Simulation Nuances

[Uthman]

I don't think i'm quite ready to actual model a polywell simulation, but at bare minimal, I wanted to model point charges and currents, in a vacuum, in 3D space.

1. Most of the polywell sims I've seen so far model the coils as a series of rings of constant current, calculating their magnetic fields by numerical integration. In reality, the current in the coils probably won't be constant, and there will be other issues like inductance. But my real question is, how come none of the sims factor in the 'electric' field generated by these coils? A 'static' charge, relative to the observer, produces a static electric field. A 'moving' charge produces a magnetic field, plus an electric field somewhat different from the original field produced at rest. Where can I go about finding the equations of the electric field produced by charge moving in a wire? I know that B of resting charges =0. But it doesn't make sense to me that E of moving charges =0 because of conservation. I would assume only a portion would be 'converted' or seen as magnetism, as the electric field and magnetic field are one of the same.

2. I've read I think in Tom's .pdf that in the polywell, the ions and electrons would have sufficient energy that recombination effects would be negligible. Where can I go, or what resources exist to calculate the cross section of recombination? Wouldn't there be some 'slower' moving ions around the outer edge of the magrid? Also, do we start with ions, or is it the responsibility of the magrid to ionize the gas particles and what is the advantage of doing it one way vs the other? Speaking of the magrid, the outer shells of the coils are kept at a high positive potential; I'm assuming the way this is done is similar to the way it's done with a capacitor. Don't these High+ plates produce an electric field that try and tug electrons out of the well?

3. If electron-ion recombination is rear, would it be safe to assume that for simulation purpose, attempting to model e- e- collisions are unnecessary?

4. Many places on this forum, the technical complexity of simulations have been discussed. I know much too little about physics to have foresight if this would even work or not, but in game programming we make use of many algorithms to produce approximations, for example the marching cubes algorithm for producing 3d surface approximation of fluids. I was wondering if the complexity of the polywell system could be reduced if every step in the simulation, the n^2 relationship between the electrons and ions were approximated as follows:

A) Create a predefined 3D lattice / grid of points. These points may either be equidistant, or can be closer grouped towards the center of the grid to provide a better resolution where most of the 'action' occurs (greatest particle density). For the sake of this example, lets assume the distance between each point is constant.

#define rez 500
struct latticepoint
{
double sumCharge, numParticles, oldNumParticles;
Vector3D B, E, oldB, oldE;
}
latticepoint grid[rez][rez][rez];


B) Each of these lattice points would have a few attributes -- a sum of charge, and vectors describing the B and E field at the points location. For every charged particle in the polywell (for each electron and each ion), we would assign the charge of the particle to the nearest lattice point. This is an O(1) operation per particle and could be done using a vector formula such as grid_location[xyz] = rez * particle_location[xyz] / polywellsize; We would also keep a tally of the number of particles that were added together to collect that charge.

C) We could then imagine of wire, connecting every lattice point to it's 6 adjacent points (above, below, right, left, forward, backward). We would assume that there is a current in each of the wires which would be some gradient function of (the number particles currently at each lattice position vs the number of particles that were in it in the previous time stamp, eg Delta numParticles) compared to Delta numParticles in the 6 nearest neighbor. In essence, figure out 'how much charge moved where' to approximate a current. From this, we could calculate a magnetic field.

D) Now going back to my very first question, these are free charges in a vacuum, I would assume that there is also some 'electric field' value associated with them. How would I go about calculating the electric field of these 'moving' charges in a wire?

E) The next time step, we would move the current E and B values into oldE and oldB, reset E=B=numParticles=0. If oldB and B are different, that would mean an electric field was generated and that would have to be factored in. If oldE and E are different, some electric field was generated, and that would also have to be factored in. Ans some other complications......

I don't know if this would work, there are too many current unknowns. But if it would work, it would essentially reduce the modeling complexity to O(numchargedparticles + numlatticepositions).... which is much better than O(n^2).[/list]

[kcdodd]

There is no electric field associated with a constant current only. You may imagine that if you get close enough to the atoms in the metal that the current is really point charges and so it is not current only, but this does not matter for practical scales since the material is overall pretty much neutral.

What you describe is called particle in cell (pic) code. You track a small number of particles (numbers on order of 10^6, instead of 10^20) and try to use that as a sample to figure out what the plasma does, which is modeled as a distribution on a grid by some kind of interpolation between grid points. This distribution is then used to calculate the fields and then repeat. Current is simply avg. velocity of the particles times avg. charge density.

[D Tibbets]

I'm uncertain that there would be no gross electrical field with a very steady direct current, but the point is moot. Any electric field created by the magnet windings are blocked by the metal walls of the magrid casings. Some inductance may occur, but again, depending on the design the magrid casings will be grounded, or connected to a positive power supply that is powerful enough to completely swamp any inductance effects- it has to be in order to maintain the positive potential that accelerates the electron gun electrons, and through a feedback mechanism, the recirculated electrons.

