Average Lorentz Self-Force From Electric Field Lines
  We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic transformations of electromagnetic fields and Thomson's construction [2]. We derive the average Lorentz self-force for a charged particle in arbitrary non-relativistic motion via averaging the fields at retarded time. 
Sandeep Aashish and Asrarul Haque
physics.class-ph