Asymptotics of physical solutions to the Lorentz-Dirac equation for planar motion in constant electromagnetic fields

摘要

We present a study of planar physical solutions to the Lorentz-Dirac equationin a constant electromagnetic field. In this case, we reduced the Lorentz-Diracequation to the one second order differential equation. We obtained theasymptotics of physical solutions to this equation at large proper times. Itturns out that, in the crossed constant uniform electromagnetic field withvanishing invariants, a charged particle goes to a universal regime at largetimes. We found the ratio of momentum components which tends to a constantdetermined only by the external field. This effect is essentially due to aradiation reaction. There is not such an effect for the Lorentz equation inthis field.