In WB6 the available power supply could only provide a few amps of current which was inadequate to maintain the desired voltage against the dozens of Amps of electron current that was being accelerated. That is why the power supply was used to charge a bank of strong capacitors which were up to the task for the required few milliseconds. I have no idea if this work around was necessary with WB7.

With increased amps in a stronger magnet, any internal electric field would be stronger and inductance could increase the charge across the metal that needs to be overcome. I'm uncertain if this would necessarily be a negative effect, it might be additive. In any case, there will need to be several layers of metal containing coolant or insulating vacuum between the windings and the outer magrid shell. Grounding any of these layers would again moot the issue.

Dan Tibbets

[TallDave]

I've read I think in Tom's .pdf that in the polywell, the ions and electrons would have sufficient energy that recombination effects would be negligible. Where can I go, or what resources exist to calculate the cross section of recombination?

I think you want ionization energy.

http://www.science.co.il/ptelements.asp?s=ionization

If you read Valencia, Bussard expects total ionization to happen in usecs -- basically the first hot electrons are enough to cascade around and quickly ionize everything. (This is one of the ways a Polywell is different than a fusor, which operates in a neutral background.) I think we dug up an equation for this in a post a ways back.

Wouldn't there be some 'slower' moving ions around the outer edge of the magrid?

Yes, but otoh you're talking about collisions at eVs in a 10KeV well, and the collision cross-section is highest where speed is lowest, meaning a very cold ion (remember we're talking about getting a collision at .001% of well depth, combined -- the large majority of ions will probably have more than that in transverse motion at any point in their orbit because the ion focus probably isn't nearly that good) that somehow picks up a very cold electron at the edge is likely to lose it again very quickly. Even if you somehow got significant neutral recombinations at the edge that managed to verrrry slllowwwly drift through the wiffleball field (which iirc has some density of random-walking electrons trying to cross-field diffuse, though I don't think Bussard shared those equations, which he references in Valencia)without being hit by anything energetic, it's hard to see how it could be a major loss mechanism since they don't carry off any energy to speak of.

[D Tibbets]

To expand on what TallDave said. The relatively slowly injected neutral gas near the border of the Wiffleball results in Nearly complete ionization. The additional dwell time for the ions in this area that might be gained by introducing ~ the same angular momentum energy probably would not add much, especially when you consider that the neutrals will be scattering randomly without containment until they escape (more may leave the Wiffleball faster if they have initial vectors that are nearly tangential to the center. Without careful calculation of scattering dispersion of neutral gas, I suspect the longest dwell time for the neutral gas is to give it an initial gentle puff straight towards the center.

The ionization rate is dependent on temperature and density. It takes a finite amount of time for a certain percentage of the neutrals to ionize.
Using some made up numbers:

Initial speed of gas injected towards the center= 10 M/S

Wiffleball diameter= 20 cm (rough guestimate for WB6)

Neutral transit time= 5 mS unscattered. With scattering a significant portion may leave much earlier. Also neutral - hot ion collisions would quickly heat the neutrals to significantly higher speeds. Assume a net effect that the neutral transit time is ~ 100 microseconds or less

Time for 90% of the neutrals to ionize= an assumed ~ 50 microseconds .

Net ionization = ~ 99% of the neutrals that have not already escaped.
This means that ~ 1 percent of the neutral gas would escape a WB6 type machine without ever having a chance to ionize.

In a larger (~ 3 M) machine the same parameters would apply except the neutral transit time would be ~ 10 X longer, so the ionization percentage would be closer to 99.9%... err- or would that be closer to 99.99999999999% ( I think that doubling the neutral transit time would increase the ionization efficiency to 99.99%, so a 10 X increase in size would be yet larger)*. This eases the magrid external pressure arcing concerns. It also means that more of the ions would be ionized near the periphery (as a percentage of the total) and the ions would have a tighter initial monoenergetic nature.

This is why Bussard said the neutral gas ionization issues disappears (or at least becomes much less relevant) as the machine size grows.

Then there are microwave effects, etc that might contribute to initial ionization and possible subsequent POPS effects. Ion guns also possibly allows for more time dependent manipulation of the ion population

* If WB 8 is ~ 60 cm wide, then as shown above, the ionization would be 100 x times better than WB6, and WB7 or ~ 99.99% in my comparison.
And the edge ionization would be ~ 2X, 4X better(?).
This may be one of the issues addressed in WB8. Is it worthwhile to continue the effort to develop extremely strong ion guns, with the problem of getting the produced ions into the Wiffleball at low energies and without disturbing the magnetic fields too much, or will the much simpler, and possibly even better gas puffing method serve? At least for the larger fixed site reactors this may be the case. For smaller next generation machines (perhaps small enough for plane, train, small ship, spacecraft use) the balance may favor ion guns.

