Re: Gap Question

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Bert Hickman <bert.hickman-at-aquila-dot-net> 

Hi Luke,

The physics of arcs is very complex, and the following is a horrendously 
oversimplified way to get a ballpark estimate for arc voltage drop. The 
steady state arc voltage drop is a function of the distance between the 
electrodes, electrode materials, and the atmospheric gas(es) surrounding 
the arc. Also, if the electrodes are made from different materials, the 
polarity of the applied current may also affect the voltage drop.

An arc has three regions - the cathode region, the arc column (called the 
positive column for historical reasons), and the anode region. The total 
voltage across the arc is the sum of the voltage drops in these three 
regions. The physical length of the anode and cathode regions and 
transition regions that grade into to the main arc column are relatively 
small - only 10^-1 cm in the case of arcs at atmospheric pressure.

An estimate for the voltage across a free burning arc that has reached 
local thermal equilibrium can be represented as:

   Varc =     Va       +      Vc       +      E*X
          [Anode Drop]  [Cathode Drop]  [Arc Column Drop]

where E is the field strength in the arc column and X is the length of the 
column. Va and Vc are relatively fixed for a given electrode material and 
the voltage drop across the arc column scales linearly with increasing 
column length. For short arcs, the first two terms dominate, while the 
third term dominates for long arcs.

A free burning, high intensity arc will dissipate a minimum of 100,000 - 
200,000 W/m depending on arc shape. A very rough approximation for the 
E-field within the arc column for air at STP as a function of arc current 
(I) is:

     E ~ 10^5/I to 2*10^5/I   (Volts/meter)

As can be seen, the approximate arc column voltage drop voltage is 
inversely proportional to current and proportional to arc length.

Using the above relationship, E is found to be approximately 10-20 Volts/cm 
for a 100 amp arc. Vc is typically 8-12 Volts, and Va is 2-12 Volts 
depending upon electrode materials. For copper, Va is about 9 Volts and Va 
is about 6 Volts, so the "ballpark" estimate for a 100 ampere arc across a 
one gap between copper electrodes would be 25-35 Volts. This would drop to 
only 16-17 volts for a 1000 amp arc. You can see a set of curves for the 
voltage drop for arcs between copper electrodes in section 5.1 of the 
reference I cited in my previous post:
http://www.elkraft.chalmers.se/GU/EEK195/lectures/Lecture7.pdf

BTW, in a copper pipe TC spark gap the actual gap voltage across each gap 
may be 5-10 times larger than the steady state values since the gaps never 
come close to reaching local thermal equilibrium.

Hope this helped and best regards,

-- Bert --
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Tesla list wrote:
>Original poster: "Luke" <Bluu-at-cox-dot-net>
>It was mentioned that a spark gaps voltage will stabilize at a
>particular voltage and the current and resistance will change.  I
>understand that but it raises another question.
>The amount of current through the arc will determine the cross sectional
>area of the arc and therefore the resistance.
>But what determines at what value the voltage drop across an arc will
>stabilize at?
>This is not in reference to a spark gap where the energy level is fading
>but with a power source that is constant.
>Luke Galyan
>Bluu-at-cox-dot-net
>http://members.cox-dot-net/bluu
>Original poster: Bert Hickman <bert.hickman-at-aquila-dot-net>
>Hi Luke,
>[LG>] Sniped portion of reply
>The resistance of an unconfined arc will tend to decrease as you
>increase
>current since the conductive channel becomes fatter. The effective
>resistance of the arc no longer a constant, but instead is a function of
>the applied current. The voltage drop across an arc that bridges a fixed
>gap length rapidly stabilizes to a comparatively low steady state
>"burning
>arc" voltage (~20 volts to ~150 volts depending on the electrode
>materials).
>As you indicate, the overall resistance of the arc is always positive.
>However, an arc has a "negative resistance characteristic" since an
>increase in current causes a rapid DECREASE in the arc's resistance such
>that the arc's voltage drop tries to approach the burning arc voltage
>for
>the gap.
>
>Best regards,
>-- Bert --
>
>.