In our last experiments I looked into how the different electrostatic parameters relate. There is one more aspect we did not explore that shapes the fields within the system. Namely the electron guns that inject electrons into the system. The key characteristic is that the electron guns are at ground potential. That will "compress" the electric potential gradient between the gun and the system.
Where should the guns be placed and how far? There are many options. Our guestimate here is to place them at faces, one coil radius away. Lets calculate a simulation with the following parameters: radius R=0.15m, coil thickness 0.07m, coil spacing 0.01m. Lets simulate the electron guns as small spheres placed at all 6 faces (the sphere's edge is actually close to the "one coil radius off the face" spot).
Lets put a sphere of uniform charge in the middle of the system and see how the fields shape up:
The electric potential
The electric field magnitude
The electric field with logarithmic magnitude
The electric field lines
The electric charge distribution (red means more positive charge, blue more negative charge, green less positive/negative charge)
Lets see how the potential well and electron acceleration from the electron gun towards the system relate to the space charge in the middle.
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