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I'm a little unclear about the charge balance aspect of an electron gun. Referring to this diagram (and some others I've seen) Referring to this diagram and similar diagrams I've seen, what I don't get is wouldn't the target of the electrons have to be connected to the positive anode so that the electrons fired at a target can be recycled if the electron gun is needs to operate continuously? Is the target generally placed on the anode opening so it's connected to the positive?

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This is an Electrical Engineering question. The target is usually not in the hole (opening) of the anode. This is because, first, the hole is small. Second, you often want to be able to manipulate the electron beam, like what people do in the CRT TV. So the target is usually at the right end of your diagram, where your blue arrow points to.

The target is usually connected to the anode so its potential is equal to the anode. You can either connect the anode (and your target) or the cathode to ground. In a microwave oven, the anode of the magnetron (a kind of vacuum tube with anode, cathode) is grounded. In a TV's CRT, the anode is at high positive voltage and other component (maybe the cathode) is grounded.

This diagram might make it clear to you,

enter image description here

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    $\begingroup$ And that is why we say that the whole space between the Anode in the electron gun and the screen is field-free. (All borders are at Anode potential, therefore there can be no Electrical field.) The electrons drift towards the screen at a constant velocity, of approx. 1/3 c ! There they will make a shattering landing, converting all their kinetic energy into light and heat. Some electrons will backscatter and they may make their light in unintended places. $\endgroup$ – StessenJ Sep 10 '18 at 10:40
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I cannot comment on the construction of a specific electron gun, but in a typical CRT, the internal surface of the tube around the screen is coated by graphite, forming the final anode electrode.

This electrode is connected to high positive voltage and one of its functions is to collect electrons arriving to the screen.

enter image description here

enter image description here

So you are absolutely right - any cathode ray tube or electron gun should have some return path for the electrons. It is not shown on your diagram, probably, because this diagram is simplified.

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    $\begingroup$ The conductive coating is known by the name "Aquadag". A higher-resistance red version on the inside serves to reduce the magnitude of a flashover current. Similar coating is also needed on the outside, for 2 reasons: to form a capacitor ("Leiden jar" type) for smoothing the anode voltage, and for keeping the outside of the CRT at low voltage and thus preventing "crackle" sounds. The "anti-crackle coating" under the deflection coils is very high impedance, for not dampening the deflection field. $\endgroup$ – StessenJ Sep 10 '18 at 10:45
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The cathode source frees up lots of thermal electrons continuously and the electric field between cathode and anode accelerate them toward a specific direction. and until these two is working electron beam continues to exist with no problem.

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  • $\begingroup$ This is correct, the amount of emitted electrons is quite small compared to the amount of free electrons in the metals. What will eventually happen, though, is that an insulated target would become negatively charged and the electron beam would avoid it. $\endgroup$ – jpa Sep 10 '18 at 6:45

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