Electrostatic fields can be used in some " particle accelerator "

In this kind od particle accelerators usually it is known the potential of different parts of the system.

Then I calculate the electric charges by using inverse matrix.

with electric charges in every point I can calculate the electric potential at any point.

With such approach I obtained different charge density but the same potential in metal plates, but I do not know if it is possible.

Do you use another method to calculate electric potential at any point?

> Well, the charge distributes at the surface such that the electric field at the surface has no component parallel to the surface, but only vertical components; otherwise a current flows until such a distribution is achieved

I agree, but in the presence of external fields, perhaps the charges distributes in non uniform manner in order to have the same potential and all electric field lines perpendicular to the surface.

I made a simple finite element code that calculates the charge distribution and I wondered because I obtained a non uniform charge distribution in the metal plate, perhaps due it is non uniform or perhaps due low resolution.

Perhaps I should increase the speed and resolution by making a multithreaded code or using the graphics card

Today I measured the field by introduction of a small metal plate that I connected to an oscilloscope, but I obtained low voltage levels, perhaps due the 5-7pF load of the scope probe. What method or sensor do you recommend to measure the electric potential?

Thank you very much, that is very useful for my.

What do you recommend to calculate the potential at any point?

Option-1: Calculate charges through matrix inverse and then calculate voltage at any point

Option-2 Through using V=sum(Vi/distance(i))

If you have a method to measure the field, it would be useful

Thank you Christian, I will look for it.

I have added following method to my contribution list to measure the field that can be used to check simulation results:

"AN ELECTROSTATIC AND SLOW ELECTRIC FIELD MEASUREMENT METHOD "