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Point out news stories, on the net or in mainstream media, related to polywell fusion.

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93143
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Postby 93143 » Mon Aug 08, 2011 3:18 am

Joseph Chikva wrote:
93143 wrote:Also, it strikes me (without having done the math) that even a fully-thermalized ion population wouldn't match the electron pressure, since the ion energy is due to the potential well. You'd have to get the ion-electron collisional energy exchange rate involved, and that's a pretty slow process...

Also without having done the math it strikes me that not ion-electron but ion-ion collisions would make more significant contribution in thermalization. And if so, that process may be not so slow as you think.

No, I mean that if you want a thermalized ion population to be hitting the magnetic field as hard as the electron population is, you will have to heat it, because otherwise it's not going to have the necessary reach, because its average energy doesn't change (actually it would go down, since upscattered ions that escape through the cusps don't come back). The obvious way to heat the ions is via collisions with the electrons, which is slow.

I know ion-ion is fast. It's also supposed to be subject to annealing, which would slow down the global thermalization rate considerably.

scattering cross-section is very big at the edge (but rare plasma), lower in the core but have significant value and particles permanently oscillate there-here (edge-core, core-edge).

The ion density at the edge is actually quite high. For constant flux, it's inversely proportional to the velocity, which gets very low at the edge. This combination of high density, high residence time, and high cross section is what makes annealing work.

Also we should recall that in case of significant fusion rate alphas also will take very significant part in thermalization.

Alphas are not well contained. The cusps look fairly large to them, so they don't last more than about 10^3 passes, according to Rick Nebel. (I believe they had a method of exciting the lower-energy alphas, perhaps with RF resonance or some such, to prevent them from contaminating the core.)

This is also one reason why the neutron rate for a p-¹¹B reactor is supposed to be so low - the alphas don't stay in the plasma long enough to fuse much.

Joseph Chikva
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Postby Joseph Chikva » Mon Aug 08, 2011 4:36 am

93143 wrote:
Joseph Chikva wrote:
93143 wrote:Also, it strikes me (without having done the math) that even a fully-thermalized ion population wouldn't match the electron pressure, since the ion energy is due to the potential well. You'd have to get the ion-electron collisional energy exchange rate involved, and that's a pretty slow process...

Also without having done the math it strikes me that not ion-electron but ion-ion collisions would make more significant contribution in thermalization. And if so, that process may be not so slow as you think.

No, I mean that if you want a thermalized ion population to be hitting the magnetic field as hard as the electron population is, you will have to heat it, because otherwise it's not going to have the necessary reach, because its average energy doesn't change (actually it would go down, since upscattered ions that escape through the cusps don't come back). The obvious way to heat the ions is via collisions with the electrons, which is slow.

I know ion-ion is fast. It's also supposed to be subject to annealing, which would slow down the global thermalization rate considerably.

scattering cross-section is very big at the edge (but rare plasma), lower in the core but have significant value and particles permanently oscillate there-here (edge-core, core-edge).

The ion density at the edge is actually quite high. For constant flux, it's inversely proportional to the velocity, which gets very low at the edge. This combination of high density, high residence time, and high cross section is what makes annealing work.

Also we should recall that in case of significant fusion rate alphas also will take very significant part in thermalization.

Alphas are not well contained. The cusps look fairly large to them, so they don't last more than about 10^3 passes, according to Rick Nebel. (I believe they had a method of exciting the lower-energy alphas, perhaps with RF resonance or some such, to prevent them from contaminating the core.)

This is also one reason why the neutron rate for a p-¹¹B reactor is supposed to be so low - the alphas don't stay in the plasma long enough to fuse much.

I do not know what is "annealing". As it not the standard term.
Yes, I heard something like: "we should smooth the hump of Maxwellian distribution".
But think that if high energetic randomly moving particles have large cross-section for interacting and also big time for that, and also move in the field accelerating them (feeding them with energy from externally) we will get more vigorous randomization (thermalization).
I do not know will that distribution be Maxwellian but surely plasma will be thermal. IMHO.

