The critical manifold of the Lorentz-Dirac equation
Zentrum Mathematik and Physik Department
TU München, D-80290 München, Germany
Corresponding author: firstname.lastname@example.org
Accepted: 11 February 2000
We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena. The physical solutions of the Lorentz-Dirac equation lie on the critical surface. The critical surface is repelling, i.e. any slight deviation from it is amplified and as a result the solution runs away to infinity. On the other hand, Dirac's asymptotic condition (acceleration vanishes for long times) forces the solution to be on the critical manifold. The critical surface can be determined perturbatively. Thereby one obtains an effective second-order equation, which we apply to various cases, in particular to the motion of an electron in a Penning trap.
PACS: 03.50.De – Classical electromagnetism, Maxwell equations / 41.20.-q – Applied classical electromagnetism
© EDP Sciences, 2000