Impedance of a plasma arc

[Etesla]

I'm trying to design a plasma tweeter. I've made about 5 of them using various strategies over the last couple years but I'm really trying to optimize this one. I plan on winding my own transformer on top of a flyback core from an old CRT tv. I was going to drive the primary with a half bridge like a normal transformer, no flyback stuff. I believe the leakage inductance in the secondary will be the primary thing limiting the secondary current, which is what I think will be related to the intensity of the arc, and therefore the audible volume, of the final design. I think the way to get maximum power into my arc would be to match the impedance of the arc to the impedance of the secondary leakage inductance roughly.

However this leaves me with a challenge. I have no idea how to characterize the impedance of an arc created by flowing current through ionized air. I would imagine the things that matter most are the distance between my electrodes, and maybe the current flowing through the arc? Did anyone every do a study characterizing the impedance of ionized air? Does anyone have ballpark number, like a plasma about 2 inches long that looks 'pretty hot' with 2mA flowing through it is about 200 ohms?

I'll take any information I can get before I get antsy and run my own experiments...

[radiolistener]

If I remember correctly, it will be close to resistance of a copper conductor at 20°C.

But it can vary depends on air chemistry, pressure and plasma temperature

[coppercone2]

nonlinear at low currents. At high currents between say 50 amps it should be around 0.5 ohms for a 1mm length welding arc (taken from old book). And at 250 amps something like 90 miliohms. (the voltage drop stays constant) *

At lower currents say 10 amps it comes out to a few ohms . (say in this case I got about 3 ohms but its hard to read these old tiny charts)


But this is for a welding arc

It changes with distance just like it does with a wire. Linearly (at high currents). The temperature of the gas is probobly the main factor for conductivity ? At low currents I don't know. I think its kinda unstable


and
At very low currents it looks like it tops out at about 30 ohms per mm (2-3 amper range)


*keep in mind its i2r, so even if you have decreased resistance, the power of the arc still goes up even if the resistance decreases. I.e. 1kW @ 50A and 4kW @ 250 amps So if that heat is being carried into the work piece you know how a welder works, its like a torch jet. Then you also have the electricity doing something on the work piece, but if you experiment, 50 amps on a piece of steel actually don't do too much ! nothing like the arc heat.

[Marco]

From Google :
https://www.researchgate.net/profile/Abdel-Aleam-Mohamed-2/publication/224074690_Direct_current_glow_discharges_in_atmospheric_air/links/55dda7e308ae591b309b7360/Direct-current-glow-discharges-in-atmospheric-air.pdf

According to that, if you current limit at 5ma to keep it not immediately lethal it's about 400kOhm per cm.

A welding arc is a lot lower, it will also blind you and throw a lot of ozone and molten electrode around.

[jonpaul]

Hello: Plasma tweeter: waste of time ...dangerous.

Low efficiency, short life, danger f ozone poinsing.

We used RAAL Ribbon tweeters for decades, MUCH better sound.

Plasma imp:
No simple answer.

Read classic books: Gaseous Conductors, Cobine,
J.J. Thompson, etc for arcs.



Jon

[CaptDon]

I would tend to agree with JonPaul. Plasma tweeters are a waste. More like a fad or "I have something you don't". Sure, you can light a cigarette with a jet engine in reheat afterburner mode, maybe even from 30 feet away? Get the similarity in practicality? There are many good conventional tweeter designs that perform accurately to around 50KHz, double the highest frequency of human hearing. If you really want to go nuts add an actual ultrasonic transducer for that extra range to 100KHz!!! I can hear the audiophools now "The mids are so open and clear and the highs now resonate in my ears like an ice pick through the brain"! Plasma tweeters are more of a fun novelty and fun is always the name of the game. Good luck and enjoy experimenting, I would never fault anyone for experimenting. Sometimes great things are discovered accidentally.

[themadhippy]

Plasma tweeters are more of a fun novelty and fun is always the name of the game.

and wiping out next doors tv reception

[jonpaul]

Rebonjour: The plasma tweeters are Tesla coils generationg a high voltage (5..50kV) high frequency (40 kHz..13.5 MHz) RF.

This can cause skin burns like a welding arc and affect pacemeker hear patients.

Besides Ozone, they generate SW UV.

After decades in sound and HiFi my HT uses the RAAL ribbon tweeters, fantastic treble, imaging.

Enjou,

Jon

[Etesla]

Ok interesting. I'm hearing that the resistance of a 1-2" arc is going to be on the order of single digit ohms of resistance? Does anyone have evidence against or for that?

Also this is obviously for the cool factor, I don't really care about the audio quality as long as it's fairly audible in a room with people talking and the arc looks scary.

If my switching frequency is somewhere in the 20-40 khz range, that means I would want my leakage inductance to be in the 10's of uH's, which would put me in the single digit to low 10's of ohms for the reactance. I think that will limit me to a much lower turn count than I was expecting which is pretty interesting. It also means that optimizing my coupling coefficient (therefore reducing my leakage inductance as much as possible) would help me out dramatically with power delivery.