93143
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Postby 93143 » Mon Aug 08, 2011 6:00 am

The term "annealing", as I understand it in the context of Polywell, means this:


The particles are continually cycling between regions with low kinetic energy and regions with high kinetic energy.

The mean free path in the low-KE regions (which have relatively high density) is short. The distribution makes considerable progress towards thermal while in the low-KE region, but of course the temperature of the resulting distribution is low, so when the particles fall into the high-KE region, the distribution is beamlike.

The mean free path in the high-KE regions is not short enough for the distribution to make comparable progress towards a high-energy thermal distribution while the particles are passing through it. Some thermalization occurs, especially in the centre where the density is high, but it does not approach equilibrium.

Thus, when the incompletely thermalized particles arrive back in the low-KE region, they thermalize there at low energy and the distribution is reset.

This need not violate the Second Law of Thermodynamics, because it only applies strictly to systems in local thermodynamic equilibrium. The equilibrium end state of a Polywell plasma will of course be higher entropy than the equilibrium initial state, but the entropy of a set of transiting particles can go up and down transiently as it cycles through the device. This is similar to how the entropy profile through a shock wave goes up and then back down - even though the end state is higher entropy than the initial state, the intermediate state is higher entropy than either.

...

As for particles not having enough energy to reach the edge with the rest, or having too much and slamming into the magnetic field at relatively high energy, it should be noted that the particles in a stream would have higher collision cross section with one another than with the opposing stream, and if the distribution of a stream were wider than a Maxwellian, thermalization would tend to narrow it. This, in combination with the effect I described above (actually they aren't entirely separate effects; they blend into one another), would also tend to damp out excursions in angular velocity, maintaining the radial motion.

Besides, if it's Coulomb collisions we're talking about, the vast majority of them are very miniscule deflections, more a stochastically-varying force field than a discrete set of bounces. IIRC the Fokker-Planck collision term assumes small-angle deflections only...

The two-stream instability would develop on a longer timescale, perhaps, such that the particles would transit and have their energies reset before it could destroy the distribution.

...

It isn't the sort of thing that can prevent thermalization indefinitely. But the electrons leak, and the ions fuse, and all it has to do is slow thermalization down so that it doesn't happen faster than those two things.

There may be a few holes in my understanding, but I think that's a decent starting point.

Joseph Chikva
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Postby Joseph Chikva » Mon Aug 08, 2011 7:17 am

93143 wrote:This need not violate the Second Law of Thermodynamics, because it only applies strictly to systems in local thermodynamic equilibrium. The equilibrium end state of a Polywell plasma will of course be higher entropy than the equilibrium initial state, but the entropy of a set of transiting particles can go up and down transiently as it cycles through the device. This is similar to how the entropy profile through a shock wave goes up and then back down - even though the end state is higher entropy than the initial state, the intermediate state is higher entropy than either.

That is very specific issue and I can not discuss without knowladge what Polywell's developers and not you mean under "annealing". I only guess that annealing is offered as method for slowing thermalization and concept is not proved yet.
93143 wrote:The two-stream instability would develop on a longer timescale, perhaps, such that the particles would transit and have their energies reset before it could destroy the distribution.

Regarding my invention that also comprises utilization of coherently moving particles with different velocities I had consultation with person involved in Heavy Ions Fusion Program. For acceleration of Cesium ions they use Induction Linacs with pulse currents about 40’000Amp.
As I know, typical number density in those beams is about 10^18-10^19 m^-3.
Dan said me that Polywell with superconducting 10T magnet should have 10^22 m^-3.

In case if that occurs for 10^19 the timescale of development of two-stream instability has an order of about 10ns.
What do you think, will that timescale be more or less for Polywell at 10^22?

93143
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Postby 93143 » Mon Aug 08, 2011 8:35 am

Joseph Chikva wrote:I only guess that annealing is offered as method for slowing thermalization and concept is not proved yet.

That's right.

93143 wrote:The two-stream instability would develop on a longer timescale, perhaps, such that the particles would transit and have their energies reset before it could destroy the distribution.

