Black body radiation vs electric discharge in a gas

[BvU]

This is exactly what it is: a small volume heats up for a ns time scale, then the ions distribution similar to that of MB is generated!
I want to understand how sensible it is physically to have such distribution for ions at high energies which behave like a BB radiation with similar curve, total power and peak.

I'm still puzzled by the tenacity to pin an underlying distribution on such meagre data. So far I 've only seen this data

And when I try to generate the two distributions (granted: meagre attempt):

(actually $x^2\,e^{-x^2}\$ and $5.7\, x^3/(e^x - 1) \$ )
the data can't distinguish between the two (and a gaussian or Poisson, Lorentzian, Voigt, ...).

Do you happen to have a statistically useful high-volume, wide energy range, set of data to subject to a decisive fitting procedure or does this all remain conjecture ?

$\$

 

[naviakam]

I'm still puzzled by the tenacity to pin an underlying distribution on such meagre data. So far I 've only seen this data
View attachment 277126

And when I try to generate the two distributions (granted: meagre attempt):

View attachment 277127​

(actually $x^2\,e^{-x^2}\$ and $5.7\, x^3/(e^x - 1) \$ )
the data can't distinguish between the two (and a gaussian or Poisson, Lorentzian, Voigt, ...).

Do you happen to have a statistically useful high-volume, wide energy range, set of data to subject to a decisive fitting procedure or does this all remain conjecture ?

$\$

Our lecturer didn't provide us with more information but said that the data is similar to that of MB. The figure I put here was from a reference, however I couldn't find anymore.
We must see if the question in post #35 is valid.

 

[artis]

No @naviakam I'm not sure why you want that Boltzmann distribution so badly for the low pressure gas discharge, is that distribution on the FBI's most wanted list?...

Low pressure gas discharges don't produce anything resembling a BB distribution
They produce a sharp peak and that's it. The spectral lines of lower energy are then added by either a mixture of other gasses or phosphors. And yet still they don't reproduce a BB spectrum.
I think you are now mixing stuff up, before you wanted to have the distribution for ions in plasma now you want it for low pressure gas discharge.

I can't say about the plasma ions as that would need more research from my side but I can surely tell you there is no BB curve for a low pressure gas discharge.
The simple test is to ask whether the object emitting the radiation is hot or cold. low pressure gas discharge tubes are cold yet shine bright , this gives you the answer.
Thermal plasma at high energies is a different subject, there at least the energies are distributed equally and a curve energy diagram could be drawn for each of the species.

The answer to the question in post #35 is No.
You are missing a lot of energy in the single peak gas discharge. To make an object emit at a BB spectrum requires much more energy input to raise the average KE energies of the particles.

 

[naviakam]

No @naviakam I'm not sure why you want that Boltzmann distribution so badly for the low pressure gas discharge, is that distribution on the FBI's most wanted list?...

Low pressure gas discharges don't produce anything resembling a BB distribution
They produce a sharp peak and that's it. The spectral lines of lower energy are then added by either a mixture of other gasses or phosphors. And yet still they don't reproduce a BB spectrum.
I think you are now mixing stuff up, before you wanted to have the distribution for ions in plasma now you want it for low pressure gas discharge.

I can't say about the plasma ions as that would need more research from my side but I can surely tell you there is no BB curve for a low pressure gas discharge.
The simple test is to ask whether the object emitting the radiation is hot or cold. low pressure gas discharge tubes are cold yet shine bright , this gives you the answer.
Thermal plasma at high energies is a different subject, there at least the energies are distributed equally and a curve energy diagram could be drawn for each of the species.

The answer to the question in post #35 is No.

Low pressure gas discharge?!

 

[BvU]

Our lecturer didn't provide us with more information but said that the data is similar to that of MB.

Oh boy, are we dealing with a homework exercise (with a known answer $-$ thus making fools of ourselves ) or with a professor with a conjecture, who is testing the waters and let's the students do the work ?

With hindsight I'm glad I took some life insurance in post #10

Can't wait to see how this develops further -- do let us know !

$\$

 

[naviakam]

To summarize:
1. Our spectrum although not continuous but follows the MB distribution
2. Peak and total power is similar to the BB radiation, furthermore we could estimate the temperature in the gas correctly by considering MB dist
3. The spectrum is for intensity against ion energy
4. The ion energy is from keV to MeV
5. Our spectrum is obtained from applying potential in an ionized gas
6. My question was to see if it is correct to consider such spectrum as an MB distribution?

 

[naviakam]

I found this explanation in an article that probably describe what I am looking for but ask to help me to understand it:

I am trying to find the equation responsible for ion spectrum. I found this paper but don't get the point for some parts. The section I put above is everything I want to realize in simple words.
The current have magnetic field around it, but here the current is a ring , r, once contracting toward axis, z, create B in theta direction and E in z. How this is explained?

