How about we call it an oscillating beam machine. (If in fact it is one - I lean in that direction, but the evidence is thin).Art Carlson wrote:Why not call it "cusp confinement", then?drmike wrote:Simon is right - "recirculation" is a bad term because it conjures up "circles".
"Bouncing" or "oscillation" makes a lot more sense.
All that can go wrong with recirculation
Engineering is the art of making what you want from what you can get at a profit.
I've thought about this very problem.
Lets start with a thought experiment, a magrid set to +30kV a vacuum vessel set to ground and a thermionic electron emitter placed at one point cusp set to +20kV, because the magrid is more positive than the emitter the electrons will be pulled towards it, but they cannot reach the vacuum vessel in this scenario.
I think everyone will agree on the last point, for to get an electron that was created on a 20kV surface to spontaneously travell and collide with a 0V surface would negate the need for any fusion reactions at all as you would have created a perpetual motion machine!!!
Thus the electrons can only intersect the surface of the magrid from an electrostatic point of view, but negating corners the magrid is insulated from them magnetically, so that just leaves our first emitter for them to intersect and they simply intersect that at the birth potential and so don't lose energy (ignoring upscattering an down scattering)
Now let's add a neutral gas in at the edge, the ions fall from their birth potential inside the magid at 30kV to the central virtual cathode potential of 20kV picking up 10kV of kinetic energy. The electrons from the newly ionized gas are trapped on the magnetic fieldlines and are created at 30kV and hover around this potential, they cannot reach either the 20 kV source or the 0V vacuum vessel, infact the only thing they can reach is the magrid. If they are properly magnetically insulated from this it is unclear what they will do.
I think the idea is these slow electrons from the newly ionized gas make their way back to the magrid somehow, but because they were born at a similar voltage, do not give up that much energy on collission, they are then replaced by more energetic convergent electrons from the emitter thereby moving the quasineutral plasma into the centre of the magrid.
At high densities inside the cusps and low densities outside, in order for the bulk electrons to escape through the cusps they would have to establish a huge local electric field (in the opposite direction to that confining the ions), however if they did that as they tried to escape through the cusps they would loose all their parallel velocity, would no longer be inside the loss cone and get refected back, if on the otherhand the ions move ahead of the electrons then they will suck electrons after them enhancing cusp losses, so the ions must lead the way. If you can imagine an ion at the edge of the polywell it is at 30kV and sees an electric field pointin to ground so from there its plane sailing all the way to the vacuum chamber wall with the electrons neutralizing it from behind.
That is, if there is no potential hump of positive charge at the entrance of the cusps which there might be. The paradox here is if there is a potential barrier at the edge of the well stopping the ions from reaching the cusps then the electrons will be drawn towards it in copious quanties if the polywell is at a high density, this will neutralize the well and allow the ions to penetrate, thus one can infer that at high densities, all potential barriers towards the cusps are broken.
Another note of interest with regard to the ions leading the way towards the vacuum vessel, they cannot stray far from the electron larmor orbit as the electrons will not be able to follow them across fieldlines in order to neutralize them so the loss hole is of order the electron larmor radius rather than the ion larmor radius. Additionally The fact that they are not free to stray an ion larmor radius away from the electrons means that they bounce about the potential of a flux tube one electron larmor rdius thick rather than an ion larmor radius.
Lets start with a thought experiment, a magrid set to +30kV a vacuum vessel set to ground and a thermionic electron emitter placed at one point cusp set to +20kV, because the magrid is more positive than the emitter the electrons will be pulled towards it, but they cannot reach the vacuum vessel in this scenario.
I think everyone will agree on the last point, for to get an electron that was created on a 20kV surface to spontaneously travell and collide with a 0V surface would negate the need for any fusion reactions at all as you would have created a perpetual motion machine!!!
