Can the Lorentz Oscillator Model be Modified to Include Radiation Force?

[hpjack]

Hi Guys,

I'm looking into the Lorentz model

Since the acceleration/de-acceleration of electron can cause radiation hence create force, can anyone tell me how to modify the above equation to include the term of radiation force?

Thanks.

jack

 

[vanhees71]

That's a delicate isssue. Have a look at Jackson, Classical Electrodynamics or Becker/Sauter under the keyword "radiation damping" or "radiation reaction".

 

[Jano L.]

Hi Guys,

I'm looking into the Lorentz model
View attachment 79181

Since the acceleration/de-acceleration of electron can cause radiation hence create force, can anyone tell me how to modify the above equation to include the term of radiation force?

Thanks.

jack

Approximately, force on extended charged object due to its acceleration is given by the result of the calculation first done by Lorentz (check his book Theory of electrons). However, it is only approximate and gives results in contradiction to the rest of physics when used verbatim.

So if you have extended electron, you can use the Lorentz-Abraham formula (or better yet, Landau-Lifshitz formula) with some ground, but learn its deficiencies (check Feynman's textbooks, Landau&Lifshitz Classical Theory of Fields).

The derivation of the Poynting theorem and the Larmor formula is invalid for point electrons, so there is no necessity and convincing reason to use the Lorentz-Abraham formula for them.

The equation above is a model of damped oscillation of electron. The damping is modeled by the last term $\gamma dy/dt$ and since there is no single reason for its presence, it is understood as a way to model the resulting motion even if we do not know the details of forces acting on the electron. That means if self-force is present, part of it may be already described by this term.

 

[vanhees71]

Another great book is: F. Rohrlich, Classical charged particles.

 

[Jano L.]

Another great book is: F. Rohrlich, Classical charged particles.

Some parts of the book discuss interesting topics and it is worth having a look, but author's views and support of procedures of questionable mathematical validity are not very convincing, in my opinion. Although the author was very self-confident in his papers and his book, I recommend taking it as one possible view on the problem, not as the work that solved it.