Investigation of the particle-particle interaction effects in the cosmic Zevatron based on cyclotron auto-resonance by particle-in-cell simulations

Cyclotron autoresonance acceleration has been recently advanced as a potential mechanism for accelerating nuclei to ZeV energies (1 ZeV = $10^{21}$ eV). All results have been based on single- and many-particle calculations employing analytic solutions to the relativistic equations of motion in the combined magnetic and radiation fields, excluding effects related to the particle-particle interactions. Here, results from many-particle calculations and Particle-In-Cell (PIC) simulations, are presented which lend support to the single-particle investigations. Each single-particle result is found to lie well within one standard deviation about the ensemble average obtained from the corresponding many-particle calculation. The PIC simulations show that, even for number densities far exceeding those employed in the non-interacting case, the energy gain drops markedly due to the particle-particle interactions, over the first $\sim 8~ mm$ of the acceleration length. Together with the substantial attenuation, this finding supports the conclusion that the particle-particle interaction effects can be negligibly small over acceleration lengths of typically many kilometers.