hanelyp wrote:I think you're confusing Coulombs and Volts. Coulombs are absolute. But I'm thinking in terms of volts, and electric field deriving from a difference in volts between 2 shell or grid levels.
The magrid has a potential higher than the trap grid. both magrid and trap grid have a potential much lower than the collector shell.
Consider what would happen if you had a hollow sphere with the outer wall at ground. The potential inside is uniform. Probably you would call it zero.
Now add a magrid at the center. What is the net charge on the magrid? Who cares? But it generates an electric field due to that charge. Since this is a conservative field, the magrid can be said to be at a different potential than the outer shell. If the field points towards the magrid, it will attract positive charges and repel negative charges, and the potential of the magrid will be negative with respect to the outer shell.
Also, regardless of the exact value of the charge on the magrid in this case, you DO know it is negative.
This remains true even if the outer shell is not at ground - if it is highly charged itself. Due to Gauss' Law, the potential inside an empty sphere is uniform regardless of the charge on the sphere, so a negative perturbation in the potential requires the presence of a negative charge.
So what happens if you stick an electron gun into this configuration and try to form a wiffleball?
Abject failure, that's what. A magrid at the bottom of a negative potential well in the MV range would leak electrons like a sieve.
Now consider the trap grid case. The magrid is only slightly more positive (in potential) than the extremely negative (compared to the outer shell) trap grid. But once again, if the magrid weren't there, the potential inside the trap grid would be uniform. Thus an absolute positive charge on the magrid is required to produce the upward perturbation in potential.
The only problem with the electrons now is that you have to get them to the electron gun through the trap grid, which is simple high-voltage electrical engineering. Once they're injected, they only see the field from the magrid and that's where they go.
What that translates to in coulombs is a messy calculation, and not needed to determine the electron and ion behavior.
It's not that messy a calculation. A spherically-symmetric ball of charge (or a reasonable approximation thereto) has the same effect outside it as an equal point charge at its center. All you have to do is integrate the field from the next shell out (trap grid or wall) up to the outer surface of the inner sphere to get the potential difference across the interval. Do it analytically and you can then reverse the equation, feed it the actual potential difference and obtain the total net charge existing within the inner spherical volume you integrated up to.