Pre-acceleration from Landau-Lifshitz Series

Understand

The Landau-Lifshitz equation is considered as an approximation of the Abraham-Lorentz-Dirac equation.

• It is derived from the Abraham-Lorentz-Dirac equation by treating radiation reaction terms as a perturbation.
• However, while the Abraham-Lorentz-Dirac equation has pathological solutions of pre-acceleration and runaway, the Landau-Lifshitz equation and its finite higher order extensions are free of these problems.
• So it seems mysterious that the property of solutions of these two equations is so different.