Does anyone know what sort of design decisions for winding a high turn count secondary help or hurt my coupling? Maybe I should use as thin of wire as I can get away with to keep the windings physically close to the core? Maybe I should segment the bobbin into as few segments as I can get away with? Maybe I should optimize the bobin material to let me get the windings as close to the core as possible? Stuff like that.

[coppercone2]

I think its a interesting equipment but it needs to be made with a copper screen and operated out doors. I don't know if a screen would work well for EMI but I would do that anyway for safety reasons.

It gets stupid if you try to use it in doors.

[coppercone2]

also IDK it does not agree with my text book at all. Maybe I am missing something. I think the arc would need to be blazing hot to register single ohms at 2 inches. Something around 100 amps. That is 50mm. For 10 ohms that means 200mOhms/mm. I don't feel like looking it up again but its not in the right ballpark. Unless the resistance is drastically reduced at very low currents and then increases for medium currents (amps) and decreases for high currents.

[T3sl4co1l]

Model it as a dielectric loss.  Mechanically, what's happening is myriad streamers discharge the strong electric field from the electrode into surrounding space, effectively growing the diameter of the electrode until field strength is below breakdown and further sparking/corona emission ceases.  Repeat ad nauseum at very fine time scales (breakdown occurs in fractions of a ns) and take the average over human time scales (ms, say) and you have the brushlike shape typical of RF corona discharge.

Each individual discharge might be some ohms, but it's only discharging some ~pC of nearby air, the reactance of which dominates.  But the discharge only lasts for a tiny instant (give or take displacement currents keeping it hot and ionized; this is more likely, close to the electrode, than far off at the periphery, where the discharges are constantly breaking out, recombining, and re-breaking), so although its instantaneous resistance can be small, the time-averaged resistance is much larger.

It's a similar effect as in a switched-capacitor circuit, or a mixer or analog switch circuit run at low duty cycle, where the switch resistance becomes divided by the duty cycle of the on-time.

I'm not familiar with typical figures, or how much goes into dissipating it, but my rough guess from Tesla coil stuff is the loss tangent is around 10 or 20%.

This must be accounted for in parallel with the natural capacitance of the secondary.  If the discharge dominates, it might well be the overall loaded Q is comparable, i.e. 10 ish, but more likely it's less than half the total, i.e. loaded Q of 20 to 60 is a reasonable starting point.

Speaking of Tesla coils, this means the unloaded Q factor of a coil, and the precision of tuning, isn't so important, because as soon as some breakdown gets going, the Q tanks, and bandwidth widens.  In an SSTC where you're pumping energy into the system during a tone burst, you tend to see the amplitude grow or decline more like linearly rather than exponentially.

This also means the resonant frequency shifts downward, which is like the discharge making itself into a conductive shell and therefore adding as much capacitance as such a shell would provide.

Tim

[Marco]

The plasma tweeters are Tesla coils

Modulated RF is but one possible way. DC+AC glow discharge is another. Ion wind is yet another.

Ion wind seems the most interesting to me, it also simplifies drive since you can use a lower voltage grid electrode to modulate the ion wind.

[jonpaul]

Ahn arc has several component areas, due to the ion density, the voltage drop is nearly constant and does not approximate an resistance.

The easy model of an arc is


Rectfier><Huge 20..60C Zener or baqttery>< reissistance of the V/I slope.

See our old freind Dr John Waymoutn,of Sylvania,  Electric Dischardge Lamps
and  classic 1930s books by Elenbas at Philips.   

Jon

[Etesla]

Model it as a dielectric loss.  Mechanically, what's happening is myriad streamers discharge the strong electric field from the electrode into surrounding space, effectively growing the diameter of the electrode until field strength is below breakdown and further sparking/corona emission ceases.  Repeat ad nauseum at very fine time scales (breakdown occurs in fractions of a ns) and take the average over human time scales (ms, say) and you have the brushlike shape typical of RF corona discharge.

Each individual discharge might be some ohms, but it's only discharging some ~pC of nearby air, the reactance of which dominates.  But the discharge only lasts for a tiny instant (give or take displacement currents keeping it hot and ionized; this is more likely, close to the electrode, than far off at the periphery, where the discharges are constantly breaking out, recombining, and re-breaking), so although its instantaneous resistance can be small, the time-averaged resistance is much larger.

It's a similar effect as in a switched-capacitor circuit, or a mixer or analog switch circuit run at low duty cycle, where the switch resistance becomes divided by the duty cycle of the on-time.

I'm not familiar with typical figures, or how much goes into dissipating it, but my rough guess from Tesla coil stuff is the loss tangent is around 10 or 20%.

This must be accounted for in parallel with the natural capacitance of the secondary.  If the discharge dominates, it might well be the overall loaded Q is comparable, i.e. 10 ish, but more likely it's less than half the total, i.e. loaded Q of 20 to 60 is a reasonable starting point.

Speaking of Tesla coils, this means the unloaded Q factor of a coil, and the precision of tuning, isn't so important, because as soon as some breakdown gets going, the Q tanks, and bandwidth widens.  In an SSTC where you're pumping energy into the system during a tone burst, you tend to see the amplitude grow or decline more like linearly rather than exponentially.

