magrid configuration brainstorming

[Curiousfusor]

Yes yes I see that facing all these magnets in would cause mini fields, and the engineering challenges and what not. The difficulty is in explaining what my idea is it isn't a monopole, or multiple magnets facing in, its creating a single spherical electromagnet wrapped in a way that creates 1 pole in and 1 out, warping a single magnetic field in on itself concentrically, and yes two cusp remain on the top and the bottom. If not this arrangement then what ever is used in Tokamaks, the idea stemmed from a schematic I saw of a spheromaks electromagnet set up and then thinking back and realizing Tokamaks are engeenered to not have field cusp. Essentially is there any way that a sphere instead of a torus could be magnetically shielded in the same way as to have no field line exiting through the containment vessel, as is done tordially in Tokamaks; basically going from a low aspect ratio spheromak to a no aspect ratio complete sphere?

If this cannot be done then further more can a traditional spheromak be used to confine electrons with a weaker magnetic field as to not interfere with ions as in a pollywell (as Tokamaks confine ions which is an advantage pollywells have only confining electrons), then injecting ions in and radially accelerating them to the negative potential well in the center? I'm assuming this could easly be done but the real question is in a spheromak the center spire would become a target in the weaker magnetic field and would fry like tue grid of a fusor, or would the ions deflect? This is the reason for the notion of a 2 cusp spherical containment setup.

The idea I have is for a polywell with no grid- if an arrangement can be found to magnetically shield a spherical vessel as is done with torus's in Tokamaks, then a weaker, more easily obtained magnetic field strength could be used to confine electrons in a negative potential well in the center. Then as in a polywell the electrons form the target for the ions, but unlike a polywell no physical structure exist in the chamber and the ions are electrostaticaly kept from wall collisions, as in the fusor. I feel like this is possible just the correct magnetic field arrangement has to be found, or am I wrong on some level?

[KitemanSA]

Yes yes I see that facing all these magnets in would cause mini fields, and the engineering challenges and what not. The difficulty is in explaining what my idea is it isn't a monopole, or multiple magnets facing in, its creating a single spherical electromagnet wrapped in a way that creates 1 pole in and 1 out,

One pole out is pretty much the definition of a monopole.

[Curiousfusor]

A monopole would require new particles of physics that as far as we know don't exist, 2 poles exist in what I'm envisioning, the geometry though results in a setup where 1 pole faces out and 1 in. Like a Tokamak, the field lines are warped to where they don't intersect the containment vessel, so the appearance is yes that of a monopole because the outside would magnetically only appear to have 1 pole, but because of the geometry the opposing pole is squeezed inward. 2 poles some really intricate geometry.

[happyjack27]

A monopole would require new particles of physics that as far as we know don't exist, 2 poles exist in what I'm envisioning, the geometry though results in a setup where 1 pole faces out and 1 in. Like a Tokamak, the field lines are warped to where they don't intersect the containment vessel, so the appearance is yes that of a monopole because the outside would magnetically only appear to have 1 pole, but because of the geometry the opposing pole is squeezed inward. 2 poles some really intricate geometry.

No, a monopole would require completely new physics altogether. No quantum physics, no M-theory, no string theory, no nothing. We'd have to throw away every mathematical model we have. We'd have to throw away Gauge Theory. The Schrodinger equation would be provably false, and so would the Dirac equation, and e would not equal mc squared.

[KitemanSA]

None the less, one pole out would be a monopole. One=mono, pole=pole. This tells me that you will not be able to wind such a magnet.

[Curiousfusor]

Yes but two poles exist in this system, oh well, whatever I'll continue to ponder it. So it there anyway to magnetically shield a spherical chamber with out any cusp, like with Tokamaks? Or is this impossible?

[happyjack27]

Yes but two poles exist in this system, oh well, whatever I'll continue to ponder it. So it there anyway to magnetically shield a spherical chamber with out any cusp, like with Tokamaks? Or is this impossible?

It is geometrically impossible to construct a surface that encloses a volume, such that the surface is everywhere convex.

[mattman]

Curiousfusor,

IDK much about Tokamaks. It has taken a so long to dig into the Polywell, I am humbled by how complex this can be.


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Dan,

I dug into this question: What was the current through each ring? From Bussard's IAF paper (page 10):

"Magnets able to run only for a few seconds at high field, and it had to be driven with (almost uncontrollable) by big capacitors, to reach the e-drive currents known from basic theory to be needed (40 to a few 100 amps)."

Answer: 40 to 100s of amps. That is current in each individual ring.

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What is the magnetic field this current produces? From his paper (page 6):

"However the machines ran only at cusp axis fields limited to 70-100 G, because of engineering limitations on drive power, cooling, and system size."

