model of a spark

From:  richard hull [SMTP:rhull-at-richmond.infi-dot-net]
Sent:  Thursday, June 04, 1998 7:30 PM
To:  Tesla List
Subject:  Re: model of a spark

At 09:32 PM 6/3/98 -0500, you wrote:
>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
>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
>	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)

I reply to very few posts now as time is precious to me, but this one is
most interesting.  One can see from the old idea of the spark channel
actually being capacitive that to transfer maximum energy to the spark we
might want to match impedances.  To achieve this we might want to make Ctop
close to Cspark.  .1cm is 1mm.  I think this is a bit thin for the whole
channel cross sectional radius. I would double or triple it to .3 CM.  The
channel has its lowest impedance internally at the center, but the tube
curent is non-linear in cross section, thus, it goes complicated and a
simple tube equation might give only order of magnitude approximations.
Still, spark impedance matching would demand the larger (giant) terminal
capacities the TCBOR has pushed for the last ten years.

Richard Hull, TCBOR