of CRs around
100 TeV from airshower observations, and the small galactocentric gradient
of low-energy CRs derived from gamma-ray observations.