model of a spark

To: "'Tesla List'" <tesla-at-pupman-dot-com>
Subject: model of a spark
From: Tesla List <tesla-at-stic-dot-net>
Date: Wed, 3 Jun 1998 21:32:47 -0500
Approved: tesla-at-stic-dot-net

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From:  Jim Lux [SMTP:jimlux-at-earthlink-dot-net]
Sent:  Wednesday, June 03, 1998 2:08 PM
To:  tesla-at-pupman-dot-com
Subject:  model of a spark

Following on Terry's analysis of what makes for a "good" coil, here is
some quick and dirty summarization of stuff from Bazelyan and Raizer,
"Spark Discharge", a useful book for anyone contemplating long sparks 

The spark can be modelled as a tube extending from the electrode. The
tube has a resistance along it, roughly related to the current in the
tube (more current makes it hotter reducing the resistance). The very
end of the spark has to be supplied with charge (i.e. current has to
flow along the tube) to keep its voltage high enough to break down the
air in front of it.  Also, the tube itself is a capacitor, and has to be
charged appropriately.

The capacitance of a long rod is 2*pi*epsilon * L / ln(L/r), where L is
the length, r is the radius. For dimensions in cm this reduces to .555
L/ln(L/r) pF/cm.  For a 10 meter rod, .1 cm radius, the C is 60.3 pF.

Typical optimum axial leader velocities are 1.8E6 cm/sec, for gaps 5-15
meters.

The channel field (i.e. the voltage drop along the leader channel) is
typically 5 kV/cm as the leader contacts the other electrode.

An empirical expression for the optimum rise time of the voltage pulse
is:

	Trise (uSec) = 50 d(meters)

so a 5 meter gap would require a pulse with rise time of 250 uSec
(That's equivalent to just a kHz, BTW)