Bookmark 3 & 19. Motion of the electron in a uniform electric field of very high intensity (to see in the same picture the zitter motion and how the external field bends the trajectory of the CM) along the negative direction of the OX axis in Bookmark3 and OY axis in Bookmark19. We see the zitter motion of the CC (blue) and the motion of the CM (red). It is also depicted the CM spin , at different CM points choosing different angles with the direction of the initial CM velocity. Note the CM trajectory deviates towards -E due to the acceleration caused by the electric field, but the spin orientation does not change in the presence of an electric field.In Bookmark 19 we can see the acceleration of an electron initially at rest due to the uniform electric field.
S
CM
11. Electron in an oscillating electric field
11. Electron in an oscillating electric field
If in the above analysis we replace E by a function E(t) = E cos(ωt + ϕ) we analyze the interaction of the electron with an oscillating electric field of angular frequency ω and initial phase ϕ.
The time has to be replaced by the dimensionless time so that the above field is
The time has to be replaced by the dimensionless time so that the above field is
To obtain how the electric field affects to the CC and CM motion when we describe the particle in natural units, we have to use very high electric fields and a small value for the dimensionless parameter ω/ in units of , because the integration time corresponds to a value of π during a turn of the CC around the CM.
If the oscillating external electric field is of a Gigahertz frequency the parameter ω/ ≃ . For this value, the electric field during few turns of the CC, can be considered as a constant electric field and no visual effect can be appreciated. To appreciate the influence of the electric field at this scale we have to take a value of the parameter ω/ greater than this value.
ω
o
ω
o
If the oscillating external electric field is of a Gigahertz frequency
9
10
-1
s
ω
o
−12
10
ω
o