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(Abridged) Following particle trajectories in the intense electromagneticfield of a neutron star is prohibited by the large ratio between the cyclotronfrequency $\omega_{\rm B}$ and the stellar rotation frequency $\Omega$. Nofully kinetic simulations on a macroscopic scale and with realistic fieldstrengths have been performed so far due to the huge computational cost impliedby this enormous scale of separation. In this paper, we derive new expressionsfor the particle velocity subject to strong radiation reaction that areintended to be more accurate than the current state-of-the-art expression inthe radiation reaction limit regime, the so-called Aristotelian regime. Weshortened the timescale hierarchy by solving the particle equation of motion inthe radiation reaction regime, where the Lorentz force is always andimmediately balanced by the radiative drag, and including a friction notnecessarily opposite to the velocity vector, as derived in the Landau-Lifshitzapproximation. Starting from the reduced Landau-Lifshitz equation (i.e.neglecting the field time derivatives), we found expressions for the velocitydepending only on the local electromagnetic field configuration and on a newparameter related to the field strength that controls the strength of theradiative damping. The new velocity expressions produce results similar inaccuracy to the radiation reaction limit approximation. We therefore do notexpect this new method to improve the accuracy of neutron star magnetospheresimulations. The radiation reaction limit is a simple but accurate, robust, andefficient way to follow ultra-relativistic particles in a strongelectromagnetic field.

A new radiation reaction approximation for particle dynamics in the strong field regime