Particle motion in neutron stars ultra-strong electromagnetic field: the influence of radiation reaction

As a follow-up to our previous work on particle acceleration simulation near neutron stars, in this paper, we discuss the impact of radiation reaction on test particles injected into their magnetosphere. We therefore neglect the interaction between particles through the electromagnetic field as well as gravitation. We integrate numerically the reduced Landau-Lifshitz equation for electrons and protons in the vacuum field of a rotating magnetic dipole based on analytical solutions in a constant electromagnetic field. These expressions are simple in a frame where the electric and magnetic field are parallel. Lorentz transforms are used to switch back and forth between this frame and the observer frame. We found that, though due solely to the Lorentz force, electrons reach Lorentz factors up to $\gamma=10^{14}$ and protons reach them up to $\gamma=10^{10.7}$. When radiation reaction is enabled, electrons reach energies up to $\gamma=10^{10.5}$ and protons reach energies up to $\gamma=10^{8.3}$. The second set of values are more realistic since the radiation reaction feedback is predominant within the magnetosphere. Moreover, as expected, symmetrical behaviours between the north and south hemispheres are highlighted, either with respect to the location around the neutron star or with respect to particles of opposite charge to mass ratio~$(q/m)$. The study of the influence of the magnetic dipolar moment inclination shows similar behaviours regardless of whether radiation reaction is enabled. Protons (respectively electrons) impact the surface of the neutron star less as the inclination angle increases (decreases for electrons), while if the rotation and magnetic axes are aligned, all the protons impact the neutron star, and all the electrons impact the surface if the rotation and magnetic axes are anti-aligned.