A still unsolved mystery is related the plot showing the flux of Cosmic Rays as a function of energy. We have experimental evidence of cosmic rays carrying energies up to 10²⁰ eV .

The enigma is:

WHAT KIND OF ASTROPHYSICAL SOURCE CAN PROVIDE SUCH ENERGY TO A SINGLE PARTICLE?

It is nice to remark that we can perform a simple physical consideration in order to discover possible candidates. We can take into account two parameters defining astrophysical sources:

1. The order of magnitude of their spatial dimension R,
2. The order of magnitude of their magnetic field B.

Having in our hands such information we can easily check if an astrophysical environment is a possible source of extremely high energy cosmic rays. The basis of our reasoning relies on the magnetic force and its ability to confine charged particles.

THE IDEA IS VERY SIMPLE:

considering the spatial dimension of an astrophysical object and its magnetic field we can compute the maximum value of the momentum of a particle trapped in its magnetic field:

P max = R q B.

If the momentum of the particle will exceed this quantity, the radius of its trajectory will get bigger than the astrophysical object, meaning that the particle will escape the object loosing the chance to be further accelerated. (!) For relativistic particles momentum = energy, so finding the maximum momentum we also find the maximum energy. (!)