A Radiation back reaction in classical electrodynamics

[HomogenousCow]

I've been doing some research on the topic of radiation reaction force/self force in classical electrodynamics and although there are some discussions on the internet I would like direct answers to these following questions:

1. Is there a rigorous and universally accepted treatment of radiation reaction force in classical electrodynamics for point particles? If so what was the breakthrough that solved the issues plaguing the seminal works such as pre-acceleration and runaway solutions?
2. If we couple Maxwell's equations to a dynamical extended body, such as a charged fluid, do the resulting equations suffer from the typical issues encountered with point sources? And if not, does this treatment predict radiation reaction force that is physically reasonable?
3. Is classical electrodynamics coupled to fluid dynamics a mathematically sound theory? As in, are there results on the existence and uniqueness of solutions in this theory.

 

[Dale]

If so what was the breakthrough that solved the issues plaguing the seminal works such as pre-acceleration and runaway solutions?

There is no such breakthrough. Those issues remain unresolved.

If we couple Maxwell's equations to a dynamical extended body, such as a charged fluid, do the resulting equations suffer from the typical issues encountered with point sources? And if not, does this treatment predict radiation reaction force that is physically reasonable?

Extended bodies with charge densities that are everywhere finite are physically reasonable.

Is classical electrodynamics coupled to fluid dynamics a mathematically sound theory? As in, are there results on the existence and uniqueness of solutions in this theory.

I don’t know, but I am not aware of problems like those with classical point particles.

 

[jasonRF]

Is classical electrodynamics coupled to fluid dynamics a mathematically sound theory? As in, are there results on the existence and uniqueness of solutions in this theory.

I don't know if existence and uniqueness has been settled (I really doubt it), but a 30-second google search yielded some interesting hits like
https://www.jstor.org/stable/20209485
http://wrap.warwick.ac.uk/66955/
This is more in the realm of mathematics than physics, in that few physicists probably have the tools (or inclination) to make much progress on that front.

Even if those issues haven't been resolved, fluid models of plasmas have been pretty successful at describing physical phenomena. So have the more accurate kinetic models that can be used to derive fluid models by taking velocity-space moments.

jason

 

[vanhees71]

According to "numerical studies" the best we have on the classical level concerning the radiation-reaction problem is the Landau-Lifshitz approximation to the Lorentz-Abraham-Dirac equation. For a nice treatment, see

C. Nakhleh, The Lorentz-Dirac and Landau-Lifshitz equations from the perspective of
modern renormalization theory, Am. J. Phys 81, 180 (2013),
https://dx.doi.org/10.1119/1.4773292.
https://arxiv.org/abs/1207.1745

K. Lechner, Classical Electrodynamics, Springer International Publishing AG, Cham
(2018), https://doi.org/10.1007/978-3-319-91809-9

 

[Meir Achuz]

In his derivation, Lechner states on page 467, "Ultimately the Lorentz Dirac equation must be postulated."

 

[vanhees71]

But the LAD equation is not the solution! The Landau-Lifshitz approximation is much better. A quantum-Langevin approach (at least for the non-relativistic case) suggests that the real matter is a non-Markovian description on the classical level, which avoids all the problems of the LAD equation right away. For this, see

G. W. Ford, J. T. Lewis and R. F. O’Connell, Quantum
Langevin equation, Phys. Rev. A 37, 4419 (1988),
https://doi.org/10.1103/PhysRevA.37.4419

or

https://doi.org/10.1016/0375-9601(91)90054-C