Thus the electrons can only intersect the surface of the magrid from an electrostatic point of view, but negating corners the magrid is insulated from them magnetically, so that just leaves our first emitter for them to intersect and they simply intersect that at the birth potential and so don't lose energy (ignoring upscattering an down scattering)
Now let's add a neutral gas in at the edge, the ions fall from their birth potential inside the magid at 30kV to the central virtual cathode potential of 20kV picking up 10kV of kinetic energy. The electrons from the newly ionized gas are trapped on the magnetic fieldlines and are created at 30kV and hover around this potential, they cannot reach either the 20 kV source or the 0V vacuum vessel, infact the only thing they can reach is the magrid. If they are properly magnetically insulated from this it is unclear what they will do.
I think the idea is these slow electrons from the newly ionized gas make their way back to the magrid somehow, but because they were born at a similar voltage, do not give up that much energy on collission, they are then replaced by more energetic convergent electrons from the emitter thereby moving the quasineutral plasma into the centre of the magrid.
At high densities inside the cusps and low densities outside, in order for the bulk electrons to escape through the cusps they would have to establish a huge local electric field (in the opposite direction to that confining the ions), however if they did that as they tried to escape through the cusps they would loose all their parallel velocity, would no longer be inside the loss cone and get refected back, if on the otherhand the ions move ahead of the electrons then they will suck electrons after them enhancing cusp losses, so the ions must lead the way. If you can imagine an ion at the edge of the polywell it is at 30kV and sees an electric field pointin to ground so from there its plane sailing all the way to the vacuum chamber wall with the electrons neutralizing it from behind.
That is, if there is no potential hump of positive charge at the entrance of the cusps which there might be. The paradox here is if there is a potential barrier at the edge of the well stopping the ions from reaching the cusps then the electrons will be drawn towards it in copious quanties if the polywell is at a high density, this will neutralize the well and allow the ions to penetrate, thus one can infer that at high densities, all potential barriers towards the cusps are broken.
Another note of interest with regard to the ions leading the way towards the vacuum vessel, they cannot stray far from the electron larmor orbit as the electrons will not be able to follow them across fieldlines in order to neutralize them so the loss hole is of order the electron larmor radius rather than the ion larmor radius. Additionally The fact that they are not free to stray an ion larmor radius away from the electrons means that they bounce about the potential of a flux tube one electron larmor rdius thick rather than an ion larmor radius.
What kind of electron temperatures and densities were at the centre of the device when said measurements were taken?rnebel wrote:Perhaps I am misunderstanding this discussion, but there are electrostatic fields along the cusp lines. We've measured them with emissive probes. If they weren't there, I don't see how the electrons would enter the device.
Art - I think "cusp confinement" is "politically incorrect" since Bussard wanted to point out this idea is similar to IEC. My original concept of "recirculation" and then reading up on things got me mightily confused, so it'd be good if we can avoid that confusion in the future. Doesn't matter what it's called, so long as it actually works.
jmc - If the electron guns are opposite each other, either on corners or faces you would hope that collisions in the center will force the majority of electrons off the cusp line so they will be trapped by the magnetic field. If they stay on the cusp line, they will just go out the other side and you get no confinement.
Bussard mentions 3 regions: The center core, an adiabatic zone, and the mirror reflection zone. At start up the device is all mirror reflection, then as density increases it is supposed to build up the other zones. It'd be nice to understand how this is supposed to work. I don't quite get it yet, but hopefully with a little math I can begin to figure it out.
jmc - If the electron guns are opposite each other, either on corners or faces you would hope that collisions in the center will force the majority of electrons off the cusp line so they will be trapped by the magnetic field. If they stay on the cusp line, they will just go out the other side and you get no confinement.
Bussard mentions 3 regions: The center core, an adiabatic zone, and the mirror reflection zone. At start up the device is all mirror reflection, then as density increases it is supposed to build up the other zones. It'd be nice to understand how this is supposed to work. I don't quite get it yet, but hopefully with a little math I can begin to figure it out.
