EMC2 has published a polywell preprint on arXiv

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

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John Gallagher
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Re: EMC2 has published a polywell preprint on arXiv

Postby John Gallagher » Sat Jun 14, 2014 11:27 pm

It seems it would require a stronger magnetic field to channel the alphas than to contain the fusion plasma due to a KE an order of magnitude or so higher. I am thinking that the alpha flux has a random distribution at least as it is created. We are also dealing will a potential of 2 mv or so on any deceleration electrode sets. This is an interesting isolation problem. Please realize that at this point I am a true believer in the necessity of PB fusion and see no other solution to our world civilizations energy needs. Just wondering what work has been done on the engineering problems of energy extraction in polywell and other PB systems.

hanelyp
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Re: EMC2 has published a polywell preprint on arXiv

Postby hanelyp » Sun Jun 15, 2014 2:43 am

For alphas it is sufficient that the thickness of the magnetic field protecting the coils is greater than the gyro-radius. large cusps for the fusion products to escape through are a feature. For the electrons we want far greater containment with small cusps. Wiffleball containment on fuel ions is a bonus on top of the electrostatic well primary containment.
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tokamac
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Re: EMC2 has published a polywell preprint on arXiv

Postby tokamac » Sun Jun 15, 2014 8:42 am

I have some questions, that maybe Dan Tibbets or Thomas Ligon could answer.

The plasma inside the Polywell is said to be nonthermal, with T_e >> T_i
It is also a magnetized plasma, with the electron gyrofrequency superior to the electron collision rate: ω_ce > ν_coll

1/ What is the magnetic Reynolds number R_m of the plasma?
Is it large (like interstellar plasmas) or small (like engineered weakly ionized gases)?

2/ What is the Hall parameter?
The Hall Parameter is the ratio between the electron gyrofrequency Ω_e and the electron-heavy particles collision frequency. It can be written as:
( e B ) / ( m_e ν )
with e the electron charge, B the magnetic field, m_e the electron mass, and ν the electron-heavy particles collision frequency.

In kinetic theory of gases, when R_m << 1 you have to made predictions by calculating with dyadic tensors in a 7-dimensional phase space, which can be a little tricky. I may be wrong, but I don't think this is something an "MHD code" can resolve by simulation.
I ask if someone at EMC2 did this calculation by hand, because I read in the preprint that they proceeded through "trials and errors" which may me think nobody calculated the optimal parameters before the experiment.

Moreover, when the Hall parameter in such a plasma is large, the electrical conductivity σ becomes a matrix, calculated with the the scalar electrical conductivity σ_s = ( n_e e2 ) / ( m_e ν)
where n_e is the electron density
And there is a critical Hall parameter is such a plasma, where the electrothermal instability arises.

What are the Polywell parameters (Reynolds and Hall) regarding these potential issues?

See http://en.wikipedia.org/wiki/Electrothermal_instability for the detailed calculus.

D Tibbets
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Re: EMC2 has published a polywell preprint on arXiv

Postby D Tibbets » Sun Jun 15, 2014 11:19 am

Concerning alpha containment, I don't think the cusps are different for elecytrons or alphas. Both are contained by the Wiffleball effect- enhanced cusp condinement. The fuel ions are primarily contained by the electrostatic potential well produced by the slight excess of electrons maintained in the machine. R. Nrbel gave an example of a machine ~ 3 meters in diameter with a B field of
~ 3.5 Tesla. This provides an alpha gyroradius sufficiently small relative to the distance from the Wiffleball border to the magnets that the alphas do not reach them. Their only escape route is through the cusps. Because of their high KE their MFP is so long that little ExB drift will occur, and also little thermalization between the alphas and fuel ions will occur over the lifetime of the alphas.