Answer: 70 to 100 Gauss. That is at the axis.

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Are these consistent with one another? Hell No.

The axis is the spot in the middle of one ring. There is a standard equation for finding the magnetic field in the middle of a current loop. Here it is (WB6 had rings 0.127m radius rings).

Axis Field (Tesla) = [Magnetic Constant * 40 Amps] / [2 * Distance to rings]
Axis Field (Gauss) = ([ 1.2566E-6 * 40 Amps] / [2 * 0.127])*10,000
Axis Field (Gauss) =1.9 Gauss

For the corner, it is modeled like a spot equidistant from 3 wires. The distance is from ring center to the corner: 0.062 meters.

Corner Field (Tesla) = [3 *Magnetic Constant * sin(90) * 40 Amps * Distance to ring] / [4* PI * Distance to rings ^2]
Corner Field (Gauss) = [(3 * 1 * 1.2566E-6 * 40 * 0.062) / (4 * 3.14 * 0.062 * 0.062)] * 10,000
Corner Field = 1.9 Gauss


That is nowhere near the 70 to 100 predicted. If I try 800 amps, it is 38 Gauss. If I do the calculation from the ring surface to the corner (40 amps, 0.03 meters) it works out to 4 Gauss. If up the current (800 amps, 0.03 meters) it works out to 80 Gauss.


What is the current if the 70 Gauss estimate is right? 1,414 amps

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Can anyone find an error here? Did I do something wrong? Tom Ligon may know the actual number...

[D Tibbets]

mattman, The quotes do not apply to WB6, but I think the 70-100 Gauss fields applies to one of the other machines. In WB6 the B field was ~ 1000 Gauss. There was ~ 1000-2000 amps delivered from a bank of marine batteries, not a capactor, at least in WB6. The capacitor bank provided the high voltage to the surface of the magnet casings. The ~ 2000 Amps through ~ 200 wire loops provided the ~ 200,000 amp turns and this resulted in the 1000 Gauss field. I once looked up how to calculate magnetic field strengths and found it was complicated by geometry, materials, etc. I've never been sure where the B field strength is determined, though I have heard that it is the field facing the central plasma. This makes sense as the Wiffleball expands outwards from the center, pushing the B field before it untill the Bets = 1 condition is reached. This border "pressure" is the working B field strength(?)*. Before Wiffleball inflation the center of the magrid confined space would presumably be at a lower B field due to the inverse square law, and more confusingly the opposing B field repulsion.

For comparison the water cooled WB4 reached up to ~ 3000 Gauss, one machine- the copper block reached ~ 30,000 Gauss, the copper tube machine may be what you are referencing and it reached below 100 Gauss (I recall the pictures, but not the names, except one was MPG and the other was ...).

Calculating the Magnetic fields may be complex. Measuring the field with a Gaussimeter is easier.

* An alternative definition of the B field strength could be the value at the surface of the can. This would be work for the conformal can shape in WB 6, but would be variable for the square can shape in WB4.


Dan Tibbets.

[mattman]

Dan,

Thanks. It is critical to get the correct numbers. I read back up in Bussard's document and I see that 70-100 G was for the two MPG devices. The 40 to 100 Amps was to prove the basic theory. I did not see an actual number for WB-6 current in the paper. At the end, he gives us a graph of WB-6 current and it shows a plateau at 4,000 amps (which is where that number came from) but this was the machine arching.


I am trying to figure out what is the appropriate electron and ion density. I have used 1E13 1/cm^3 for the electrons. But, as you pointed out, this would be somewhere near the Brillouin limit - which as I understand it, is a physical limitation on how much stuff (charged stuff?) you can pack in space.

Bussard estimates 1E13 1/cm^3 as the number density, for the deuterium gas, being puffed in. I went online and looked at the number densities for dry air (0.02E21 cm^3) so this number seemed reasonable, save that nasty Brillouin limit.

Bussard also listed 1E13 1/cm^3 as the number density for the electrons, needed "..to be of interest for fusion". So, I did not see a real estimate of the number density, of the electrons, in WB-6, anywhere in the paper. If you (or anyone else) do not know it, I can try and estimate it, based on an estimated cloud volume, and 2E12 net electrons in the center.

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Also, where did you get your numbers? I need a source, I cannot just say you told me.

[D Tibbets]

Mattman, several points; The electron current during steady state was ~ 40-45 amps at ~ 12,000 volts in WB6. This comes from the final report on WB6. This was in a document provided on the EMC2 web site at one time. It was subsequently withdrawn, and due to copyright concerns it cannot be reproduced. But the knowledge was out there at one time and cannot be forgotten.