Re: Excuse my ignorance
In polywell orthodoxy the ions run out of energy before they can reach the edge of the potential well. So except for up-scattering there are no ions reaching the edge of the well.Art Carlson wrote:The only loophole I can see at the moment is that if the ions are cold at the edge (as they are according to polywell othodoxy)
(emphasis added)Art Carlson wrote:Since the ions are only confined electrostaticly by the electrons, they can only be where electrons are, but they can be everywhere that electrons are.
Incorrect. The ions are confined in a potential well created by the electrons, and only have energy to climb so high within that well. If the well is deeper than the ion energy, there are portion of the well the ions can't reach, and the profile of the well at those areas the ions can't reach is of no importance to ion confinement.
Related to the ion convergence thread, the edge of the electron cloud is bound to deviate from a sphere. But how much would the portion of the well the ions can reach deviate from a sphere?
Depends on how close the "wiffle-ball" gets to the coils. The closer it gets, the more distortion you would expect.
The potential is going to be shaped by the electrons, and they follow the B field lines, so the more currents you have running close to the MaGrid coils, the more distortions from spherical you will have in the potential distribution.
I would expect it is a second order affect. We still have to see if zeroth order will work yet!
The potential is going to be shaped by the electrons, and they follow the B field lines, so the more currents you have running close to the MaGrid coils, the more distortions from spherical you will have in the potential distribution.
I would expect it is a second order affect. We still have to see if zeroth order will work yet!
Re: Excuse my ignorance
I don't get this. How come the ions can be everywhere the electrons are? Ions aren't confined by a sphere of electrons. They are simply heavily attracted to the charge of the mass of electrons in the center. They keep having to dive back in. That was my picture. How they overcome that massive attraction and suddenly start following some far less heavily charged gang of rouge electrons that are populating your blowfish spike, I don't understand.Art Carlson wrote: You can start with a sphere of electrons confining a sphere of ions, but when you add the cusps, electrons leak out along them, so your electron sphere now has spikes like a blowfish. Since the ions are only confined electrostaticly by the electrons, they can only be where electrons are, but they can be everywhere that electrons are. So the ions start creeping out along the spikes, too. You might think of the cusps as a tunnel that allows the ions to get through the wall of high potential and hemorrhage into space.
If I stand at the bottom of Mt Everest, there isn't any chance that I may suddenly be pulled to the top by the force of gravity of some random outcrop of rocks up there.
Can you explain this further?
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Art Carlson
- Posts: 794
- Joined: Tue Jun 24, 2008 7:56 am
- Location: Munich, Germany
Re: Excuse my ignorance
My mantra is "quasineutrality". If there is a region of a significant size, with a significant density of electrons, and the density of ions there is significantly lower, then there will be a big mother electric potential. More precisely, the densities can only differ on a scale of the Debye length or less. Somewhere above I did an illustrative calculation of this effect.hanelyp wrote:In polywell orthodoxy the ions run out of energy before they can reach the edge of the potential well. So except for up-scattering there are no ions reaching the edge of the well.Art Carlson wrote:The only loophole I can see at the moment is that if the ions are cold at the edge (as they are according to polywell othodoxy)
(emphasis added)Art Carlson wrote:Since the ions are only confined electrostaticly by the electrons, they can only be where electrons are, but they can be everywhere that electrons are.
Incorrect. The ions are confined in a potential well created by the electrons, and only have energy to climb so high within that well. If the well is deeper than the ion energy, there are portion of the well the ions can't reach, and the profile of the well at those areas the ions can't reach is of no importance to ion confinement.
Related to the ion convergence thread, the edge of the electron cloud is bound to deviate from a sphere. But how much would the portion of the well the ions can reach deviate from a sphere?
It is possible that the potential well is too deep for the ions to get out, but that voltage drop must be across vaccum. Either the electrons are already up against the magnetic wall, or both species are back from it, in which case they will stream together at the sound speed until they reach the wall. Once both electrons and ions are at the magnetic "wall", the electrons can start leaking out through the cusps, and the ions can follow them.
