model of a spark

From:  Jim Lux [SMTP:jimlux-at-earthlink-dot-net]
Sent:  Saturday, June 06, 1998 10:12 AM
To:  Tesla List
Subject:  Re: 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:
> >
> 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
> 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 0.1 cm "effective radius" is from Bazelyan and Raizer. They point out
that the conductivity of the air in the leader is quite low until it gets
above about 5000K, even though it is luminous starting quite a bit lower (
2800K). They cite a whole raft of experimental measurements (typically
using a narrow slit and a spectrograph). This is for an arc carrying around
a amp, which apparently is the typical current in a leader, and is a
suitable number to use in a rectangular approximation (the actual
distribution is a Bessel function with a flat center)

They also go through quite a bit of analysis (which I am attempting to
summarize for list consumption) of the space charge sheath around the
conductive core. In fact, this sheath accounts for most of the stored

There is a fairly complex tradeoff between the diameter of the core, the
speed at which it moves, and so forth. As the core gets larger, it cools
slower (area/volume), but it requires more energy to heat it in the first
place. The heat comes from the I^2R losses in the leader current feeding
the head of the leader. The speed of the leader is determined by the local
E field at the head, which in turn is determined by the voltage drop along
the leader, which in turn is determined by the current flowing through the
leader (more current = less drop = more voltage at the head = more field at
the head = faster movement = more charge required to fill the leader and
the sheath).

> 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.

Raizer and Bazelyan feel that a rectangular approximation with suitable
"pseudo radius" works quite nicely. They provide convincing data to show
that the deviations from a simple model (rectangular cross section) to the
real one shouldn't change the behavior much (at least not more than a small
fraction of an order of magnitude).

> Still, spark impedance matching would demand the larger (giant) terminal
> capacities the TCBOR has pushed for the last ten years.