Synchrotron-cooled Plasma Distribution in the Outer Magnetosphere of a Neutron Star

The guiding center formalism is employed to analyze the motion of a charged relativistic particle in an inhomogeneous magnetic field subject to magnetic mirroring and energy loss due to cooling. The governing equation for the evolution of the magnetic moment is derived. An example representing a neutron star's (pulsar or magnetar) magnetosphere is presented to illustrate typical particle orbits. Notably, radiative losses are most pronounced near a trapped particle’s turning point. Depending on the initial particle’s pitch angle, energy loss can become catastrophic, resulting in the rapid migration of the particle into the loss cone and subsequent precipitation onto a neutron star. Conversely, particles with larger pitch angles remain temporarily trapped and form a gradually decaying “cooled-loss-cone” or “funnel” distribution, characterized by the maximum momentum space particle density being located at the edge of the loss cone. The size of the loss cone is energy dependent and scales as α_c ∝ γ^3/10. Synchrotron losses are strongest in a well-localized region of the magnetosphere, a few hundred to a thousand stellar radii under typical pulsar and magnetar conditions. This region is a plausible site for synchrotron radiation originating in the outer magnetosphere, and could also be responsible for nonpolar coherent pulsar emission, as well as weak fast radio bursts.