Except for possible convergence effects (if convergence would work), this effect results in a flat potential over most of the volume, a feature you can see in Bussards simulation results (at least the ones he made on Tuesdays).
Sure, but what's significant? Only 1/1000th (1/10,000th if we're being nice to Bussard) will be outside the cusps, so the proportion of electrons in the cusp channels themselves must be very tiny indeed.If there is a region of a significant size, with a significant density of electrons, and the density of ions there is significantly lower, then there will be a big mother electric potential.
It seems unlikely the ions would follow the tiny percentage of electrons in the cusps. The electrons in an IEC machine form a potential well that peaks at the center; this was disputed for decades but recently LIF has shown it pretty clearly. The ions see the bottom of this well and move toward it.Once both electrons and ions are at the magnetic "wall", the electrons can start leaking out through the cusps, and the ions can follow them.
Cusp confinement questions
Reading the various posts I'm becoming more enlightened and confused at the same time.
My current impressions:
When a charged particle enters a 'cusp' there are three possibilities (in an isolated system)-
1) it has enough kinetic energy to escape in a hyperbolic path and is lost.
2) it is traped in the cusp and ocillates back and forth.
3) it orbits the magnet on the same field line. Or takes a parabolic orbit that brings it back to the central portion of the well, where the electron is diverted and rejoins the general population.
It also could stop befor becoming 'commited' to the cusp, possibly from a combination of deflections or vecter changes from electrostatic fields and the effects of the magnetic field.
In the second possibility the electron( in this case ) would have a semiperminate presence within the cusp and I could see this being an electrostatic 'plug' against other electrons entering the cusp. A positively charged ion would have a similar effect on other ions, but the effect would be less because of the lower concentration in the central portions of the cusp. Since the electron is so much lighter than an ion, I'm guessing that a much larger portion of them would have much shorter osillation ranges that would keep them within the narrow and congested regions of the cusps. I know that if an equvalent number of pos. ions were present they would essentially tug the electon's osillation lengths to match their own, but the proportion of pos. ions is much, much less due to the presumed sucessful electrostatic confinement.
Because of the pos. charge on the magrid the 3rd possibility would result in a tighter orbit-for electrons, which would help prevent the electron from hitting the vacuum vessel wall, untill it was diverted by a close encounter with a pos. ion inside the magnets and reentered the general electron population in the well.
Also, considering the positively charged magrid and the geometry of the 'cusps' the cusp traped electrons might migrate towards the closest points between the magnets ( where the positive electrostic field is strongest) untill they strike the bridging supports and are lost. I wounder if this is why a magrid with more faces is expected to be be more efficient. Well, that and I presume steeper, narower cusps. Is this what Bussard was thinking when he described them as "funny cusps" as opposed to line cusps? As the electrons migrated towards these midpoints between the magnets they would become more concentrated and 'plug' the 'line portions' of the cusps even better. And as thy became more concentrated they would repell each other more. Would this increase or decrease the electron loses from finally reaching and hitting the bridging supports?
Even based on these very simple (and hopefully acurate discriptions) the possible permutations are inspiring. I can see why predicting plasma behavior when dealing with large populations becomes increasingly more difficult and fragile.
Dan Tibbets
My current impressions:
When a charged particle enters a 'cusp' there are three possibilities (in an isolated system)-
1) it has enough kinetic energy to escape in a hyperbolic path and is lost.
2) it is traped in the cusp and ocillates back and forth.
3) it orbits the magnet on the same field line. Or takes a parabolic orbit that brings it back to the central portion of the well, where the electron is diverted and rejoins the general population.
It also could stop befor becoming 'commited' to the cusp, possibly from a combination of deflections or vecter changes from electrostatic fields and the effects of the magnetic field.