Cusp size , due to the sharp border of the Wiffleball effect results (I think) in the escape cusp area being effectively a hard surface so hole size is not directly related to gyro radius. Having said that, I may be wrong. The turning is still gyroradius mediated. But, remember the gyro radius is based on the charged particle speed perpendicular to the B field line. Generally, or at least ideally, most alpha production occurs in the core near the center, so that despite isotopic vectors, by originating from the center all vectors are radial. As the alphas have little chance for collisional scattering they will maintain this radial vector dominance till they hit a cusp and escape. Almost all of their KE is radially directed, which means their motion to the cusp surface B field is minimal because it is oriented almost radial to the center also (at least that part of the cusp that is the escape hole through which the alpha exits. The fuel ions, even optimistically, will not be so radially vector dominated, so the KE perpendicular to the B field line in the cusps may actually be similar between the alphas and the fuel ions- which would allow for Nebel's statement. Acutually, perhaps I should say theelectrons and the alphas, as it is the electrons (and alphas) that are contained magnetically. The fuel ions are primarily contained electrostatically, so their pass lifetime is not directly cusp (or ExB drift) limited.

I think this reasoning is why R. Nebel said the alphas have a ~ 1000 pass lifetime(near the regular Wiffleball trapping factor), while A. Carlson (who perhaps did not consider this) said only a few passes for the alpha lifetime was expected. Also, this must apply I think, for the alphas to squeeze through the cusp at the midplane radius of the magrid where the magnets may be much closer than the gyroradius of the alpha particle if you do not consider the vector contribution.

PS: With the core born aplhas, they travel outward and if they escape they will already have transferred some of their energy to the internal potential well. eg: if the alpha has a KE of 4 MeV, and they travel through a 200KeV potential well they will transfer this much of their energy to the potential well. They would escape with 3.8 MeV of retained KE. Some direct conversion of the apha KE has already occurred. How this would effect the energy balance and dynamics of the potential wells is intriguing. Even if no further direct conversion occured, it would at least counterbalance the KE the alpha would gain once it passed beyond the positively charged magrid. If the magrid is at ground (a condition that I think is undesirable), the balance would be different. In the EMC2 patent application, Bussard mentioned the dynamics of the alphas carrying away positive charge such that injected electron rates might need to be curtailed significantly to compensate. This raises questions about being able to maintain energetic electron levels to heat (accelerate) the fuel ions. The above may satisfy this concern.

Dan Tibbets
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Re: EMC2 has published a polywell preprint on arXiv

Postby D Tibbets » Sun Jun 15, 2014 11:39 am

tokamac wrote:I have some questions, that maybe Dan Tibbets or Thomas Ligon could answer.

The plasma inside the Polywell is said to be nonthermal, with T_e >> T_i
It is also a magnetized plasma, with the electron gyrofrequency superior to the electron collision rate: ω_ce > ν_coll
....



The Polywell plasma is non thermal in the sense that it does not (at least that is the claim) reach Maxwellian thermalization statistics. That doesn't mean the ions and electrons have different average temperatures. Assuming good potential well transfer of energy to the ions and the ions being introduced near the top of the potential well, the average temperature is the same (well, almost).

What is important is that the potential well for the ions and the electrons are in opposite in directions. With the quasi spherical geometry it means that on the edge ions are slow and electrons are fast, while near the center ions are fast and electrons are slow. The relative energy is dependent on the radius you are looking at. Overall though the temperatures should have near the same value. This assumes some significant confluence (central focus) of the ions. With this, the greatest concentration of ions is near the center of this spherical convergent plasma, despite the greater speed of the ions through this region- the spherical compression is greater than the shorter transit time/ unit of length. Since the electrons are slowest in this region, the Bremmstruhlung is less in this core region where a disproportionate collection of ions are present. This is why Bremsstruhlung maybe less that Rider predicted. If there is no confluence, the Polywell reaction space is just a bag of mixed ions and electrons . It still may not be Maxwellianized, but the ion and electron temperatures do not have the radial temperature gradients opposite of each other. I think Nebel felt this was ok for D-D fusion, but it would rule out P-B11 profitable fusion.