 

[naviakam]

Text format of the image above:
This model assumes an axisymmetric, cylindrical current distribution j(r, t) which is finite in thickness and initially annular in shape. The distribution is then assumed to contract rapidly to the axis in some manner. Such a time variation in the current density gives rise to both an azimuthal magnetic field By(r, t) and an axial electric field E(r, t) whose values are derived from Maxwell’s equations:

d(rB)/dr=rj(r,t)

dE/dr=dB/dt

The equation of motion in two dimensions is

mr’’ = -ez’B (r, t),

mz’’ = er’B (r, t) +eE(r, t)

where m is the ion mass, e is the ionic charge, and r’ and z’ are the velocity components.

 

[naviakam]

Maxwell equations:

Cylindrical coordinates:

 

[vanhees71]

It would help a lot to quote the paper properly. Maybe somebody can help then. For me there's not enough context to know what the question is. Is it about the calculation of the em. field? Then just use the retarded potentials. Is it about a self-consistent solution of the equation of motion of some charge-current distribution and the em. field? Then it's more complicated but perhaps doable due to high symmetry.

 

[naviakam]

It would help a lot to quote the paper properly. Maybe somebody can help then. For me there's not enough context to know what the question is. Is it about the calculation of the em. field? Then just use the retarded potentials. Is it about a self-consistent solution of the equation of motion of some charge-current distribution and the em. field? Then it's more complicated but perhaps doable due to high symmetry.

It says that current density changes (while it is a annular) leads to azimuthal B and axial E. I don't know how this happens.
Then based on this, and using Cylindrical Maxwell two equations appeared in the paper which I don't know mathematically how they are obtained.
And finally how E and B are used to obtain the energy from equation of motion presented in the paper?
Full paper attached.

 

[artis]

@naviakam what is the thing that you want to understand here ? I am asking because if it's simply ion or electron energy distribution within a plasma then why make it more complicated by introducing an electric discharge pinch device?

You might as well just analyze a plasma at thermal equilibrium which means that the temperature is similar between ions and electrons but if you only care about one species distribution then you might as well take as an example a plasma that is not in thermal equilibrium. Although I think it is easier to estimate the electron temperature distribution than the ion one.

I think you can see from the paper you attached that determining ion energies in a plasma that changes it's energy fast or basically a gas that gets ionized rapidly and compressed due to current discharge is quite complicated and there is no "plug n play" type mechanism or "probe" which you could stick in such a plasma to know the ion distribution.
Getting to this parameter requires some painfully complicated maths and analyzing , like if you have a certain plasma volume and pressure and you get say neutrons as a byproduct then you would analyze their energy and flux to then estimate the number of fusion reactions taking place that made them versus the number of ions total which would then give you a rough estimate of the ion energy distribution.
Although I'm sure members like @mfb or @vanhees71 or @BvU could explain this better

 

[naviakam]

@naviakam what is the thing that you want to understand here ? I am asking because if it's simply ion or electron energy distribution within a plasma then why make it more complicated by introducing an electric discharge pinch device?

You might as well just analyze a plasma at thermal equilibrium which means that the temperature is similar between ions and electrons but if you only care about one species distribution then you might as well take as an example a plasma that is not in thermal equilibrium. Although I think it is easier to estimate the electron temperature distribution than the ion one.

I think you can see from the paper you attached that determining ion energies in a plasma that changes it's energy fast or basically a gas that gets ionized rapidly and compressed due to current discharge is quite complicated and there is no "plug n play" type mechanism or "probe" which you could stick in such a plasma to know the ion distribution.
Getting to this parameter requires some painfully complicated maths and analyzing , like if you have a certain plasma volume and pressure and you get say neutrons as a byproduct then you would analyze their energy and flux to then estimate the number of fusion reactions taking place that made them versus the number of ions total which would then give you a rough estimate of the ion energy distribution.
Although I'm sure members like @mfb or @vanhees71 or @BvU could explain this better

Now what I need to understand is from basic physics and math:
how the current density here produces such B and E in the mentioned directions. Then how the Maxwell and coordinate gives this B and E. And finally how to use B and E to estimate energy from provided equation of motion.
Everything is available, current configuration, and formula but I need someone to explain in simple words!

 

[artis]

@naviakam So you say you just need to understand

basic physics and math:

yet you go on to describe very complicated setup and conditions which are normally analyzed by people working decades in the field or folks writing PhD papers.
And then lastly you say

but I need someone to explain in simple words!

from which I see you don't understand the concepts as they are complicated ,so how about accepting the given advice and learning the basics first?

 

[naviakam]

@naviakam So you say you just need to understand

yet you go on to describe very complicated setup and conditions which are normally analyzed by people working decades in the field or folks writing PhD papers.
And then lastly you sayfrom which I see you don't understand the concepts as they are complicated ,so how about accepting the given advice and learning the basics first?

It's for our BSc course to understand how the Maxwell in a Cylinder gives the B and E in first equations based on the assumptions made.
Then from equation of motion, calculate the energy. Seems that I should be able to understand it but couldn't do that. Then I must understand in simple words.

 

[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?