In the second possibility the electron( in this case ) would have a semiperminate presence within the cusp and I could see this being an electrostatic 'plug' against other electrons entering the cusp. A positively charged ion would have a similar effect on other ions, but the effect would be less because of the lower concentration in the central portions of the cusp. Since the electron is so much lighter than an ion, I'm guessing that a much larger portion of them would have much shorter osillation ranges that would keep them within the narrow and congested regions of the cusps. I know that if an equvalent number of pos. ions were present they would essentially tug the electon's osillation lengths to match their own, but the proportion of pos. ions is much, much less due to the presumed sucessful electrostatic confinement.
Because of the pos. charge on the magrid the 3rd possibility would result in a tighter orbit-for electrons, which would help prevent the electron from hitting the vacuum vessel wall, untill it was diverted by a close encounter with a pos. ion inside the magnets and reentered the general electron population in the well.
Also, considering the positively charged magrid and the geometry of the 'cusps' the cusp traped electrons might migrate towards the closest points between the magnets ( where the positive electrostic field is strongest) untill they strike the bridging supports and are lost. I wounder if this is why a magrid with more faces is expected to be be more efficient. Well, that and I presume steeper, narower cusps. Is this what Bussard was thinking when he described them as "funny cusps" as opposed to line cusps? As the electrons migrated towards these midpoints between the magnets they would become more concentrated and 'plug' the 'line portions' of the cusps even better. And as thy became more concentrated they would repell each other more. Would this increase or decrease the electron loses from finally reaching and hitting the bridging supports?
Even based on these very simple (and hopefully acurate discriptions) the possible permutations are inspiring. I can see why predicting plasma behavior when dealing with large populations becomes increasingly more difficult and fragile.
Dan Tibbets
To error is human... and I'm very human.
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Art Carlson
- Posts: 794
- Joined: Tue Jun 24, 2008 7:56 am
- Location: Munich, Germany
This was in response to hanelyp, who was talking about the large scale potential well in the high density central region, where my arguments certainly apply.TallDave wrote:Sure, but what's significant? Only 1/1000th (1/10,000th if we're being nice to Bussard) will be outside the cusps, so the proportion of electrons in the cusp channels themselves must be very tiny indeed.If there is a region of a significant size, with a significant density of electrons, and the density of ions there is significantly lower, then there will be a big mother electric potential.It seems unlikely the ions would follow the tiny percentage of electrons in the cusps. The electrons in an IEC machine form a potential well that peaks at the center; this was disputed for decades but recently LIF has shown it pretty clearly. The ions see the bottom of this well and move toward it.Once both electrons and ions are at the magnetic "wall", the electrons can start leaking out through the cusps, and the ions can follow them.
Still, I have also been applying them to cusp loss, which has a much smaller spatial scale, so it is reasonable to ask if quasineutrality also holds there. My picture is a straw attached to a balloon through which electrons can freely flow. The diameter of the straw is a few electron gyroradii. With acoustic flow, the density in the straw should be a significant fraction (1/2, for example) of the density in the balloon. If the Debye length is much less than the diameter of the straw, then I would expect ions to be sucked in to neutralize the electrons. If the Debye length is large, then I wouldn't be surprized if the beam is purely electrons. So the question is the ratio of gyroradius to Debye length, which is equal to the ratio of the electron plasma frequency to the electron gyrofrequency. Whipping out my NRL Formulary, I see that this ratio (blame Huba for the Gaussian units) is
omega_pi/omega_ce = 3.21e-3 (n_e/cm^-3)^1/2 * (B/G)^-1
Note that
beta = 4.03e-11 * (n/cm^-3) * (T/eV) * (B/G)^-2,
so we can also write
omega_pi/omega_ce = 3.21e-3 * sqrt[ beta / (4.03e-11*(T/eV)) ]
= sqrt[ beta / (T/(250 keV)) ]
Since we should have beta = 1 and T ~ 100 keV, Debye length and gyroradius will be the same order of magnitude.
Rats. What conclusion can we draw from that?
