Black body radiation vs electric discharge in a gas

[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.