The rest of you questions are beyond my pay scale.

Dan Tibbets
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CelticWarrior72
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Re: EMC2 has published a polywell preprint on arXiv

Postby CelticWarrior72 » Mon Jun 16, 2014 4:38 am

I have been a frequent lurker here since 2007/2008. This is great news. About time too!

mattman
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Re: EMC2 has published a polywell preprint on arXiv

Postby mattman » Tue Jun 17, 2014 5:55 am

Tokamac,

I am going to look into calculating those dimensionless numbers.
=====

Looking for some feedback here - I am trying to put this together.


The biggest issue from a theory standpoint is the electron or ions’ behavior at the cusp. This seems to be where the paper breaks from convention and why Park mentions it right away.


There seems to be two cases: a high and low beta. So far, we (all of us, for 50+ years) have operated in this low beta case. The low Beta case is basic magnetic mirror confinement. This formed the basis of 20 years of a huge Livermore effort to build a fusion machine. Here is a picture of a particle beam, showing mirror confinement:

Image

But, now we have "cusp confinement". When we get allot of plasma in there, the behavior at the cusps behave very differently... With very different loss mechanisms. I tried to draw this out. I also included the case for Magnetic Reconnection, for comparison.

Image

Anyone know what the loss equation is for standard Magnetic mirrors?

=====

The other thing that seems changed is the boundary conditions. They have gone from loose, magnetized plasma to the idealized "free boundary." Working through the theory of that now (from these papers). I drew out a comparison of these ideas:

Image


Feedback/Criticism Appreciated.

hanelyp
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Re: EMC2 has published a polywell preprint on arXiv

Postby hanelyp » Tue Jun 17, 2014 4:59 pm

from http://en.wikipedia.org/wiki/Magnetic_mirror
r(mirror) = Bmax/Bmin
a particle will be reflected by a magnetic mirror if v(perpendicular)/v(parallel) > 1/sqrt(r(mirror))

In a high beta reactor the magnetic field is excluded from the body of the plama, giving a near zero Bmin. Cusp effects that are negligible in a low beta mirror come to dominate losses.
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D Tibbets
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Re: EMC2 has published a polywell preprint on arXiv

Postby D Tibbets » Tue Jun 17, 2014 5:32 pm

Cusp confinement and Wiffleball confinement are two different things. Using the terminology from the EMC2 patent application, mirror confinement refers to, well mirror confinement, and applies to the biconic opposing magnet mirror machine. This consists of two opposing magnet rings, spaced apart the diameter of the ring. This gives an aspect ratio of one and provides an internal volume comparable to a similar diameter Polywell magrid. The losses in this mirror machine consists of two point cusps and one linear equatorial cusp. The truncated cube Polywell has 6 point cusps, and two highly modified line cusps. The key is that these two line cusps are much narrower than the single line cusp in the traditional mirror machine, so the net losses are substantially less. The two line cusps are usually described as 8 corner cusps with losses similar to or less than the face centered point cusps. According to the patent application typical mirror confinement is ~ 5-8 passes, modified mirror confinement (at low Beta) or "Cusp" confinement was given as ~ 60, and Wiffleball confinement (high Beta) was given as several thousand passes.

Cusp confinement is just mirror confinement applied to the Polywell geometry. It reflects the preservation of internal volume while moving the magnets (more of them) closer together and thus narrowing the problematic line cusp(s)

An example with arbitrary numbers would be a mirror line/ equatorial cusp that is 1 cm wide with a 1 meter diameter. The loss area would be 314 cm^2. The point cusps contribute 2 cm^2 more loss area.
In the Polywell, there are two modified line cusps. With a resultant average width of perhaps 0.1cm. Multiplied by the circumference of two cusps now gives 62.8 cm^2. Add 6 point cusp contributions of 6 cm^2 and your total losses for the same confined volume is now ~69 cm^3. In this example the confinement is about 5 times better than the biconic mirror machine confinement. It is still the same mirror confinement physics, just modified by clever geometry.