It is my understanding that "funny cusps" result from magnetic fields that intersect the metal used to contain the magnets. Thus, "square" cross-section magnets create funny cusps, while "circular" cross-section (i.e. toroidal) magnets, spaced greater than the electron gyroradius, do not. Also, Bussard's "funny cusps" always refer to line cusps, but not all line cusps are funny. For example, in the toroidal pollywells (WB 6 and 7) the line cusps are not "funny cusps". Funny cusps were a source of major electron loss in earlier WB models.Is this what Bussard was thinking when he described them as "funny cusps" as opposed to line cusps?
(Unless I'm wrong
)And better qualified experts abound here.
Heh, that we need experimental data.If the Debye length is much less than the diameter of the straw, then I would expect ions to be sucked in to neutralize the electrons. If the Debye length is large, then I wouldn't be surprized if the beam is purely electrons...Debye length and gyroradius will be the same order of magnitude.
Rats. What conclusion can we draw from that?
Also: in addition to the electron well at the center, you also have the large positive charge on the Magrid. If the ions can see it, that will tend to push them back as well.
I'm sorry it took so long to reply. I decided it would be better to have something to look at instead of just trying to reason it out. So I hacked together a method to determine the steady state potential along the cusp axis, outside the machine. In this I assume the drive potential is from a sphere (ie the magrid) with radius 0.25m at 10kV, and the wall is at radius 1m at 0v. Also the electrons are confined only to the cusp axis; your straws that are coming out of the balloon. The program determins a charge distribution based on the potential by assuming the kinetic energy is inverse to the potential energy, obtaining the velocity which gives the amount of time the electrons spends in each delta-R segment. Normalizing give the distribution for one electron, then multiply by the total number and elementary charge to get the charge distribution. That is then recalculated iteratively producing new potentials and distributions etc.Art Carlson wrote:I'm with you. Please go on. I'm especially interested in the part about how you recirculate electrons when there are none outside the machine.kcdodd wrote:Well, as I see it there are only two possibilities for keeping the potential in the outer region within the boundaries of the machine. Either there are ions there to balance the electron's charge, as you say, or the electron density is just not very high outside to begin with. And, like I already said, I don't see how you could hope to keep even one ion in that region, much less get a high density. So assuming that ions cant stay in the outer region that only leaves the electron density outside being rather low, at least to the point that the potential generated from the spatial electron's is below that generated between the magrid and wall from the external power source.
Let me know if we are agreeing or not on those two points before I go on.
The potential energy is as seen from the electron, not the absolute voltage. I included an animation so you could see how the simulation works. But keep in mind the dynamic is non-physical. What it is doing is attempting to converge to a steady state solution for the potential. The discretization and steping seems to result in a lot of noise in the plateau region. But hopfully it's clear enough what the trend is.
This is with 1e14 electrons. As you can see, it attempts to converge pushing to potential gradient closer to the magrid. However, the electron density after the potential plateaus is very small. It is pushed toward the magrid as well. The first picture is after the first iteration. The potential spike is the result of all the electrons from the first step. The second picture is the result of 100 iterations, as it seemed to stop changing significantly. Third link is the animation, requires divx codec.
http://www.andromedaspace.com/files/dyn ... 000001.png
http://www.andromedaspace.com/files/dyn ... 000100.png
http://www.andromedaspace.com/files/1e14.avi
This is with 1e15 electrons. The gradient is pushed almost all the way to the magrid. Pictures mean the same as with 1e14 pics just with higher density.
http://www.andromedaspace.com/files/dyn ... 000001.png
http://www.andromedaspace.com/files/dyn ... 000100.png
http://www.andromedaspace.com/files/1e15.avi
So, what I think this shows is that you can have great density near the core, but very small density outside as you increase core density. This is a result just of potential equilibrium.
Carter
The thing which has been left out of the discussion in this thread is the role that electron inertia plays in maintaining these discharges. If you were to turn off the electrostatic drive or you had electrons with an infinite confinement time, then potentials would equilibrate along flux surfaces as well as the ions and electrons. Basically, Art has described the plasma in the thermalized limit.
