  We propose a new hypothesis for the origin of the major part of non-solar
hadronic cosmic rays (CRs) at all energies: highly relativistic, narrowly
collimated jets from the birth or collapse of neutron stars (NSs) in our Galaxy
accelerate ambient disk and halo matter to CR energies and disperse it in hot
spots which they form when they stop in the Galactic halo. Such events are seen
as cosmological gamma-ray bursts (GRBs) in other galaxies when their beamed
radiation happens to point towards Earth. This source of CRs is located in the
Galactic halo. It therefore explains the absence of the
Greisen-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 Galactic
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.