Regarding my invention that also comprises utilization of coherently moving particles with different velocities I had consultation with person involved in Heavy Ions Fusion Program. For acceleration of Cesium ions they use Induction Linacs with pulse currents about 40’000Amp.
As I know, typical number density in those beams is about 10^18-10^19 m^-3.
Dan said me that Polywell with superconducting 10T magnet should have 10^22 m^-3.

In case if that occurs for 10^19 the timescale of development of two-stream instability has an order of about 10ns.
What do you think, will that timescale be more or less for Polywell at 10^22?

That was a guess, which is why I said "perhaps". EMC2 says that two-stream is not an issue for these machines, and I do not know why.

Also, it should be noted that the particle density in a Polywell is not uniform and varies with the kinetic energy as well as the radius. It is far too late at night for me to do any calculations now, so I will shut up and go to bed.

D Tibbets
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Postby D Tibbets » Wed Aug 10, 2011 3:50 am

Annealing is a Bussard term. I don't know if it is used by any others to describe local thermalization within a system. Annealing is absolutely not a process that slows thermalization. Always remember Bussard's insistance that static considerations can be misleading. This is a highly dynamic system. Edge annealing depends on two very well accepted physics properties. Potential wells will cause a charged particle to oscillate back and forth exchanging potential energy for kinetic energy. At the top of the potential well the ions have slowed to a near standstill. Depending on how you define this area it may be very near the turn around point where the average speed of the ions is very slow. It could also be a larger region close to the edge but containing a much larger volume. A useful definition of the annealing edge region may be the region where the Maxwellian thermalized spread about the average slow speed of the ions in this region is <10% of the maximum KE of the ions as they approach the bottom of the potential well (center.).
The Maxwellian thermalization will occur within a few high angle/ energy exchange collisions) s defined as the MFP. Many small angle collisions would have the same effect. Because of the slow speed (KE) of the ions near the edge, along with the dwell time in this slow ion velocity region mandates that the ions thermalize here (the density achieved with Wiffleball trapping is also important). As mentioned multiple times, the key point here is that the Maxwellian distribution around this slow average ion speed may be only 1 percent, or 10% in my example above, of the KE of the ions as they fall to the bottom of the potential well. This would be equivalent to collecting the ions and reemmiting at the monoenergetic potential well voltage +/- 10%.
Any upscattered ion that manages to get through the annealing region will continue outward, where one of two primary things will occur.There is about a 1/1000 chance that the ion will hit a cusp and exit, picking up KE from the now centrally located positive magrid and fly to the walls. If the ion does not hit a cusp, it will hit the magnetic field surface , compete 1/2 of a gyro orbit and fly back into the Wiffleball. But the gyro orbit is a corkscrew, so the reflected ion could not fly towards the center but at an angle to it. This would reduce the radial magnitude of the vector. Of course the high energy ion is passing through the annealing region again so some of this may be dampend down to almost the transverse motion of the edge region annealing zone ions whose possible transverse speeds are limited by the maxwellion distribution in this low ion energy region. But, Bussard did state that this was a concern that might effect confluence.

Electrons can heat ions through collisions, but not very effectively. It is the space charge from the excess electrons that dominates the acceleration forces acting on the ions.
In fact I believe heating of the ions or electrons by the other is frowned on both for bremsstrulung reasons and bipolar flow considerations in the cusps..

Alphas do not heat the plasma to any significant extent. This is not an ignition machine. The alphas at several million eV have a MFP that is perhaps ~ 1000 times that of the fuel ions. Even with a few thousand bounces around inside the Wiffleball before a cusp is hit, the alphas collide/ interact with the slower ions very little. They escape in the same way that upscattered fuel ions escape. If the potential well cannot hold onto the ion it is purely a matter of a brief amount of time till the ion escapes a cusp.

In my limited understanding, the idea of cusp plugging by a collection of static electrons in the cusp is a minor concern- it would have to be in a region extremely close to the midline of the charged magrids. Even a small distance past this point and the electron will see the charge/ potential on the magrid and be accelerated back inside at near the full speed. This is due to another property of Gauss's Law. A charged particle above a plane with a potential will result in the charged particle to be accelerated an equal amount irregardless of the particles starting point above the plane. The magrid is not a perfect plane, but presumably close enough to approach this effect. An electron that manages to reach a point where the outward electron potential well equals the inward magrid potential, might hover there briefly, but with a collisional plasma, it would quickly be knocked away from this fragile balance point. There may be a small dynamic population that could hover here, but this ignores ExB drift of these slow electrons that would drain them away towards the magrid metal surface. Even then, as they spiral along the magnetic field lines they may reach a region where the electrostatic charges nudge them to a region where it is thrown away from this central cusp region.

