Dex Dexter wrote:
Sorry ,neither do I have the books you are referring to. Conductivity of the ionized plasma increases very fast yes . But the resistance of the arc in gap depends of the effective column cross-section,which doesn't change so fast as you desribe. Expanding shock wave expands radially with velocities in the order of 1 Mach. How much time it takes to expand from diameter 0.1 mm to diameter 10 mm calculate yourself.
Actually, it can easily go supersonic, so the shock wave isn't an issue. Imagine a thin core that is hot, the air right outside the core heats by conduction and radiation both. Radiation obviously goes at 3E8 m/sec. Conduction is somewhat slower. Another transport mechanism is ionized particles actually moving, but that's just like conduction, with the interesting side effect that if enough ionized atoms move, then current can flow, and self heating can heat the air up (which is a VERY fast process)
Bear in mind also that sonic velocity is pretty high at 7000K. So Mach 1 is a lot more than 300m/sec (around 2000 m/sec?) moving 0.1mm at 2m/msec only takes 50 microseconds.
10mm is a pretty large diameter spark, too (lightning is about that size).For the sparks we're talking about in tesla coils, the sub-mm size is probably more accurate.
I don't recall who derived it (Goncz?.. probably earlier than that, Somerville perhaps), but I think spark diameter in a free burning arc goes as the square root of current (that is, the current density in all sparks is about the same) On that basis if a 10-20kA spark (lightning) is a cm in diameter, a 100A spark (TC primary) is on the order of 1mm.
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