This also means the resonant frequency shifts downward, which is like the discharge making itself into a conductive shell and therefore adding as much capacitance as such a shell would provide.

Tim

Ok this is interesting. So you're implying that I should model the arc as a series RC circuit? I don't really understand why that's a good approach, probably I'm misunderstanding.

Going by definitions, 1/Q = tan(delta), where delta is the angle between the vectors R and the reactance of the capacitor [1/(2*pi*frequencySwitchingHz*C)]? So if I assumed R was 1, and you're telling me Q is 30, then delta is like 2 degrees ish, and at 20 khz C would be like 500uF? I guess if I model it as a series RC thing, how would I get the R or the C?

[coppercone2]

Ahn arc has several component areas, due to the ion density, the voltage drop is nearly constant and does not approximate an resistance.

The easy model of an arc is


Rectfier><Huge 20..60C Zener or baqttery>< reissistance of the V/I slope.

See our old freind Dr John Waymoutn,of Sylvania,  Electric Dischardge Lamps
and  classic 1930s books by Elenbas at Philips.   

Jon

constants at high currents. The voltage drop increases at low current < 40A

[NiHaoMike]

Also this is obviously for the cool factor, I don't really care about the audio quality as long as it's fairly audible in a room with people talking and the arc looks scary.

A few tabletop Tesla coils will do.

[T3sl4co1l]

Ok this is interesting. So you're implying that I should model the arc as a series RC circuit? I don't really understand why that's a good approach, probably I'm misunderstanding.

Going by definitions, 1/Q = tan(delta), where delta is the angle between the vectors R and the reactance of the capacitor [1/(2*pi*frequencySwitchingHz*C)]? So if I assumed R was 1, and you're telling me Q is 30, then delta is like 2 degrees ish, and at 20 khz C would be like 500uF? I guess if I model it as a series RC thing, how would I get the R or the C?

I explained why R isn't ~1 on average.  An RF discharge is billions of microscopic events; it is not a continuous process.  This is simultaneously why so much wideband noise is emitted.

I don't know how you would get 500uF out of, say, a sphere a couple inches diameter at most; more like a couple pF.  The ESR will be in the kohms to Mohms range, depending on frequency and Q.  Connect this to the secondary coil, modeled as a parallel RLC circuit; and couple this to whatever the primary driving winding and amplifier is.

The methods won't make a whole lot of sense without some network theory, but I would suggest just putting together a basic circuit in SPICE and playing with values.

Tim

[Berni]

The resistance of a plasma arc is heavily dependent on the plasma temperature, so it is not something you can just easily calculate or lookup in a table.

The shorter, hotter and more confined you can make the arc the lower resistance it will have. The current flowing trough it affects the temperature a lot, giving it a unstable negative resistance slope, making things even more unpredictable.

In general any equipment that maintains an arc (like welders or arc based or gas discharge lamps) have a power source that behaves more like a constant current source, so that the current is kept fairly constant while the voltage becomes whatever it needs to be to maintain the current in the given arc conditions.

If you were to use a fictional perfect ideal voltage source to draw a plasma arc it would not work. Either your voltage would be too small by 0.0000001% and cause the arc to slide down the negative resistance curve until the arc extinguishes or you have a voltage that is too large by 0.0000001% causing the arc to get hotter and hotter drawing more and more current, to the point where you are drawing many many milions of amps of current, nuclear fusion is happening in the arc, irradiating the area around you with intense gamma radiation. Hopefully soon destroying the fictional ideal voltage source so that the resulting explosion only levels the town rather than destroy the entire planet Earth.

But in all seriousness plasma speakers for HiFi are not that great of an idea as stated above.

[radiolistener]

Ok interesting. I'm hearing that the resistance of a 1-2" arc is going to be on the order of single digit ohms of resistance? Does anyone have evidence against or for that?

As I remember from science paper, it has fraction of Ohms and very close to a copper conductor of the same size. But it depends on conditions (air pressure, temperature, chemestry, etc), which also depends on the voltage and current. So, there is no exact value and it can be higher than copper, but in average you can assume it the same as a copper conductor.

[Smokey]

I have an Everlast MIG welder that has an "inductance" setting.  Anything other than maxing out that inductance setting causes excessive spatter on just about all current and wirefeed settings.  Dunno what they are actually doing there, maybe it's just the constant current PID gains or something.

[CaptDon]

I would suppose it also depends on if you have truly generated a plasma or simply a low power sustained arc like the corona off of a flyback in a C.R.T. television.

[Terry Bites]

Pretty hot?
Start with some basic measurements. An HF CTR and a high voltage divider would be a start.
IR thermometer gun?

[Marco]

You don't need an arc, a glow discharge is hot enough for thermally driving sound production (Tesla coil streamers too). An arc will be more violent and high power than needed.

[Etesla]

Also this is obviously for the cool factor, I don't really care about the audio quality as long as it's fairly audible in a room with people talking and the arc looks scary.

A few tabletop Tesla coils will do.

I've already built a couple DRSSTC's for that haha. Not my goal on this one.