# [TCML] Spark gaps (again)

Dex Dexter dexterlabs at dcemail.com
Mon Mar 9 13:02:56 MST 2009

```I'm not so sure about thin that much final diameters for a Tesla gap spark.
http://www.mintek.co.za/Pyromet/Files/1997Curr.pdf
I took in my estimate 1000 A primary current arc to expand to about d=10 mm.
100 A current is probably closer to low powered coil,but it depends also
on operating frequency.
What is radial average velocity of expanding column of such arcs it's hard to tell.
I don't have data and I'm interested to learn.

Dex

To: Tesla Coil Mailing List <tesla at pupman.com>
Cc:
Subject: Re: [TCML] Spark gaps (again)
Date: Mon, 09 Mar 2009 06:37:56 -0700

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
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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