As far as two stream instabilities, I think it is at least partially misleading to consider the ion streams as well collumated beams. The ions are ideally created or injected just within the Wiffleball border, and tend to be pulled towards the center, but this center is a sphere defined by the shape of the potential well, not a central point. The near spherical shape of the Wiffleball also helps. but beam - beam collisions in this regard is a compromise, if there is some moderate confluence- equivalent to a modestly collimated beam with perhaps a 1-30 degree angle of dispersion, many of the collisions will be near head on, but few would be exactly head on. Even if the ions start with high radial purity, the vertual anode that would form in the center would prevent maintenance of this high radial purity from one pass through the core to the next. . Then there is the transverse deflections introduced by the upscattered ions reaching the magnetic domain. Considering the relative long lifetime of the ions (compared to the electrons)comments about the uncertainty of maintaining a high confluence is warranted. I have generally heard annealing in the frame of up scattering and down scattering. But transverse or angular momentum thermalization may also benefit from annealing. Annealing would thermailize both the radial velocity and the angular motion velocities within this narrow low energy distribution. Even in the best case scenario, the ion paths are narrow ellipses passing near the center, not lines moving back and forth from the edge to the center.

Dan Tibbets
To error is human... and I'm very human.

Joseph Chikva
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Postby Joseph Chikva » Wed Aug 10, 2011 4:58 am

D Tibbets wrote:At the top of the potential well the ions have slowed to a near standstill.

"Oscillation" means that ions' velocities pass through zero when changing there direction on the opposite.
So, they have slowed to standstill (and not near standstill) and then are accelerated again.

Yes, alphas will have thousands times less scattering cross section on reacting ions. But they will be created in the core in which density will maximum. But scattering rate is proportional to cross section linearly and to density by square.
What a difference between “ignition machines” and others? If we have 10^22 m^-3 number density? Heavier alphas will effectively pass the part of their momentums to lighter reacting ions taking a significant part in thermalization.

When I talk about two-strem instability I mean electron beam with non-zero velocity and electrons being in plams and having zero average velocity.
Charged Particle Beams, Stanley Humphries, Jr., Department of Electrical and Computer Engineering University of New Mexico, John Wiley and Sons, 2002 (page 675)
Two-stream instabilities are a major concern when beams propagate through plasmas. Examples include long-distance propagation of high energy electron beams, transport of low-energy ion beams emerging from high-current injectors, and the propagation of heavy ion beams in an inertial fusion reaction chamber. The two-stream instability may be desirable in applications such as plasma heating by intense electron beams.

93143
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Postby 93143 » Wed Aug 10, 2011 7:34 am

D Tibbets wrote:Annealing is absolutely not a process that slows thermalization.

It slows global thermalization. It relies on differences in local thermalization rates to do this.

Joseph Chikva wrote:Yes, alphas will have thousands times less scattering cross section on reacting ions. But they will be created in the core in which density will maximum. But scattering rate is proportional to cross section linearly and to density by square.
What a difference between “ignition machines” and others? If we have 10^22 m^-3 number density? Heavier alphas will effectively pass the part of their momentums to lighter reacting ions taking a significant part in thermalization.

It isn't just that the alphas are fast; it's that they are poorly confined. They don't spend very long in the plasma, and the concentration never gets very high. So says Rick Nebel, at any rate...

He wasn't talking about thermalization, though, but about neutron production via side reactions. Apparently a p-¹¹B Polywell would have a neutron rate several orders of magnitude lower than a thermal reactor would running the same fuel, and one of the reasons is the poor alpha confinement...