The Brillion limit is a quoted limit for plasma density under certain conditions, but this has been exceeded and there is at least one paper on this issue.
As far as density in the Polywell, I cannot quote the paper, but I think 10^13/cc was claimed (?). The Brillion limit is several orders of magnitude below this.

Working the numbers: 10^13 particles /cc = 10^19 particles /M^3. With atmospheric pressure at ~ 10^25 particles / M^3, this represents ~ 1 Micron pressure or ~ 1/1,000,000th of an atmosphere. This was at ~ 0.1 Tesla B fields in WB6. Scaling to ~ 10 T results in a density increase of B^2 or 1000 ^2 or ~ 1,000,000. This results in a density of ~ 10^25. As I have seen estimates of a working Polywell achieving densities of ~ 10^22 particles / M^3, the 10^13 number may have been an operating minimum for useful fusion as you quoted and not the density achieved in WB6.
This does introduce some confusion. Paschin breakdown and glow discharge/ arcing does occur in the region of ~ 1 Micron or perhaps a little less depending on the gas and geometry of structures (sharp edges). I believe the starting pressure in WB6 was ~ 0.01 to 0.1 Microns, so if the Wiffleball trapping factor allows this to increase ~ 1000 fold within the magrid, then the supposed density would have been ~ ! 10-100 Microns or ~ 10^20 to 10^21 charged particles / M^3. There are some discrepancies here (or miscalculations). Perhaps the Wiffleball trapping factor relates to a projected operating Polywell and not specifically to WB6. Also, considerations of ExB drift- cross field trassport of electrons across the B fields may play a more significant role as the density increases so the maintainable density does not increase at B^2 but at a smaller rate, perhaps closer to B^1.5 Or...

Without the detailed data and internal papers of EMC2 the uncertainty is considerable.

Note that 10^13 to 10^14 particles /cc is the projected density in a basic Tokamak. Nebel's claim of Polywell performance of ~ 62,000 times the power density of Tokamaks is consistent with the final projected densities of ~ 10 ^22/M^3 in a Polywell without much central focus of the ions.

Also note that arcing becomes visible at ~ 5 Microns in a fusor. This does not mean that this is a hard limit. Some glow discharge will occur at lower pressures, it is just that it is much less as a self reenforcing cascade cannot be maintained. I speculate that the amount of glow discharge tolerable before the potential well drains may be significantly less than 1 Micron. This could shift the Wiffleball Trapping factor density gain to perhaps ~ 1/10th of the above example. This would bring the calculated estimates closer in line.

Dan Tibbets

[happyjack27]

Yes but two poles exist in this system, oh well, whatever I'll continue to ponder it. So it there anyway to magnetically shield a spherical chamber with out any cusp, like with Tokamaks? Or is this impossible?

It is geometrically impossible to construct a surface that encloses a volume, such that the surface is everywhere convex.

I should clarify... Regarding tokomaks and reverse field pinches... There Are field lines that are closed. But the same holds true for a polywell. The problem is that, while there are no cusps and those closed field lines, electrons can still leave the field lines; it is, in the classical view of elwctromagnetics, a null manifold -- the electrons can wander outward or inward with equal probability. So they can escape just fine. That is, it is not sufficient for confinement to simply have closed field lines.

The tokamak and I presume also RFP's gain a confinement advantage from quantum physics: there are energy level gaps, however tiny, that they have to jump to travel orthogonal to the field lines, esp. near the chamber walls. But they can jump nonetheless. That's why the tokamak has to be so large, as bussard said in the google talk - to make the number of energy gaps between quantum energy levels large enough so that the losses to the chamber walls gets small enough to be economical. So that's a physics restriction that posses a definite minimum bounds on the size. And that minimum size is very large.

[happyjack27]

... Not to mention that magnetic field lines concave to electromagnetic pressure are unstable.

[Curiousfusor]

All well and good and correct; but after some pondering and taking a look at both what I proposed and the feed back and ideas. I realize that north and south exist in this system and that two cusps, provided the engineering is done correctly, will pinch off most electrons from escaping; along side the positively charged shell.

So what in reality I am envisioning is an electromagnetic ring, such as one of the toroidal electromagnets from the polywell. Stretching it out into more of a hula hoop shape instead of a donut. Then warping it up and around and down and around. So that one pole isn't on the outside as I had originally thought but that, one pole on the top and one on the bottom. Completely within physics, so then the geometry of the electromagnetic sphere leaves 2 cusps 1 at the axis of each pole. The idea is that then the internal wall of the electromagnet will form the positive cathode and when electrons are introduced the negetive potential well will form in the center because of bothe electrostatic forces and the magnetic fields. When ions are injected like in a polywell they "fall" down this potential well and fuse, basically a gridless fusor is formed.

[happyjack27]

*sigh*