Ultra-high energy cosmic rays from white dwarf pulsars and the Hillas criterion

The sources of ultra-high-energy cosmic rays ($E\gtrsim10^{19}$ eV) is still an open question in astroparticle physics and in the last years some efforts were made to understand its origin. In this work we consider white dwarf pulsars (WDPs) as possible sources of these ultra energetic particles. If some Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) are considered as white dwarf pulsars, these sources can achieve large electromagnetic potentials on its surface and possibly accelerate particle almost of speed of light and with energies $E \sim 10^{20-21}$ eV. We show that the new scale of star surface magnetic field and size of SGRs/AXPs as very magnetized white dwarfs are well described in the Hillas diagram together with the AR Sorpii and AE Aquarii white dwarf pulsars recently found. SGRs/AXPs described as magnetars are much above the Hillas line and out of it is expected for normal neutron star pulsars.