Re: Why the electrical arc has a negative dynamical resistence?

Hi Alf!

The reason that an electrical arc has a negative dynamical resistance is 
that the voltage required to start an arc streamer is generally pretty 
high.  Once the ions and the electrons that make up the plasma are created 
by the initial gas breakdown, the residual voltage is usually high enough 
to accelerate them (the ions to the negative electrode, the electrons to 
the position electrode) a lot.  As they accelerate and gain energy, they 
hit other, neutral atoms hard enough so that they are broken up into ions 
and electrons.  These are subsequently accelerated, and so on in a giant 
chain reaction which is called avalanche breakdown.  This progressive 
breakdown continues until the electrical source just can't supply enough 
energy to keep the process going, and the voltage drops to the point where 
there isn't enough acceleration to create more electrons and ions.

Recapping the whole process...

1.  The initial gas is composed of neutral atoms, so it has a high 
electrical resistance.
2.  A voltage is applied across the gap (and sometimes other tricks are 
played, too, but that's too complicated to talk about now), causing the 
creation of one or more electron-ion pairs.
3.  The voltage produces avalanche breakdown, creating tons of additional 
electon-ion pairs.
4.  Because electrons and ions are mobile electrical charges, their 
presence causes the resistance of the gas to drop when more of them are 
created.
5.  The whole process stops when the power source can't keep the voltage 
across the gas high enough to support continuing avalanche, and the arc 
either reaches steady state or goes out.

This explains why fluorescent lights always have something called 
a "ballast" in them.  "Ballast" in this context is just a term referring 
to an inductor, a coil of wire which has the property that the voltage 
across it depends on the rate at which current is increasing.  This 
interesting property is exactly opposite to that of the arc discharge 
process described above.  Now let's go to the fluorescent lamp problem...  
Fluorescent lights are really low pressure mercury vapor lamps.  The 
ballasts are generally wired in series with the lamps.  When voltage is 
applied, the unionized mercury vapor lamps exhibit almost infinite 
resistance so that all the voltage appears across them.  The lamp pressure 
is established so that the voltage is somewhat above the breakdown 
voltage, so that ions and electrons are created and avalanche begins.  
But, as the current starts to rise, the ballast starts to look like a 
impedance to the current and -- after the current reaches a certain point -
- the ballast chokes off further current increase.  Voila -- stable 
operation of the plasma and reliable lamp operation.

Now, it turns out that real fluorescent bulbs are a little more 
complicated than this.  They use alternating current from normal home or 
office or factory wiring, which means that the voltage oscillates at 60 Hz 
in a sine wave form.  No problem there... that just means that the arcs 
start and stop 120 times a second (they start and stop on each up and down 
cycle... or at least they can on many devices).  Unfortunately, you 
wouldn't be able to see the output from the mercury discharge -- since 
it's in the UV and (1) your eyes couldn't see it, and (2) the glass in the 
tube envelope would stop it.  So, what the lighting companies do is to put 
phosphors on the inside of the tube that very efficiently absorb the UV 
and turn it into blue, yellow, and red light... The "turning" process is 
called fluorescence and is what gives the lights their name...  Yep, 3 
phosphors are generally combined in exact proportions to make white light 
output.  If you don't believe me, get a prism and do the experiment!  The 
amazing thing about these lamps is that they really can make the light any 
color they want by mixing the phosphors differently.  The sickening blue-
white color of most fluorescents must have been devised by a sadist (who 
also, by the way, was more concerned about the lifetime and efficiency of 
the phosphors than user acceptability).  Newer bulbs -- in fact the one in 
the table lamp in front of me on my desk right now, designed to replace 
light bulbs -- has a more yellow-red balanced phosphor set that, while not 
so efficient and long-lasting (only 8000 hours!), is a lot more pleasant 
to look at.

Actually, I'm lying slightly when I mention fluorsecent lamps in the same 
context as arc discharges.  While the general avalanche discharge process 
is the same in both, fluorescent lamps generally have ionization filling 
most of the tube volume in a diffuse glow discharge.  The term "arc" is 
usually used to describe a more violent, filamental discharge -- often in 
air.  The same ideas apply, however, regarding negative resistance 
requiring an external ballast (even if imposed via a power supply that has 
an internal limiter on its current/voltage capability) for stability.

That's probably more than you ever wanted to know about discharge 
dynamics, but what the heck... You asked so you might as well get a 
complete dump (or avalanche) of info.

Oh, by the way, that flickering of fluorescent lights that sometimes 
drives people nuts...  Yep, it's due to the 120 Hz flicker in the light 
from the AC input.  Interestingly, it's possible to select phosphors 
(again, with some trades in efficiency and life) so that their rate of 
release of the light they absorb from the mercury vapor is slower than 
1/120th of a second, so that they don't appear to flicker.

Thanks for the question!



Steve Guch