Oscillating Electron Beam potential between metal plates

[SunRay-dvsh]

Take the case where the electron-beam is oscillating between two parallel metal plates, there will be alternating potential developed between the plates as metal tries to negate all external electric fields.
My query is,
(1) How to calculate the potential developed and possible way to simulate it ?

(2) Will the potential developed be significant ?

 

[mfb]

Where and why do you expect any oscillation?

 

[SunRay-dvsh]

Where and why do you expect any oscillation?

It's an equation i have derived with time varying magnetic field. At this moment before journal publication i really can't say much but i have simulated the particle trace of electron on simulation software and it gave a perfect match. The electron traverses undulatory motion(like in an undulator) but in time varying magnetic field.
Please i need help with finding the potential developed by bunches of electrons, all in same phase oscillating up and down at same frequency(also moving forward but don't require that component) between the two ends of each metal plates !

 

[SunRay-dvsh]

Where and why do you expect any oscillation?

Thanks For the reply btw

 

[BvU]

Fair enough, but your account, nor the pictures, allow anyone to construct the situation you are trying to describe. So help the helpers help you if you can

 

[mfb]

Please i need help with finding the potential developed by bunches of electrons, all in same phase oscillating up and down at same frequency(also moving forward but don't require that component) between the two ends of each metal plates !

Retarded potentials should help, alternatively use the simulation software.

There is an electron beam shot between the two plates at some fixed point? The variable magnetic field is some external input? How does it vary in time, and does it vary in space? Why is there a charge on the metal plates? It is impossible to figure out what your experiment is if you don't describe it.

 

[SunRay-dvsh]

Retarded potentials should help, alternatively use the simulation software.

There is an electron beam shot between the two plates at some fixed point? The variable magnetic field is some external input? How does it vary in time, and does it vary in space? Why is there a charge on the metal plates? It is impossible to figure out what your experiment is if you don't describe it.

One can visualize the motion of electron like that of the dielectric material(which is basically electron mass in my case) oscillating between the two parallel plates at fixed frequency:

The kind of charge distribution in the plates will be like this due to induced electric field of the electrons:

The electrons are NOT touching the plates, the magnetic field is varying only in time and is externally applied. Just consider the electron motion in undulator with the electrons oscillating between the metal plates(like an undulator with two side walls)

 

[SunRay-dvsh]

Fair enough, but your account, nor the pictures, allow anyone to construct the situation you are trying to describe. So help the helpers help you if you can

True, will try to be more expressive then .