CRT electron gun In CRTs, how does the control grid determine the current of electrons when its voltage is very low compared to the anode? And shouldn't it control the velocity of electrons rather than the current intensity? Say we have a control grid of -20V and an anode of 500V, when we determine the voltage the electrons are subjected to we can just say that it's (-20+500)V and that their velocity was decreased but their numbers would stay the same so the light intensity when they hit the screen would be the same. So how come?
 A: Let's start with a simple case: A vacuum tube with a hot cathode, and a cold anode, no applied voltage. Every second N electrons evaporate from the cathode. Every second N electrons return to the cathode. This is called "dynamic equilibrium".
Next case to consider is a vacuum tube with a hot cathode and a cold anode, and an applied voltage V. Every second N electrons evaporate from the cathode. Every second X electrons are absorbed by he anode. Every second N-X electrons return to the cathode. N electrons per second is called "saturation current". The negative charge of the vacuum is called "space charge". If V is small, then current through the tube is small, for some reason. When V is increased then current through the tube increases, for some reason. It would be good if we knew the reason. Well it happens to be so that the only thing that changes in the tube when the voltage is increased is that the space charge decreases. So the space charge is the reason that that the current is not the saturation current, and the voltage has the effect of decreasing the space charge.
And now we can talk about the CRT: Putting some extra electrons onto the control grid is equivalent to increasing the space charge. If the control grid is close to the cathode, then many electrons can be put on the control grid by using just a small voltage. Like when the plates of a capacitor are close together, then a large amount of charge can be stored by a small voltage.
