To ionize air, you have to have immense heat. The bolt leaves a path of ionized air after the "spark". A leader is something slightly different and is not true ionizing as the correct use of the term exists. Science knows that leaders exist and they reaches up high into the air, but there is still a substantial jump of Bolt to leader through non-ionized air. And so far as science understands it, there is no other path. The same result has been proven in the lab with giant lightning machines. A enormous charge is raised and when the Pd reaches a high enough potential to jump the gap, it does so with out the help of leaders.
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you can't create a spark from a 12 volt battery by shorting out the terminals as the conductor is brought up to the battery post. The spark only occurs after the conductor is brought in contact with the other terminal and then removed. It is the back EMF generated by the collasping of the current flow in the conductor
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Only if the conductor has a coil. The back EMF is a current produced by a collapsing mag field in the coil. But if you place a plain wire across the terminals, you will still get sparks when removed. That is due to a plasma being set up between the terminal and the wire. This plasma is the sole reason why we can arc weld. If the plasma and current can be maintained, the electrons will happily cross the gap via the highly charged bridge and create more heat. A soon as oxygen gets into the gap, the transfer stops and the arc ceases.
I did say this earlier, the brush was theorized as creating many smaller leaders instead of one leader reaching high up. But the theory is one thing, the reality seems to be another.
So another theory is, "well if you are going to get hit anyway", why not make something that the bolt will happily go to and lesson the excess going else where as much as possible. So copper being an excellent (and cheaper than other higher conductors), conductor, a Copper rod is used to "attract" the bolt to it instead of the mast. However, once again in reality, we are talking several million volts and several hundred thousands of amps. That takes a lot of conductor diameter to be effective. Remember that you are trying to tens or even hundreds of millions of watts of energy to ground at the speed of light. Any conductor not up to that job means the excess still waiting to go to ground will take the next available path = Mast.