## superconductor quenching at high Beta

Discuss the technical details of an "open source" community-driven design of a polywell reactor.

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Tyler Jordan
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### superconductor quenching at high Beta

I've been pondering magnetic fields as a small distraction in between my bouts with another project and I've learned more about superconductors and critical current carrying capacity - wherein the magnetic field, which is normally pushed outside the superconductor, begins encroaching into the superconductor causing it to stop superconducting ... it is very bad when that happens as they heat up and explode.

In thinking about this, I wondered what would happen at high Beta where the core-facing edge of the magnetic field is being compressed. Does this lower the critical current capacity of the superconductor? If so, how do we know how far we can push the superconductors? Or perhaps the question is how high Beta can we go? The problem boggles me a bit. Do we need to blow up a few reactors to find out

see also, the conversation here: viewtopic.php?f=4&p=122214#p122214

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D Tibbets
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### Re: superconductor quenching at high Beta

Sometimes I wander if magnetic compression is the best term. The magnetic field is created by the ampturns in the can. Along with shielding and cooling layers, this makes up the internal volume of the electromagnet cans. This creates a magnetic field ofr X strength at the surface of the can. The permittivity (?)constant applies and is far different inside and outside the magnet. For instance a microwave oven transformer may have several Teslas magnetic fields inside the iron core, but outside the transformer the magnetic fields in air are much smaller. The magnetic field in a constant permittivity falls off with the inverse square law,or if two opposing magnets then something close to the inversed cube with distance.

When you see magnetic field lines what you are seeing is generally isophotes , like altitude lines on countour maps. A stteper slope equates into closer isophotes. The cliff (magnet can surface) gets steeper but it does not move outward. The plasma pressure pushes the magnetic field outward or compresses it outward or increases the gradient outward but does not change the strength locally immediatly before the can surface is reached. If the B field at the can surface is your measure for Beta=1, then beyond this point the plasma is hitting the can (actually before this much plasma is lost due to ExB diffusion issues) and plasma pressure is lost through particle loss and/ or kinetic energy loss. Certainly you can erode the surface of the can and heat it more, but inside the can the magnetic fields would be unchanged (I think) until the can failed or the increased heat reaching the cans resulted in wire resistance changes, ie : quenching due to insufficient cooling capacity for the increased thermal load.

You are not increasing the magnetic field strength inside the can, you are only excluding the field from the interior. I don't think that there is any change in the current carrying, wire magnetic field exclusion, or other properties within the electromagnet itself.

With cusps another consideration is the area of the cusp holes. It essentially narrows to the smallest diameter at Beta of 1, but then begins opening up again.I have used an analogy of two funnels with collecting cones facing away from each and the spouts touching each other. Once Beta=1 is exceeded the cusps open up and the leakage returns to that of low Beta. It is a self limiting situation. If you have a stupendous power supply that can drive the magnetic field out past the mid plane of the magnets, the losses increase and the increasing power only results in increased leakage. If the power supply can push the plasma pressure up further despite the increased leakage, the particles beginning to hit the magnet cans en mass, and things start melting, or at least the plasma cools and thus again an equilibrium is reached, at least till something breaks.
Also, with cusp geometries I think the narrowest width of the cusps is reached at some distance between the magnets and at the radius of the mid plane of the magnets. This distance would, I think, be no more and presumably closer to the can surface than same B field strength distance from the cansthan would a center facing portion of the confining magnetic field (where the field is perpendicular to the center). As such, as Beta=1 is exceeded, the cusps open back up before the magnetic field is pushed entirely to the can surface. Losses through the cusps would dominate over any direct particle impingement upon the cans. At least this would be the case in a collisionless plasma. With collisions ExB issues arise and the picture is more foggy. This is part of what resulted in the changed design of WB6- that is magnet spacing and field conformal can shapes.

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

Tyler Jordan
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### Re: superconductor quenching at high Beta

D Tibbets wrote:
With cusps another consideration is the area of the cusp holes. It essentially narrows to the smallest diameter at Beta of 1, but then begins opening up again.I have used an analogy of two funnels with collecting cones facing away from each and the spouts touching each other. Once Beta=1 is exceeded the cusps open up and the leakage returns to that of low Beta. It is a self limiting situation.

