Black body radiation vs electric discharge in a gas

[artis]

@naviakam what is the name of your BSc course?
was this problem of ion energy distribution given directly to you to solve in the course?

If this is from your curriculum then I guess you will need to solve it using maths anyways ,

 

[naviakam]

@naviakam what is the name of your BSc course?
was this problem of ion energy distribution given directly to you to solve in the course?

If this is from your curriculum then I guess you will need to solve it using maths anyways ,

It's the phys 2 lab. Given to everyone in the class.

 

[artis]

How far are are you within the BSc? which year ?To describe what you want in simple words is not even that simple in itself...
If you consider the Z pinch or any other current being pulsed through a plasma you also have to consider other parameters like whether the current pulse also ionizes the gas or is there already plasma present and the current is introduced then.
ANd by the way running current through a plasma or gas is not the only way to achieve Z pinch, you can also compress the plasma mechanically, this is done in the Sandia laboratories Z machine , apart from the electronics to make a fast current pulse , the very fusion part is rather simple, you take a small copper cylinder fill it with a gas mixture like D-T and seal it, place the so called "liner" between two electrodes and supply a very sharp fast rise time large current pulse through the copper liner, the liner implodes and the walls of the liner compress the gas inside. The pressure increase is so abrupt and strong that the gas is ionized and turns into a plasma and undergoes a very short burn time, where the temp is high enough for fusion reactions to take place.If I had to guess in an electrical discharge pinch , since electrons are much lighter than ions the electrons interact more with the current than ions, so the energy distributions between species are not equal , ions need some time to thermalize with the electrons via collisions and radiation transfer, depending on how long is the current pulse and how long the plasma is kept in a "hot" state this equalization of energies might start to happen after some time after the current pulse or not at all if the pulse is short and the plasma is then allowed to relax and thermalize back down to it's initial conditions.
The energy distributions between electrons and ions only start to become similar for plasmas that are kept confined for longer times, like seconds.

Short pulses of current discharge through a gas which then produce a plasma , even if that plasma reaches very hot temperatures for a brief moment during the pulse maximum are not at equilibrium between the species. Simply beacuse the time is not enough to reach that point. Or they might reach something close to that but for a very brief moment.

Anyway all of this is very complicated and I would need to read and refresh memory and probably learn additional stuff to go further. So if you want to understand this you have to start reading about it and then ask specific questions here.

 

[naviakam]

How far are are you within the BSc? which year ?To describe what you want in simple words is not even that simple in itself...
If you consider the Z pinch or any other current being pulsed through a plasma you also have to consider other parameters like whether the current pulse also ionizes the gas or is there already plasma present and the current is introduced then.
ANd by the way running current through a plasma or gas is not the only way to achieve Z pinch, you can also compress the plasma mechanically, this is done in the Sandia laboratories Z machine , apart from the electronics to make a fast current pulse , the very fusion part is rather simple, you take a small copper cylinder fill it with a gas mixture like D-T and seal it, place the so called "liner" between two electrodes and supply a very sharp fast rise time large current pulse through the copper liner, the liner implodes and the walls of the liner compress the gas inside. The pressure increase is so abrupt and strong that the gas is ionized and turns into a plasma and undergoes a very short burn time, where the temp is high enough for fusion reactions to take place.If I had to guess in an electrical discharge pinch , since electrons are much lighter than ions the electrons interact more with the current than ions, so the energy distributions between species are not equal , ions need some time to thermalize with the electrons via collisions and radiation transfer, depending on how long is the current pulse and how long the plasma is kept in a "hot" state this equalization of energies might start to happen after some time after the current pulse or not at all if the pulse is short and the plasma is then allowed to relax and thermalize back down to it's initial conditions.
The energy distributions between electrons and ions only start to become similar for plasmas that are kept confined for longer times, like seconds.

Short pulses of current discharge through a gas which then produce a plasma , even if that plasma reaches very hot temperatures for a brief moment during the pulse maximum are not at equilibrium between the species. Simply beacuse the time is not enough to reach that point. Or they might reach something close to that but for a very brief moment.

Anyway all of this is very complicated and I would need to read and refresh memory and probably learn additional stuff to go further. So if you want to understand this you have to start reading about it and then ask specific questions here.

Semester 3.

Seems that my question was not clear enough. Current passing though a wire produces B around it, but how a current density variation in r produces B in theta and E in Z. I don't want the complicated physics behind which I do not understand. Just how this happens? please show even by drawing arrows.

