Re: Spark Gap Sustaining Current (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Sat, 29 Sep 2007 14:16:17 -0500
From: Bert Hickman <bert.hickman@xxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Spark Gap Sustaining Current (fwd)

Tesla list wrote:
> ---------- Forwarded message ----------
> Date: Thu, 27 Sep 2007 12:55:46 -0500
> From: Crispy <crispy@xxxxxxxxxxx>
> To: tesla@xxxxxxxxxx
> Subject: Spark Gap Sustaining Current
> 
> Hello,
> 
> I have a quick question about spark gaps.  How much current is required
> to sustain an established arc in a spark gap in "dead air"?  Let's say
> that there are two tungsten contacts about an inch apart, and an arc is
> ignited by a voltage of a little over 20kV.  Say that the ambient
> temperature is room temperature and that there is not significant
> airflow through the gap other than that which is generate by the gap's
> heat itself.  Is the sustainability of the arc purely a function of
> current through it?  

Hi Chris,

The short answer to your first question is YES.

A somewhat longer answer:
There's nothing simple about sparks, arcs, or plasma in general. The 
answer depends on current limiting by the external circuit, whether you 
have AC or DC and, if AC, the frequency. AC and RF arcs must be 
reignited after each current zero crossing. This makes low frequency AC 
arcs easier to extinguish than DC arcs. It also depends on the electrode 
shape and material, and the orientation of the gap (vertical arcs behave 
somewhat differently than horizontal ones).

Arcs require the formation of a "cathode spot" - a small incandescent 
region at the cathode root of the arc - which injects large numbers of 
electrons to help sustain the arc. For most metals, a true arc occurs 
when the current reaches a level of amperes or, at most, tens of 
amperes. The actual electron injection mechanisms into an arc differs 
significantly between electrodes made from refractory metals versus non 
refractory metals. A refractory metal, such as tungsten, develops a 
stable incandescent cathode spot which liberates large numbers of 
electrons via thermionic emission. Non-refractory metals such as copper 
(with boiling temperatures below the point of substantial thermionic 
emission, ~ 3000 degrees C), are "cold cathode" materials. The cathode 
spots of these metals are in constant motion, with electrons being 
liberated via field emission. The high E-field is created between 
between the cathode and positive ions just above the cathode (called the 
cathode sheath).

If you're able to limit short circuit current to tens of milliamperes, 
the voltage across the gap climbs sharply. Gap voltage vs current begins 
to follow a curve that is heading towards a low current glow (or corona 
discharge) or to the initial spark-over voltage of the gap. In an AC 
arc, the reignition voltage also begins to climb, ultimately approaching 
the initial breakdown voltage for the gap or a stable glow/corona 
discharge point. This phenomenon can be seen for low current AC arcs 
(such as from a low current NST's), where the arc really can't be drawn 
out much further than the point of initial breakdown before being 
extinguished.

If the short circuit current from the power source is even further 
decreased, once the gap breaks down, the low impedance of the spark 
drops the voltage below the gap's instantaneous sustaining voltage. 
Without using a careful low capacitance design approach, this usually 
leads to unstable operation when short circuit current is limited to a 
few milliamperes or less. The result is usually repetitive spark-like 
discharges as the circuit operates as a relaxation oscillator. The 
discharge tries to follow the sharp negative resistance curve heading 
towards an arc, but the voltage across the gap collapses and kills the 
arc, so the circuit cannot achieve stable "arc-like" operating point.

 > If so, in such a theoretical gap, how much
 > sustaining current would normally be required?
 >
 > Thanks,
 > Chris
 >

Again, it depends on the external circuit and whether you apply AC or DC.

For a HV DC source, with little capacitance, resistively current 
limited, you can actually follow the progression of the gap breakdown 
process from the glow discharge, abnormal glow (for refractory metals), 
down to a full fledged arc discharge. Once you have exceeded the 
breakdown threshold for the gap, the "sustaining current" simply is 
either the stable or unstable operating point(s) defined by the external 
circuit. Simply stated - for a resistively current limited low 
capacitance DC HV source, there is no minimum sustaining current once 
you've successfully bridged the gap. Practically speaking, the discharge 
ceases being "arc-like" in air once you go below a few mA and, for most 
circuits, the discharge is no longer stable.

For a low frequency HV AC source, reignition after each current zero 
becomes increasingly difficult as you begin lowering shirt circuit 
current, and a single failure to reignite after a zero crossing leads to 
almost complete dielectric recovery of the gap. Again this is with 
milliamperes of current - higher than for the DC case with an identical 
gap. Because of the shorter zero crossing intervals and capacitive 
effects, an RF arc is somewhat harder to extinguish, with "sustaining 
current" falling somewhere between low frequency AC and DC case.

As with all things arc-ish and spark-ish, YMMV... :^)

Bert
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