Dan Tibbets
Assuming there is some plasma pressure 'x' at which B=1; and assuming that plasma leakage is at it's minimum at B=1; then might it be possible to design the rings onto some sort of shock absorber platform such that the effective normal force that resists the force applied to the rings (by the magnetic field as it is pushed by the plasma) is equal to 'x'. As such B=1 might be easier to maintain assuming variation in plasma pressure.

Such a shock absorption system may need to be adaptive - for instance, by adjusting the pressure of the gas in the absorber. Perhaps an algorithm could be used to adjust this pressure to accommodate the various inputs to the reactor.

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D Tibbets
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### Re: superconductor quenching at high Beta

Using a mechanical shock absorbing spring arrangement to allow for some magnet movement relative to variations in plasma pressuer might be reasonable IF there are actual plasma pressure variations of sufficient scale and if these variations occur slow enough. A variation over one tenth of a second may be doable, a variation over one tenth of a microsecond is not. If you need to vary magnetic pressure against a variable plasma pressure the quickest responding and most convenient method would to vary the plasma/ electron injection intensity and or vary the current in the electromagnet.

The most basic Polywell mode would be steady state. The electron, ion injection current and voltages remain constant, the B field remains constant and the magnetic field strength and geometry remains constant. Also, the fusion remains constant. There are no pulsations, etc. This is a simpified and perhaps unobtainable goal though. Start up conditions are complex, approachable from different directions and may require temperary major concesions in confinement. It appears that getting electrons into the machine that is doing a good job of preventing their escape is challenging. Pulsations in the cusp openings coupled to plasma pressure variations might be needed. These plasma pressure waves are probably measured in microseconds or less so machanical actuators would be very difficult. Variations in voltage or current into the plasma may keep up. Also microwave bursts for additional global or pulsation heating may be employed.

The problem with varying magnet current is that the wires move and this can lead to wear. A pure superconductor magnet would be difficult to vary in the short term- a hybird with both superconducting and conventional conducting wires would be needed. This has been done in some super strong magnets, but I don't know if this could be applied to the Polywell geometry.

Plasma pressure variations locally or globally may be needed in order to facilitate input, or to enhance fusion- POPS effects. The machine may look different in terms of input energies and B field strength at startup versus steady state. Steady state may be the goal, or a pulsating machine may offer the best solution.

I do not see moveable magnets as part of the design. Certainly the magnet shapes may be far different when looking at minor radius. They do not need to be round, only conformal to the magnet windings. Sharp corners are undesirable due to arcing concerns, but otherwise the geometry may be complex. This to perhaps aid in the relationship between injection resistance and confinement efficiency. A hint of this is shown in the image of a Polywell design Dr Parks presented near the end of his Microsoft presentation.

The whole reactor may be on shock mountings if on a ship, but internally I don't see an application. Things happen too fast and faster and more finely tunable alternatives exist.

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

Tyler Jordan
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### Re: superconductor quenching at high Beta

So the plasma is pushing the electrical field that in turn is pushing on the B-field that in turn is pushing on the magnet and it's housing ... so rapid pulsing in plasma pressure is not going to be translated instantly, but rather would be felt as an overall but smaller increase in force on the magnets and their housing. Makes sense, now I can stop thinking about shock absorbers. Even thinking back on it now this seems a really dumb idea - don't worry though, I have many more dumb ideas where that one came from! So for now, another thought experiment falsified - progress - thanks!

Possibly then, the only potentially reasonable means we have to to adjust the B-field on the fly - perhaps some sort of very simple feedback loop (simple to prevent delaying the adjustment) - how to detect the pulse though (assuming we can't fully predict them), perhaps x-ray variations? Adjustments themselves would cause feedbacks though ... and the complexity reaches a point where we need real hard data.

I'm interested in the magnet design. I've very briefly thought about using both superconducting and non-super magnets together (I've seen similar in ITER magnet design) - like many aspects of the polywell, it seems complicated, but perhaps such will be needed to enhance the overall efficiency, if not the very viability of a net-positive machine.

Much to think on.

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