Vassago
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Thanks

Postby Vassago » Wed Aug 10, 2011 9:11 am

Just wanted to say thanks to 93143 and D Tibbets... I've been lurking around on this site for nearly two years now and I think that's the first time I've actually understood what you guys mean by the term "annealing" :)

Great explanations... now I just hope it actually works that way!
Hard work pays off later... Laziness pays off now!

Joseph Chikva
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Postby Joseph Chikva » Wed Aug 10, 2011 10:43 am

93143 wrote:
Joseph Chikva wrote:Yes, alphas will have thousands times less scattering cross section on reacting ions. But they will be created in the core in which density will maximum. But scattering rate is proportional to cross section linearly and to density by square.
What a difference between “ignition machines” and others? If we have 10^22 m^-3 number density? Heavier alphas will effectively pass the part of their momentums to lighter reacting ions taking a significant part in thermalization.

It isn't just that the alphas are fast; it's that they are poorly confined. They don't spend very long in the plasma, and the concentration never gets very high. So says Rick Nebel, at any rate...

He wasn't talking about thermalization, though, but about neutron production via side reactions. Apparently a p-¹¹B Polywell would have a neutron rate several orders of magnitude lower than a thermal reactor would running the same fuel, and one of the reasons is the poor alpha confinement...

I understand that depth of potential well is much lower than 3.5MeV (if considering D-T fuel).
Now I do not take into consideration what does Dr. Nebel say, but only try to think according very simple logic.
By which: alphas are not confined by well and so escape reaction zone with energy equal to (3.5MeV - depth of potential well - energy lost per collisions with mostly reacting ions). As 10^22 dense plasma will not at 100% transparent.
And alphas will leave for plasma's thermalization not all their 3.5MeV but for example a few tens of keVs. Not enough for thermalization?

Joseph Chikva
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Re: Thanks

Postby Joseph Chikva » Wed Aug 10, 2011 6:29 pm

Vassago wrote:Just wanted to say thanks to 93143 and D Tibbets... I've been lurking around on this site for nearly two years now and I think that's the first time I've actually understood what you guys mean by the term "annealing" :)

Congratulations, you won.
As 93143 says that annealing for slowing of thermalization. And Dan disagree with that.

TallDave
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Postby TallDave » Wed Aug 10, 2011 8:19 pm

93143 wrote:That was a guess, which is why I said "perhaps". EMC2 says that two-stream is not an issue for these machines, and I do not know why.


I assume this has been thoroughly examined in simulation, but I think one would expect two-stream issues would be minimal because you're not heating the electrons (well, not much anyway) at the edge -- the electrons at the injection point are pretty energetic anyway, being near the bottom of their well. The "bump in the tail" might push some waves toward the center but they have to climb up the potential well to get there, and presumably lose energy to Landau damping on their way up.

Thanks for the excellent explanation of annealing, which replaces Rick's somewhat more brief explanation as my new favorite. (I'm not sure how much we can infer on the existence of annealing from the paucity of information we've been given, but we might throw a few synaptic cycles at at wondering how different confinement would look without annealing...)
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

D Tibbets
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Postby D Tibbets » Wed Aug 10, 2011 9:44 pm

93143 wrote:
D Tibbets wrote:Annealing is absolutely not a process that slows thermalization.

It slows global thermalization. It relies on differences in local thermalization rates to do this.


Indeed the global thermalization is slowed. This is important to remember. But the reason annealing does this is because of the dynamic situation. I wanted to emphasize that the mechanism for annealing is straight forward local Maxwellian thermalizarion physics. There is not magic here, only careful consideration of the ion velocities in different parts of the machine.


As for a distance where the ions turn around and thus have zero radial velocity. This of course occurs on a per ion basis. But, monoenergetic terminology in the Polywell context does not mean all ions start or maintain tightly defined velocities in different parts of the machine. It is a relative term. It is nonthermalized in the mantle and core regions, but may be anywhere from ~ 0.1 % to 99% thermalized and still fit this definition. I conveniently assume the ions maintain ~ < 10% thermalization in the core., at least in the small machines. This is a purely arbitrary assumption.