With Wiffleball confinement the physics change, the internal volume is increased while the cusp loss area is unchanged or shrunken, depending on the definitions you use. The electron behavior is better described as rebounding from a hard surface rather than spiraling along field lines. The confinement per unit of volume is improved. This is the critical consideration- the volume versus the losses. You can consider constant volume with increased density, or constant density with increased volume, or some combination of both. The bottom line is that you can contain more plasma for longer.

Note that the relative improvement in this machine and WB6 between cusp (low Beta) and Wiffleball (high Beta)was probably the same. The starting line for this machine was worse than WB6, 7 pass cusp confinement versus perhaps 60 for WB6, but the improvement (7 to 300 passes and 60 to several thousand passes)is ~ the same.

I blame the relatively poor cusp confinement in this 'mini B' on the relatively huge corner cusps due to spacing in this small machine. The two cables sticking into the machine didn't help either. Still, it got the job done, thanks to the power of the plasma injectors, and the chosen instrumentation.

PS: Since the confinement in this machine was similar to a typical opposed magnet biconic mirror machine, I wonder if some University could replicate this experiment with an old mirror machine and various plasma apparatus stored in their basement. For that matter, I wonder if this has already been done, or is Dr Parks approach of using a powerful plasma gun injection unique? Perhaps injecting bulk low energy plasma has been done, but not coupled with high energy electron injection with appropriate instrumentation to measure the effect through a marker like bremsstruhlung.

Dan Tibbets
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Re: EMC2 has published a polywell preprint on arXiv

Postby D Tibbets » Tue Jun 17, 2014 7:03 pm

hanelyp wrote:from http://en.wikipedia.org/wiki/Magnetic_mirror
r(mirror) = Bmax/Bmin
a particle will be reflected by a magnetic mirror if v(perpendicular)/v(parallel) > 1/sqrt(r(mirror))

In a high beta reactor the magnetic field is excluded from the body of the plasma, giving a near zero Bmin. Cusp effects that are negligible in a low beta mirror come to dominate losses.


This is flawed reasoning I think, or at least applied in an inappropriate fashion.. It is referring, I think, to B field gradient change. If the B flield gradient is unchanged the charged particle will spiral along the field line for ever without reversing. But if the gradient increases(like near poles or locally stronger magnets or magnets closer together, the particle may mirror. The center of the gyro motion remains the same (same B field strength), but the rate of change on either side of this B field line is greater and this leads to the mirroring. I may not be making much sense, but what I am implying is that the above Bmax/ Bmin expression refers to this gradient as the charged particle gryrates along a fixed B field strength field line. The greater the parent magnet strength and / or the closer two opposing magnets are the greater is this gradient as you approach a pole or closest approach between magnets.

With the Wiffleball border, this spiraling motion with mirroring does not apply to any significant amount. The particle completes only ~ 1/2 of a single gyro orbit before it reenters a B field absent region. No spiraling, no chance for the mirroring effect to manifest. The behavior is essentially like bouncing off of a hard wall. The geometry of the particle bouncing of of these walls determines whether it will return to the interior or ricochet through the cusp.

Bmin essentially does not approach zero, it is zero, and the equation becomes meaningless. Zero in the sense that it's effect is greatly dominated by other interactions like space charge, collisions, and inertia.

