What's the figure-eight solution for charged particles? I've recently come across this term called "Figure-eight solution" of charged particles in EM fields, in the context of plasma physics. I'm aware of the helical orbit solution (drift due to electric field and rotation due to magnetic field) but I'm not sure what the figure-eight orbit is. Where can I read more about it?
I've googled this term to no avail, so could someone please explain what this solution is and/or provide references?
 A: This figure of eight motion arises when the charge is subjected to a plane electromagnetic wave with sufficient intensity as to accelerate the charge to relativistic speeds. You can find a derivation in Landau & Lifshitz "The Classical Theory of Fields".
This motion has only recently been unambiguously observed for electrons: "Experimental confirmation of electron figure-8 motion in a strong laser field".
The original orbit theory of an electron under the influence of a plane, elliptically polarized electromagnetic wave can be found in Classical Theory of the Scattering of Intense Laser Radiation
by Free Electrons, Sarachik & Schappert (1970)
A: I am presenting here a physical picture.
The figure of 8 motion is observed in electrons when they are interacting with a very high-intensity electromagnetic field. As you know that in the electromagnetic wave, the electric and magnetic fields are perpendicular to each other. Now the electron starts to oscillate in the electric field (F = eE). At a high electric field, the velocity of the electron reaches close to light velocity. At this velocity, the effect of the magnetic field becomes significant (F = evB). The magnetic field tries to oscillate the electron in the direction of electromagnetic wave propagation.
The combination of these two fields caused the figure of 8 motion. One may note here that the frequency of figure of 8 motion is double the frequency of electromagnetic radiation ($\omega$) because the velocity (v) and magnetic field (B) both are at frequency $\omega$.
