Self force on an accelerating electron

[Boltzmann2012]

In Feynman lectures vol 2, chap 28, it is given that for an electron at rest, the net self force exerted on itself is zero(due to repulsions etc.). But when accelerated, owing to the retardation of the electromagnetic fields, there would be a net self force. A series expansion(with unknown coefficients )has been provided. Can we actually calculate the self force? Does it ever exist?

 

[vanhees71]

Yes, it exists. This is a major problem for high-energy accelerators for electrons. There you need to use linear accelerators since in ring accelerators you loose too much energy in synchrotron radiation. On the other hand synchrotron radiation itself is also an interesting light source that can be used for many applications in material sciences, chemestry, and biology.

The theoretical issue is not completely solved, even today. For a very detailed recent review on this matter, have a look at

Fritz Rohrlich, Classical Charged Particles, World Scientific 2007

 

[Boltzmann2012]

Does that mean the electromagnetism is not complete? Or is this outside the domain?

 

[chrisbaird]

...

The theoretical issue is not completely solved, even today. For a very detailed recent review on this matter, have a look at

Fritz Rohrlich, Classical Charged Particles, World Scientific 2007

There are a lot of problems that arise when using point particles or infinitely thin current sheets, but these are problems with using unrealistic mathematical idealizations in order to describe charges or currents, not problems with Maxwell's equations. In this sense, classical electromagnetism is complete (within the macroscopic realm where it is valid).

Since the self-force only arises under accelerations, it is not a self-force in an absolute sense. Visualizing it as a "self-force" may even be misleading. An accelerating charge emits radiation and loses some energy in the process, just like a gun recoils when it shoots off a bullet, to satisfy conservation of momentum and energy (traveling electromagnetic waves carry both momentum and energy). So it is more of an interaction of a charge with the fields than with itself.

 

[Boltzmann2012]

Thank you chrisbaird. How is, exactly, an electron imagined to be? Is it a charged sphere or what is its geometry? If we have to discuss about theself force then we have to assume the electron to be a spherical surface distribution of charge. But another question, doesn't the electron undergo Lorentz contraction while accelerating?

 

[Dickfore]

Does that mean the electromagnetism is not complete? Or is this outside the domain?

Yes, it does. According to relativity, all "elementary" particles must be point-like. Otherwise, as you pointed out, it would have to have "internal" degrees of freedom to account for the finite time of propagation of a deformation from one end to the other. But, point charged particles create electric fields that would contain infinite energy. This is a paradox in Classical Electrodynamics, and is addressed through Renormalization in Quantum Field Theories.

 

[mfb]

Is it a charged sphere or what is its geometry?

If you want a model for its "shape", the best one is probably a point. However, keep in mind that this point is not classical, it is "distributed" according to its wave function. If you want a better model, look at quantum field theory.

 

[chrisbaird]

Thank you for helping to clarify. I meant that Maxwell's equations are complete on the macroscopic level. Asking "What is the shape of an electron according to classical electromagnetics?" is a nonsensical question because classical electromagnetics only describes macroscopic charges (it's like asking what is the shape of the cheese contained in rainbows). An electron is too small to be addressed by Maxwell's equations. You have to go to quantum theory to talk about elementary particles. When we talk about "point particles" in classical electromagnetic, we mean spheres of charge that are small enough compared to the rest of the system that they look like points, but big enough and containing enough charges (millions) to be considered classical.

 

[Boltzmann2012]

To compute the self force, i assume we must take the electron to be a charged sphere.

 

[Dickfore]

No, you can still use a point particle, and use Abraham-Lorentz force.

 

[Boltzmann2012]

Is this one of the reformulations of electrodynamics? Like Feynman-wheeler and bopp?
Thanks for the link and reply.

Boltzmann

 

[Dickfore]

You may look up Wheeler-Feynman absorber theory. As for bopp, I don't know what it stands for.

 

[Boltzmann2012]

By Bopp I mean the field theory developed by him , which is in a way a modification of maxwell electromagnetism.It was also mentioned briefly in Feynman vol2

Can you suggest any references for an introduction to Qft?

Boltzmann.

 

[Dickfore]

A. Zee, QFT in a nutshell