Spark Gap Realization
This circuit varies the electric potential in the space within and around the steel pipe. It does so by varying the voltage, and thus the surface charge density, on the pipe.
A single conductor in free space has some amount of capacitance. A lenth of pipe is a conductor in free space. Therefore, it has some amount of capacitance.
Q = CV
Charge equals capacitance multiplied by voltage.
The quantity of charge on the pipe is proportional to the voltage on the pipe, when the voltage is measured with respect to something that is neutrally charged, such as the earth.
The surface charge density on the pipe is proportional to the quantity of charge on the pipe.
The electric potential in the volume of space within and around the pipe, is proportional to the surface charge density.
Therefore, the electric potential is proportional to the voltage.
By varying the voltage with respect to time, we vary the magnitude of the electric potential.
It is important that the electric potential remain negative at all times. The pipe is always charged negatively, just more and less so.
The two resistors form a voltage divider. The voltage on the pipe is approximately -3.82 kV, which is a 6 kV difference from the -10 kV rail.
This difference in voltage causes the spark gap to fire.
As soon as the spark gap begins arcing, a short circuit exists between the pipe and the -10 kV rail, so the voltage on the pipe drops to -10 kV.
Now the voltage on the pipe is the same as the voltage on the other side of the spark gap, so no difference in voltage exists between them. Therefore, the spark gap extinguishes itself.
Once the spark gap extinguishes, the voltage on the pipe returns to approximately -3.82 kV. This is a 6 kV difference in voltage between the pipe and the -10 kV rail. Thus, the spark gap fires again, and the cycle repeats.