 

[artis]

Just imagine a vertical column, place your fist such that your thumb aligns with the vertical direction , once you have done that then your thumb is parallel or in the same direction as the current would go in a gas discharge or plasma that is arranged as a vertical pinch. Also current goes the same direction in a fluorescent tube if placed vertically.
now your fingers as they are curled and closed in a fist resemble the B field lines that wrap around a current.
The B field that loops around a current in the theta direction as you say is there by default for any current. There is nothing special about it. Any wire in this world ever that has had or still has a current through it has a B field curled around it.
They use this effect to confine a plasma simply because it's simple , but in order for the field to be strong enough to actually do anything the current has to be very large.

The E field in the Z direction is simple. Think of a cylinder of gas , vertical , and electrodes at top and bottom. In the simplest case you apply a potential difference a the electrodes and if high enough gas breakdown occurs, if during this breakdown the current is strong enough it can completely ionize the gas fast and produce a plasma.
The E field would be much stronger before the breakdown, because after breakdown the electrodes get shorted aka short circuited through the plasma so the E field strength decreases because the voltage has decreased.

 

[naviakam]

Just imagine a vertical column, place your fist such that your thumb aligns with the vertical direction , once you have done that then your thumb is parallel or in the same direction as the current would go in a gas discharge or plasma that is arranged as a vertical pinch. Also current goes the same direction in a fluorescent tube if placed vertically.
now your fingers as they are curled and closed in a fist resemble the B field lines that wrap around a current.
The B field that loops around a current in the theta direction as you say is there by default for any current. There is nothing special about it. Any wire in this world ever that has had or still has a current through it has a B field curled around it.
They use this effect to confine a plasma simply because it's simple , but in order for the field to be strong enough to actually do anything the current has to be very large.

The E field in the Z direction is simple. Think of a cylinder of gas , vertical , and electrodes at top and bottom. In the simplest case you apply a potential difference a the electrodes and if high enough gas breakdown occurs, if during this breakdown the current is strong enough it can completely ionize the gas fast and produce a plasma.
The E field would be much stronger before the breakdown, because after breakdown the electrodes get shorted aka short circuited through the plasma so the E field strength decreases because the voltage has decreased.

What I got was that these three (current, B, and E) are connected at the same time. Means that if current contracts in r, as a result B will be produced in theta and E in axial. But could not get the relation.
Current contraction produces B and E? How?

 

[hutchphd]

There is changing magnetic field so Faraday's Law.

 

[naviakam]

There is changing magnetic field so Faraday's Law.

Which approach is correct:
1. there is initially a current ring that contracts (somehow, but don't know how) then this produces a B field (how and which direction?) and E field (how and which direction?)
2. B field in theta contracts the enclosed current ring and E filed is produced (how and which direction?)

 

[artis]

Neither approach is correct. There is no ring, and current does not contract. I already told you simply.
PD (potential difference) is applied, gas molecules undergo electrical breakdown, as electrons get stripped from their atoms they become free to flow in the direction of the E field which is vertical within a vertical column that has electrodes at top and bottom. So the E field is vertical and so is the current because current is nothing more than a flow of charge between two points of different potential. In this case two electrodes.

As the charges move now, B field is created, the B field representing that of a current carrying wire. This field because it is changing then exerts force on the moving charges , pushing them closer together.
The reason why is because charged particles curl around magnetic field lines due to the Lorentz force they experience. if the magnetic field is increasing in strength the field lines become tighter and more cramped together so the particles have no other option but to be squeezed closer together.
If the B field was static for example and the current was also static and not increasing then the radius of the column would also stay static and not decrease further.

@naviakam you really need to read some physics books and basic concepts about this, I feel from your responses this is over your head a bit.

 

[naviakam]

Neither approach is correct. There is no ring, and current does not contract. I already told you simply.
PD (potential difference) is applied, gas molecules undergo electrical breakdown, as electrons get stripped from their atoms they become free to flow in the direction of the E field which is vertical within a vertical column that has electrodes at top and bottom. So the E field is vertical and so is the current because current is nothing more than a flow of charge between two points of different potential. In this case two electrodes.

