Q on Jackson. Lorentz force modification for radiation?

[Peeter]

Reading Jackson this morning, where it was stated that the Lorentz force equations:

$$\frac{dU^\alpha}{d\tau} = \frac{e}{mc} F^{\alpha\beta} U_\beta$$

are sufficient to describe the motion of a charged particle in an external field, neglecting the effects of radiation.

That radiation qualifer suprised me. What is the modification of the Lorentz force equation (or Lagrangian) that correctly models radiation too?

 

[Bob_for_short]

Isn't it given in Jackson book later on?

 

[Peeter]

Isn't it given in Jackson book later on?

If it is I wouldn't know yet. The qualification is made in passing, and there's no hint of what to look for. Does the corrected force law have a name that I could look for in the index?

 

[Count Iblis]

Jackson (or for that matter any other textbook) does not give a rigorous derivation; this was one of big problems of classical electromagnetism: How to take into account the interaction of a point charge with its ow electromagnetic field in a rigorous way?

The solution to this problem is given here:

http://arxiv.org/abs/0905.2391

 

[Bob_for_short]

If it is I wouldn't know yet. The qualification is made in passing, and there's no hint of what to look for. Does the corrected force law have a name that I could look for in the index?

Yes, there is a name, it is the Abraham-Lorentz force. Try Wikipedia.

 

[jtbell]

In my old 2nd edition of Jackson, the Abraham-Lorentz force is in chapter 17 which discusses radiation damping.

The question now arises as to how to include the reactive effects of radiation in the equations of motion for a charged particle. [...]

 

[Peeter]

thanks for the paper and the name.