Let me try again. Bmax/ Bmin , in a constant B field would be 1/1. I think everyone would agree that no mirroring would happen here. If you were talking about the motion of a charged particle perpendicular to the field, the constant strength would turn the particle with a given constant radius of curvature. How this particle reached this B field region is ignored, it is just there. There is also a lateral displacement depending on B field strength, mass and Z and polarity. A constant spiraling velocity with a fixed frequency and perfectly round orbit occurs. If this B field strength is greater or lesser, nothing changes except this constant orbit radius and associated frequency. No slowing or reversal, no mirroring. You have to consider variable B field strength relative to the reference gyroradius mid line reference point. Here if this variance is constant the gyro orbit will become parabolic, not perfectly circular, but so long as this relative strength variation is constant so is the spiraling motion. If this variation changes along the path of the spiraling axis though, things change. The gyro orbit becomes more parabolic. For some reason this increases the frequency, slows the lateral motion and can eventually reverse. I don't know why except to invoke the magic term Lorentz force. The B max/ Bmin refers to the B field strength on the inner edge and the outer edge of the gyro orbit and thus the radius of the gyro orbit of that specific orbit. Progressive spiraling orbits enter regions where this inner to outer B field strength ratio becomes greater. I'm supposing that the increasing parabolic shape counterbalances the total orbital excursion so that the gyro orbit radius looks unchanged. But like planets in parabolic orbits, less volume is swept out so orbital speed (orbits per second) can increase. Eventually forward motion ceases. There is no reason to reverse, except due to chaotic(?) motions, if the particle moves slightly backwards it has less KE and thus travel down the potential well commences. There is a limit where the differential between the inner and outer B field strength gradient breaks down, Here the outer parabolic portion of the orbit becomes so great that the particle escapes the B field dominance and other influences dominates. This is represented by the Wiffleball border.

Another perspective- Arrange constant B fields parellel to each other, each successfully stronger. Introduce a charged particle with a given KE to the weakest field, it assumes a given gyroradius and spirals into the second stronger field, its gryroraduis shrinks and frequency increases, continue this process till the gryoradius is very small and the frequency is very high, The forward spiraling motion per orbit slows, till eventually it is so small that it can randomly reverse with out having to overcome a significant energy barrior, now it unwinds in the opposite direction. This is mirroring. I think the magnetic field is transferring energy to the particle during wind up and recovering it during wind down. The net effect is that the particle is confined, without net energy loss (ignoring gyrotron radiation losses).

This rumination, perhaps nonsensical, is a consequence of the last quoted statement, but perhaps I am merely obsessing with the terminology. Mirror machines have cusps. Mirroring is just the mechanism for a magnatized plasma to avoid those cusps for a time. If by "cusp" losses they refer to plasma escape due to mechanisms not related to mirroring it makes sense. But, it seems to imply that this cusp confinement is worse than mirror confinement. That need not be the case. Another way of stating it, perhaps more relevantly is that:

Cusp Confinement in High Beta conditions is mechanistically different than mirroring. And this mechanism can be more efficient at containment than mirroring mechanisms.

Dan Tibbets
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mattman
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Re: EMC2 has published a polywell preprint on arXiv

Postby mattman » Fri Jun 20, 2014 5:53 pm

Some more questions:

What is the composition of this plasma?

    The plasma injectors form the plasma from a polypropylene film.
    Polypropylene is hydrogen and carbon.
    If they were containing just hydrogen and carbon, it would jive with using photodiodes to measure H and C line emission.
    It looks like the team is trapping H and C in this test, not ionized deuterium

How do you make the first plasma from a polypropylene film?

    There are many of ways to make plasma: microwaving, sparks, flaming ionization or applying a voltage.
    How would they make it from a hydrocarbon film?

As I understand it, plasma guns consist of:

    1. “Generator/containment” section, where the plasma is made.
    2. “Valve/injection” section, where the plasma is pushed into a long parallel plate/tube.
    3. “Acceleration” section, where a current (60,000 – 150,000 amps) is applied over a gap (2 mm) to make a Lorentz force, which flings the plasma outward.

The navy had two of these guns facing one another, just off the rings. Each could put 500 megawatts of power. How is this power rating connected to a plasmas’ velocity, density and rate of flow into the rings?

mattman
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Re: EMC2 has published a polywell preprint on arXiv

Postby mattman » Fri Jun 20, 2014 8:53 pm

The plasma inside the Polywell is said to be nonthermal, with T_e >> T_i


Your talking about an energy distribution. For WB6, I have argued that the energy distribution looked like this:

Image

The key question here is: What is the electron to ion energy transfer rate? Rider wrote an additional paper looking at this for polywells, but its highly theoretical (i.e. prone to errors) and in the 20 years since almost no one has cited it.