As the charges move now, B field is created, the B field representing that of a current carrying wire. This field because it is changing then exerts force on the moving charges , pushing them closer together.
The reason why is because charged particles curl around magnetic field lines due to the Lorentz force they experience. if the magnetic field is increasing in strength the field lines become tighter and more cramped together so the particles have no other option but to be squeezed closer together.
If the B field was static for example and the current was also static and not increasing then the radius of the column would also stay static and not decrease further.

@naviakam you really need to read some physics books and basic concepts about this, I feel from your responses this is over your head a bit.

Then initially there is E in z that produces B around it (theta) and this B contracts electron density toward axis in r. Thank you.
One more question: Is it possible to obtain the ion energy from the equation of motion mentioned in the text?
This is to establish a possible correlation between the measured ion spectrum and the ion energy from theory.

 

[vanhees71]

A very simple example I've put in the Insights article about the straight current-carrying wire in full relativistic treatment. In this case it's pretty academic, but for a plasma the self-induced Hall effect is very important:

https://www.physicsforums.com/insights/relativistic-treatment-of-the-dc-conducting-straight-wire/

 

[naviakam]

A very simple example I've put in the Insights article about the straight current-carrying wire in full relativistic treatment. In this case it's pretty academic, but for a plasma the self-induced Hall effect is very important:

https://www.physicsforums.com/insights/relativistic-treatment-of-the-dc-conducting-straight-wire/

How the ion energy is calculated from the equation of motion given above (if possible at all)? Or there is some other form of energy equation for such condition?

 

[artis]

@vanhees71 From what I can tell you are a true professional and a good fellow here , but that article you made I think is way too complicated for this thread and the OP. I Read it through and even though I understand the concept the mathematics were over my head.

 

[hutchphd]

@vanhees71 From what I can tell you are a true professional and a good fellow here , but that article you made I think is way too complicated for this thread and the OP. I Read it through and even though I understand the concept the mathematics were over my head.

There is a point at which circles and arrows and body contortions with the right hand rule are either insufficient or insufferably convoluted.
I am reminded of the classic suit joke:

 

[artis]

@hutchphd , well maybe true but one also can't jump from start to finish in just one hop.

 

[naviakam]

@vanhees71 From what I can tell you are a true professional and a good fellow here , but that article you made I think is way too complicated for this thread and the OP. I Read it through and even though I understand the concept the mathematics were over my head.

Then one last question I hope: if the velocity of ion in E and B field is $V=E/B$ then $E(i)=1/2mE^2/B^2$, and before we had got the ion spectrum say as $N=kE(i)^{-n}$. If B is known and E is responsible for such ion spectrum, how these two equations could be correlated?

 

[artis]

@naviakam where did you get these equations?

E is not directly responsible for ion spectrum. E field can accelerate charged particles like electrons or ions. It is easy to calculate the added KE for a single electron or electron beam in a E field. A plasma is different , first of all it consists of two main species of particles that are charged (electrons, ions) (more if you count neutrons and other particles) The average KE distribution within a plasma for a given species is the result of multiple processes not just E field.
In a Z pinch energy is given to the plasma by a fast high current discharge. Once the electric field breaks down the gas and ionizes it a current flow starts to happen. As the current flows it heats up the ionized gas rapidly , this heating is rapid in itself so the gas become fully ionized very quickly.
This is the first heating process, the next one is bit more complicated, as the gas is now ionized and a plasma it conducts current, the current continues to flow through it and a B field has been rising until the plasma reaches it's highest conductivity state and/or the power supply reaches it's current limit. At this point the current reaches a steady value, so does he B field.
While this was happening as the B field was increasing the plasma contracted more and more.
This action is similar to a piston compressing a gas. You decrease the available space for the ions and electrons so they rebound from one another at faster rates, their KE goes up.
While this is happening at the same time charged particles radiate, so one species heats up the other and vice versa via EM interactions like Compton scattering.
The ion spectrum for the time it lasts is a result of all these processes not just the E field.

 

[naviakam]

@naviakam where did you get these equations?

