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I don't get corona discharge. There's an electrode (say naked high-voltage wire) and a current develops from that wire and ionizes gas (air) on its way.

But where does this current go? What's the destination of that discharge?

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First try to understand the case in which there is another electrode.

You have a pointy electrode and a flat electrode. You apply a high voltage across them. The pointiness of the first electrode concentrates the electric field to the extent that electrons are stripped from atoms and the air around the tip becomes conductive, a plasma. The plasma is the part that glows. The flat electrode spreads out the electric field, so the air around it stays normal, an insulator.

If the voltage is high enough, the electric field around the pointy plasma will also be strong enough to ionize air, and the plasma region will get bigger. If this continues extending itself until it touches the flat electrode, there is a complete conductive path, and an arc forms.

If the voltage is not high enough for an arc, the plasma will stop increasing in size, and just remain in a layer around the pointy electrode. The plasma is then surrounded by normal insulating air. There is not a complete conductive path between the electrodes, but a current can still flow. The way it happens is that ions from the plasma are repelled away from the electrode, and migrate slowly through the neutral air (like any other molecule diffuses in air by bouncing off of air molecules, but combined with a drift in one direction because it's repelled by the pointy electrode and attracted to the flat one). Eventually it will reach the flat electrode and discharge. This current is much smaller than the arc, though, because the charges have to diffuse through the region of insulating air.

It's not correct to say "a current develops from that wire and ionizes gas (air) on its way". The gas is ionized by the electric field, and then a current flows because the ionization allows it to.

So to understand how it works without an obvious flat electrode: All voltages are really a difference between two points. We say things like "this point is at 20 kV", but what we really mean is "this point is at 20 kV with respect to another reference point". This reference point is referred to as "ground", and can be any point in a circuit. It doesn't have to be connected to the physical Earth. So the other electrode is whatever your voltage source is connected to. If the voltage source is connected to the planet Earth, then the planet and anything connected to it becomes the flat electrode. If it's connected to a metal sphere, then that sphere is the flat electrode and the charges will try to migrate to it.

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