# How to calculate the voltage needed to create a plasma

• ahmed11
Increasing the voltage won't increase the density of the plasma. Increasing the voltage will create an arc and increase the distance between the electrodes.f

#### ahmed11

i've been reading on plasma physics and i have a couple of questions.
how to calculate how much volts needed to create plasma with distance x from the electrodes of a certain gas with certain pressure?
and to increase the distance do i have to increase voltage or once i have an arc or plasma in a tube i can just increase the distance without increasing voltage?
what are the equations used? in account for the density of the gas and it's pressure.

also how to calculate the pressure exerted by plasma?
will it be p=Nkt or is there something else, and also does the pressure exerted by plasma depends on the volume it's in or it's the same in every volume unlike gas?

It sounds like you want https://en.wikipedia.org/wiki/Paschen's_law

p=nkT works for plasma. n is the number density of all plasma species, i.e. sum of densities of electrons, other ions, and neutrals.
The volume dependence is contained inside the definition of number density = number / volume.

can i substitute the T in the equation with eV to know how much pressure will a certain gas with it's number density and using eV Boltzmann's constant?
also i really have a zero information about electricity and voltages and everything about electricity. i was trying to calculate if plasma can exist between two cathodes placed a 100 feet away or does that need really really high voltage and if it needs high voltage how much will it need and how much to sustain plasma in a 100 feet tube?
i know that 137 volts is the breakdown voltage of argon so do i calculate like how many volts needed to for 100 feet and do cross multiplication or is it more complicated?
and more importantly how much voltage needed to keep plasma and it's pressure stable?
thank you

can i substitute the T in the equation with eV
Yeah, we do that all the time. kT is usually measured in eV.

100 feet away
100 feet? Man, what the hell? That's twice as long as the https://en.wikipedia.org/wiki/Large_Plasma_Device

For such dimensions, you will need to generate the plasma at one end and let it flow down the tube, rather than trying to achieve a breakdown of the plasma across the entire length of the tube. You need some source of electrons which can ionize the gas. Paschen's law won't apply then.

• ahmed11
For such dimensions, you will need to generate the plasma at one end and let it flow down the tube, rather than trying to achieve a breakdown of the plasma across the entire length of the tube. You need some source of electrons which can ionize the gas. Paschen's law won't apply then.
ok this is great but one more question, after i generate plasma at one end of tube and then increase the gas and let it flow, can i add more gas inside the tube and increase the electric current to sustain the plasma i have now and try to increase the plasma by the newly pumped gas( same gas)?

You need to continuously generate the plasma. It will become harder to maintain the plasma as you increase the gas pressure. If you want a high density plasma, then you will need some ways to heat the plasma, such as microwave sources.

What is it that you are trying to accomplish? It sounds like you are envisioning something larger than university research lab scale. It's an absurd scope since you seem to not know much about plasma physics.

i know that 137 volts is the breakdown voltage of argon so do i calculate like how many volts needed to for 100 feet and do cross multiplication or is it more complicated?
The breakdown voltage is not a material property but it depends on your setup. Mainly, on distance between electrodes.
The relevant material property is breakdown field (or dielectric strength). measured in V/m.

As they said in the article, for argon you have 137 V for a distance of 12 microns and some specific pressure.
To calculate for your setup you will need to know the pressure in your tube as well as the values of the material parameters entering the formula. Or you could get an estimate by using the graph included in the article.

You need to continuously generate the plasma. It will become harder to maintain the plasma as you increase the gas pressure. If you want a high density plasma, then you will need some ways to heat the plasma, such as microwave sources.

What is it that you are trying to accomplish? It sounds like you are envisioning something larger than university research lab scale. It's an absurd scope since you seem to not know much about plasma physics.
no I'm not trying to do an experiment i just wanted to know the limitations of using plasma on a larger scale.
if i just increase the voltage when i pump more gas to stabilize the plasma will that do the trick or is when i pump more gas in the plasma tube i will have to breakdown the voltage of that pumped gas. like start all over again for every time i pump gas.
Also another idea i thought of if i have a 3 electrodes 2 at each end and 3rd placed a little bit away from the first electrode this one is used to breakdown every pumped gas and the 3rd at the end is used to maintain the plasma will that work.

imagine it's a 10 meter long for example or even more. and 3 electrodes 2 at each end and 3rd placed 3 cm away from first one. 3rd electrode is used to breakdown any more pumped gas and pass it through the 3rd when turned to plasma. now if there is already plasma in the tube and 3rd electrode is turned off and i pump more gas now and turn 3rd electrode on to generate plasma then pass it to the farther electrode. if this is correct, will i have to turn on 3rd electrode to just generate plasma from extra pumped gas then turn it off to pass it through last electrode or i can just have 3 electrodes in the tube

This is a very ODD thread.

Let's get a few facts out of the way first:

1. The discharge tube that we all know and love contains a plasma when it is ignited. This means that one can easily create plasma. Your fluorescent lamp is a clear evidence of that.

2. This means that you don't need to go to such extremes if the intention is to create a plasma. You can create one simply by having a cathode emitting energetic electrons (keV) and bombarding a gas. This is not that difficult to do with household voltages as we can already see with those lamps.

3. It is unrealistic to think that one can simply crank up a voltage on a gas without expecting that dark currents will come in and disrupt things.

4. Unfortunately, you DO need to learn a bit of E&M here. Otherwise, how are you going to understand the terms we use such as potential gradients and electric fields? This is especially true if you have an intention of "... using plasma on a larger scale... ". Plasma physics is messy, non-linear, and it is not easy.

Zz.

• ahmed11
Khashishi
also would it be easier to use electromagnetic induction instead of having three electrodes inside the tube. so the induction coils can be placed along the tube to separate the distance? if yes then please explain to me will it be cost effective than using electrodes and will it work or not.
i've been reading a lot and this is driving me crazy and hope that you could help me understand if my idea of this system will work or not. thnak you[PLAIN]https://www.physicsforums.com/members/khashishi.331471/[/PLAIN] [Broken]

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