E is not directly responsible for ion spectrum. E field can accelerate charged particles like electrons or ions. It is easy to calculate the added KE for a single electron or electron beam in a E field. A plasma is different , first of all it consists of two main species of particles that are charged (electrons, ions) (more if you count neutrons and other particles) The average KE distribution within a plasma for a given species is the result of multiple processes not just E field.
In a Z pinch energy is given to the plasma by a fast high current discharge. Once the electric field breaks down the gas and ionizes it a current flow starts to happen. As the current flows it heats up the ionized gas rapidly , this heating is rapid in itself so the gas become fully ionized very quickly.
This is the first heating process, the next one is bit more complicated, as the gas is now ionized and a plasma it conducts current, the current continues to flow through it and a B field has been rising until the plasma reaches it's highest conductivity state and/or the power supply reaches it's current limit. At this point the current reaches a steady value, so does he B field.
While this was happening as the B field was increasing the plasma contracted more and more.
This action is similar to a piston compressing a gas. You decrease the available space for the ions and electrons so they rebound from one another at faster rates, their KE goes up.
While this is happening at the same time charged particles radiate, so one species heats up the other and vice versa via EM interactions like Compton scattering.
The ion spectrum for the time it lasts is a result of all these processes not just the E field.

The processes mentioned above are responsible not for very high energy part of the spectrum, then it is fairly safe to say that the MeV ions are due to the E only!
Therefore, if everything is neglected except E and B, and the ion KE is due to the presence of these two only, then the final step is to correlate it with the spectrum, I was wondering how to do such correlation.

 

[artis]

The processes mentioned above are responsible not for very high energy part of the spectrum, then it is fairly safe to say that the MeV ions are due to the E only!

What makes you think that ? It's a rather bold claim and I'm not sure it's correct. If I had to bet I'd say it isn't.

@naviakam This is the part I don't quite understand, you don't have the knowledge so you ask and that is fine, but then you go on and make your own assumptions, why?

Current ionizes and then heats up the gas rapidly, that is the first process but then the plasma is compressed which in a z pinch is the main heating process, rapid compression of a conducting plasma. E field doesn't compress the plasma, B field does but that doesn't mean the B field is directly responsible for particle heating. The B field here is like a piston, it constrains charged particle trajectories, it is this decrease in the available trajectory space that heats the plasma so rapidly.
Here is the interesting thing, not all Z pinches use current to directly influence plasma.
The Sandia Laboratories Z pinch machine for example implodes a cylindrical copper liner, basically a small closed tube with D-T gas inside.
The current runs through the copper liner and the gas is ionized by extremely rapid mechanical compression.
So how would you correlate E or B field with the plasma ion energies here?

Spoiler alert: you won't.
What happens here is you simply mechanically compress a gas to the point where it becomes plasma. If we would have a engine with pistons that could move fast enough and be strong enough to endure such pressures and heat we would pretty much be having fusion right now.

PS. Why fast enough? Because if you do it slowly you can still achieve the same pressure but your gas/plasma has lots of time to cool down by giving off heat/radiation to the surroundings.

 

[naviakam]

What makes you think that ? It's a rather bold claim and I'm not sure it's correct. If I had to bet I'd say it isn't.

@naviakam This is the part I don't quite understand, you don't have the knowledge so you ask and that is fine, but then you go on and make your own assumptions, why?

Current ionizes and then heats up the gas rapidly, that is the first process but then the plasma is compressed which in a z pinch is the main heating process, rapid compression of a conducting plasma. E field doesn't compress the plasma, B field does but that doesn't mean the B field is directly responsible for particle heating. The B field here is like a piston, it constrains charged particle trajectories, it is this decrease in the available trajectory space that heats the plasma so rapidly.
Here is the interesting thing, not all Z pinches use current to directly influence plasma.
The Sandia Laboratories Z pinch machine for example implodes a cylindrical copper liner, basically a small closed tube with D-T gas inside.
The current runs through the copper liner and the gas is ionized by extremely rapid mechanical compression.
So how would you correlate E or B field with the plasma ion energies here?

Spoiler alert: you won't.
What happens here is you simply mechanically compress a gas to the point where it becomes plasma. If we would have a engine with pistons that could move fast enough and be strong enough to endure such pressures and heat we would pretty much be having fusion right now.

PS. Why fast enough? Because if you do it slowly you can still achieve the same pressure but your gas/plasma has lots of time to cool down by giving off heat/radiation to the surroundings.

ٍE cross B is the drift velocity of the charged particle leading to $v=E/B$ which is independent of q and m. Then the ion energy is available from this velocity. Now this energy should be correlated with the ion spectrum. How that one is done?

 

[vanhees71]

As I said, that's the Hall effect (in the limit where the conductivity of the plasma is very large, i.e., $\sigma \rightarrow \infty$, you have $v=E/B$, because $\vec{E}+\vec{v} \times \vec{B} \stackrel{!}{=}0$ in this limit.