On trapped particle motion in a strong magnetic field

Neutron stars and magnetars possess extremely strong magnetic fields, so that radiative cooling of particles in their magnetospheres can be short compared to a plasma dynamical time. The magnetospheres are observed to produce strong flares, possibly due to reconnection, which is a source of high-energy particles. How does the particle distribution change as these particles propagate in the magnetospheric `magnetic bottle'? Here we derive the equations that describe the motion of a relativistic `larmor particle' in a straight magnetic bottle subject to synchrotron energy loss. This result can be important for studies of a plasma around neutron stars and magnetars.