However, that’s not how these systems work. Inertia is continually injected into the electrons through the electric field and the electrons aren’t confined long enough to thermalize. As far as electrostatics are concerned, the direction parallel to the magnetic field looks just like there is no magnetic field there at all. Consequently, you expect it to behave much like a gridded system does. It’s well established that you can convert electron inertia into electrostatic fields in the gridded systems. If you want some experimental evidence for that, look at
J. Park, R. A. Nebel, W. G. Rellergert, M. D. Sekora, "Experimental Studies of
Electrostatic confinement on the Intense Neutron Source-Electron (INS-e)
Device", Physics of Plasmas 10, 3841 (2003).
R. A. Nebel, S. Stange, J. Park, J. M. Taccetti, S. K. Murali, C. E. Garcia,
“Theoretical and Experimental Studies of Kinetic Equilibrium and Stability in
the Virtual Cathode of the Intense Neutron Source (INS-e) Device”, Physics of
Plasmas 12, 12701 (2005).
J. Park, R. A. Nebel, S. Stange, S. K. Murali, “Experimental Observation
of the Periodically Oscillating Plasma Sphere (POPS) Oscillation in a Gridded
Inertial Electrostatic Confinement Device”, Phys. Rev. Lett. 95, 15003 (2005).
J. Park, R. A. Nebel, S. Stange, S. K. Murali, “Periodically Oscillating Plasma
Sphere (POPS)”, Physics of Plasmas 12, 056315 (2005).
These aren’t the original references, and of course the original idea dates back to Farnsworth in the 50s. You can see some of the early work on this in:
W. C. Elmore, J. L. Tuck, and K. M. Watson, Phys. Fluids 2, 239 (1959).
P. T. Farnsworth, U.S. Patent No. 3, 358, 402 (28 June, 1966).
R. L. Hirsch and G. A. Meeks, U.S. Patent No. 3,530,497 (22 September,
1976)
One way to make this work is to make the electron particle confinement time less than the thermalization time. That’s true in the present generation machines.
However, that’s not how these systems work. Inertia is continually injected into the electrons through the electric field and the electrons aren’t confined long enough to thermalize. As far as electrostatics are concerned, the direction parallel to the magnetic field looks just like there is no magnetic field there at all. Consequently, you expect it to behave much like a gridded system does. It’s well established that you can convert electron inertia into electrostatic fields in the gridded systems. If you want some experimental evidence for that, look at
J. Park, R. A. Nebel, W. G. Rellergert, M. D. Sekora, "Experimental Studies of
Electrostatic confinement on the Intense Neutron Source-Electron (INS-e)
Device", Physics of Plasmas 10, 3841 (2003).
R. A. Nebel, S. Stange, J. Park, J. M. Taccetti, S. K. Murali, C. E. Garcia,
“Theoretical and Experimental Studies of Kinetic Equilibrium and Stability in
the Virtual Cathode of the Intense Neutron Source (INS-e) Device”, Physics of
Plasmas 12, 12701 (2005).
J. Park, R. A. Nebel, S. Stange, S. K. Murali, “Experimental Observation
of the Periodically Oscillating Plasma Sphere (POPS) Oscillation in a Gridded
Inertial Electrostatic Confinement Device”, Phys. Rev. Lett. 95, 15003 (2005).
J. Park, R. A. Nebel, S. Stange, S. K. Murali, “Periodically Oscillating Plasma
Sphere (POPS)”, Physics of Plasmas 12, 056315 (2005).
These aren’t the original references, and of course the original idea dates back to Farnsworth in the 50s. You can see some of the early work on this in:
W. C. Elmore, J. L. Tuck, and K. M. Watson, Phys. Fluids 2, 239 (1959).
P. T. Farnsworth, U.S. Patent No. 3, 358, 402 (28 June, 1966).
R. L. Hirsch and G. A. Meeks, U.S. Patent No. 3,530,497 (22 September,
1976)
One way to make this work is to make the electron particle confinement time less than the thermalization time. That’s true in the present generation machines.