The Origin of Ultra-High-Energy Cosmic Rays

A.M. Hillas

• The existence of cosmic rays with energies up to \(10^{20}\) eV casts doubt on the most popular shock-wave process for accelerating particles to ultra-relativistic energies.
• Origin Problems
• SIZE OF ACCELERATING REGION The Larmor radius of a relativistic particle of charge Ze in a magnetic field BI'G (strictly the component of B normal to the particle's velocity) is \(rL = 1.08 E_{15}/ZB_{\mu G}\) pc, where \(E_{15}\) is the particle's energy in units of \(10^{15} eV\), and \(B_{\mu G}\) is in microgauss. Clearly, in gradual modes of acceleration, where the particle makes many irregular loops in the field while gaining energy, the size L of the essential part of the accelerating region containing the field must be much greater than 2 rL '" 2E 1 5/BI'G' In fact, a characteristic velocity f3c of scattering centers is of vital importance, and it turns out (Section 3) that L has to be larger than 2rJf3, so BI'GLpc > 2EI 5 /Zf3, 1. where Lpc is in parsecs. This limitation arises also in one-shot acceleration schemes, where an emf '" LvB/c (cgs) arises from the motion of a conductor (speed v = f3c) in a magnetic field and may be partly available for particle acceleration (L may be the diameter of a rotating neutron star, for instance).