Since there is some variation in the ion radial velocities near the edge, there is no specific turn around point, but there is a region where statistically speaking the vast majority of the ions are turning, An absolute is to consider the average speed here is zero, but in reality I doubt such a small average speed is meaningful. I assume for calculation purposes the average ion speed/ KE may be ~ 10-100 eV in the defined annealing region. The thermalized spread that results is based on this arbitrary average energy. There has to be some volume for ions to collide. The MFP is very short, but not zero.

My understanding of the alpha slowing from the potential well (assume 200 KeV for P-B11) is almost purely from the potential well space charge. The alphas are not slowed significantly by collisions with themselfs or the slower fuel ions. Now, if one of the emitted alphas have ~ 700 KeV as suggested by a recent study, things may change some.
If the Wiffleball trapping factor is in the upper range of general predictions. Bussard has used the term -"many thousands" This could mean anything from perhaps ~ 2,000 to 20,000 density enhancement. The final density may range anywhere from ~ 10^21 to 10^23 charged particles / M^3. This range would result is a decrease in the MFP by up to a factor of~ 10,000. As Nebel liked to say there are a lot of knobs adjustments that might be useful. The Polywell may be capable of Wiffleball trapping factors that are too extreme for practical use. It may need to be throttled back . The Polywll MAY perform so well, that engineering concerns about thermal wall loading, thermalization concerns of the fuel ions and yes, possibly the fusion ions, may drive the machine to larger lower B field machines. The Goldilocks analogy again. Bussard in one interview did speculate that an advanced Polywell might be made small enough to power a semitrailer truck, at least theoretically, but considering the many compromises, such is improbable.

The two stream instability issue has been discussed in another thread There are references there that address this issue, at least in part.

Dan Tibbets
To error is human... and I'm very human.

D Tibbets
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Postby D Tibbets » Wed Aug 10, 2011 10:20 pm

Some possibly pertinent links to previous recent posts.


http://adsabs.harvard.edu/abs/2005APS..DPPBP1137M



I said that transverse annealing was not mentioned, but I was apparently wrong. Also note the term used which I believe is = 'annealing' in the transverse momentum frame.

http://www.askmar.com/Fusion_files/EMC2 ... oncept.pdf

In fact, Rosenberg and
Krall14 have shown that transverse momentum will not
build up, due to rapid isotropization at the system edge.




http://www.askmar.com/Fusion_files/Inhe ... ystems.pdf

Nearly all fusions take place within one or two core radii
of the central core. The mean free path for fusion product
interaction with the core region ions is very much
larger than the core size, so much so that the interaction
probability is < 10-9. Thus, the fusion products cannot
deposit their energy in the core or in the confined volume.
They will escape directly, radially through or to the
boundary of the confinement region, and they escape
with the energy of their formation and do not thermalize
as in LTE machines.


Transverse momentum will be added to the ions by ion-
ion collisions in their radial counterflow in the mantle
region i.e., between core and edge in every pass
through the mantle. However, analysis8 shows that this
is not a problem because edge region collisionality anneals
out all anisotropy from this or any other source
in each pass. Edge region ion energy is so low a few
electron volts that the ion-ion Coulomb cross section is
suciently large to ensure such isotropization in each
edge reflection in the combined electric potential gradient
and surface magnetic field. This prevents growth of
the momentum limited converged core and preserves
the system power output and gain.


Dan Tibbets
To error is human... and I'm very human.

Joseph Chikva
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Postby Joseph Chikva » Thu Aug 11, 2011 5:54 am

D Tibbets wrote:Some possibly pertinent links to previous recent posts.


http://adsabs.harvard.edu/abs/2005APS..DPPBP1137M

Previous work based on fluid models suggested that the electron-electron two-steam instability would become unstable when the well depth of the virtual cathode was 14% of the applied voltage

If so, I think that feasible number density will be defined not by beta (ratio of magnetic pressure to kinetic pressure) but by this factor: "14% of the applied voltage"

Regarding annealing I think that is certain process making the temperature (measure of thermalization) isotropic in all points of volume occupied by plasma. Temperature is the same anywhere but its value defined by collision intensity, scattering cross-section, etc. And temperature will permanently grow till enery input by electric field will not become equal to energy losses mainly via Bremstahlung. I do not see any other mechanism limiting thermalization.


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