It is also a magnetized plasma, with the electron gyrofrequency superior to the electron collision rate: ω_ce > ν_coll



If the navy has achieved a "free boundary" than the bulk plasma is NOT magnetized. The external field does NOT penetrate it.

That means the: gyroradius - larmor radius - gyrofrequency concepts, we are used to modeling are not the same.

There certainly should still be lorentz forces and correlating the corkscrewing motion of electrons and ions.

The bulk plasma looks more like a web of coulomb forces. That is assuming they are quasinuetral, i.e. (+) and (-) evenly mixed.

The better questions are: what is the Debye length? What is the value of the coulomb logarithm?

Image

Just looking at this depiction bothers me: how does a B-field not make another E-field, ect.. in this plasma? How does the fields' influence stop?

This system is supposedly very stable. Meaning it does not see magnetohydrodyanmic instabilities (I find this hard to believe).

I need to dig into the Electrothermal instability you that mentioned. It may not apply.

1. What is the magnetic Reynolds number of the plasma?
2. What is the Hall parameter?


Going to figure this out.

mattman
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Re: EMC2 has published a polywell preprint on arXiv

Postby mattman » Mon Jun 23, 2014 2:18 am


tokamac
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Re: EMC2 has published a polywell preprint on arXiv

Postby tokamac » Sun Jun 29, 2014 9:34 pm

Imagine breakeven is achieved with a polywell. How energy is extracted from the fusion reactions occurring in the middle? I can't find in the literature how Bussard imagined to do it. I think no heat exchanger/steam turbine, more probably direct energy conversion. But how? Long channels with electrostatic collectors? How to channel the ions from the middle, if you want the vacuum chamber to be isolated? Maybe inductive EMF while the fusion plasma is expanding?

Based on this, could the MaGrid run as a four-stroke engine, with 4 steps:
    [1] magneto-electrostatic confinement
    [2] fusion
    [3] plasma expansion
    [4] refuel with new cold gas puff

At step [3] the MaGrid would act like an electric generator and not as a magnetic confinement (Mirror/Wiffleball) like in step [1].
At step [3] the fusion plasma expands against the magnetic field and while pushing the field lines, it induces an EMF in the coils. This voltage could then be collected.

Is it valid? Could this process be repeated tens of times per second, with cold gas puff injection, then magnetic confinement, mirror regime, wiffleball regime, electrostatic potential well, ion cloud, fusion reactions, magnetic expansion/compression and power generation, and so on? I do not quantify well the rough time estimate that each step takes to complete.

DeltaV
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Re: EMC2 has published a polywell preprint on arXiv

Postby DeltaV » Sun Jun 29, 2014 11:52 pm

tokamac wrote:Imagine breakeven is achieved with a polywell. How energy is extracted from the fusion reactions occurring in the middle? I can't find in the literature how Bussard imagined to do it. I think no heat exchanger/steam turbine, more probably direct energy conversion. But how?

It is in the literature. For the preferred proton-11Boron reaction, the primary fusion product is energetic alpha particles. Based on comments by Dr. Nebel and prior discussions here, the best guess is that alphas exit the 6 point cusps as cones (not tight beams) after about 1000 passes, with energies up to a few MeV. Direct-conversion collectors inside the vacuum chamber, having a suitable geometry, convert the kinetic energy of the alphas to electrical current (UHVDC). Ideally, the deceleration of the alphas by the collector E-fields leaves them with very little energy as they contact the collectors, leading to a high conversion efficiency (>90%, some say >95%). The direct conversion into high-voltage power, without need for a steam cycle, is the beauty of p-11B.


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