Dan Tibbets

[D Tibbets]

Also, from an energy loss perspective, as TallDave said, I don't think it is a concern. Bussard repeatedly stressed that the electron losses, and specifically the cusp electron losses, dominate over everything else. The issue with the neutrals is where they ionize (preferably near the edge of the Wiffleball border) and the rate that they can leak out, thus contaminating the magrid external enviornment and raise the density in this region to the level where arcing (glow discharge or Pashin breakdown) to much more vulnerable surfaces can occur. As the Wiffleball containment factor allows for the concentration of charged particles only, the baseline density that this Wiffleball effect builds on is dependant on this background neutral density / pressure. This background pressure is somewhere around 0.000001 atmospheres (~ 10^19 particles /M^3) so this limits the internal density due to Wiffleball confinement to ~ 10^22 or 23 charged particles/M^3, depending on how good the Wiffleball confinement actually is. This density advantage is the key for all of the other Polywell compromises, dynamics, etc. that allows for the projected positive performance.

Dan Tibbets

[D Tibbets]

Also (not again!) I wonder if neutral gas injection is actually needed.
ASSUMING a surge of ions or ionizing internal neutrals is not needed to form the Wiffleball, the background neutral population at ~ 1 Micron, or ~ 0.000001 atm, is drifting around. As they enter the Wiffleball they are ionized and trapped. Additional neutrals would need to be fed into the system to replace these neutrals, but they would not need to be injected directly into the magrid.
At least in principle this might work in a steady state machine. Of course you need to consider all of the fusion ions, etc finally being neutralized outside the magrid and the need to pump them out. The pumping concerns may not be changed, but the need for the gas puffer tube entering the magrid space would be. Also, a consideration of heating these neutral externally by x-rays, etc is a concern, but again this would be no different than the situation with neutrals that escaped from the puffer configuration.

Dan Tibbets

[happyjack27]

my simulations ( viewtopic.php?t=2720 viewtopic.php?t=2741 ) included all particle-particle electric and magnetic interactions.

agreed that ion-electron recombination would be negligble. (de-ionization) if i were to model it, i'd model it on a more fundamental level - that is, on the quantumn physics level, rather than a classical approximation. i'd do this by way of fourier transforming back and forth to fourier space each iteration.

as to methods of doing it faster than n^2 (brute force n-body). the method that you discuss is already the dominant method for doing so, it's called a "tree-code". http://en.wikipedia.org/wiki/Barnes%E2% ... simulation most of the algorithms have been developed for astro-physics (gravity simulations), but they can be modded to do electromagnetics.

however, using a GPGPU to massively parrallelize it, it still takes very large N before the fast tree-code method starts to beat out brute force N^2.

At which point in order to simulate it in a practical amount of time you'd have to use very large time steps (relatively speaking), and that's going to impact the accuracy of the simulation.

way around that is you use multiple gpus - but then you have to worry about bandwidth between the gpu's and there's just not enough of that, and n-body problems don't scale well that way. so long story short we don't have the tech yet we're using a fast-tree code on a problem like this is really going to pay off.

the fourier-transform method might actually be more scalable. (maybe?) and with it you can include quantumn physics (to limited resolution).

EDIT: i should add that, though it takes very large N for a tree code to beat brute force n-body, since tree-codes are NlogN, when they do pay off, they pay off big. sim time grows at roughly N. (logN is nearly constant for very high N)

[kcdodd]

I think the main object of simulation should be to go far above n=10^17m^-3 with a full EM code. Low density plasma is not very interesting here because it is high density where the debye length gets so small that one should not see any charge separation (ie no polywell, no ion trapping in the cusps, etc). Don't worry about recombination or collisions or any of that stuff. Just try to get a stable simulation at high density. However, what happens is that the granularity of PIC codes becomes a huge problem as it will lead to large non-physical instabilities in the simulation. I have tried to go to this high regime myself but simply could not get adequate stability to get anything useful. Especially around n=10^19m^-3 simulation became impossible, as I remember. At low density the polywell idea did not seem very promising either which is why I moved on to other confinement schemes. Ions simply follow the electrons out of the core. To continue to high density one may have to go to a 1-D code and simply see if polywell is possible in 1-D at all, if not its pretty much a futile effort in 3-D, since the cusps become approximately 1-D problems. In 1-D one can go straight to full-f simulation using the Vlasov equation. At least, that is my suggestion to anyone looking to do serious work on this.

[D Tibbets]

I think the main object of simulation should be to go far above n=10^17m^-3 with a full EM code. Low density plasma is not very interesting here because it is high density where the debye length gets so small that one should not see any charge separation (ie no polywell, no ion trapping in the cusps, etc). Don't worry about recombination or collisions or any of that stuff. Just try to get a stable simulation at high density. However, what happens is that the granularity of PIC codes becomes a huge problem as it will lead to large non-physical instabilities in the simulation. I have tried to go to this high regime myself but simply could not get adequate stability to get anything useful. Especially around n=10^19m^-3 simulation became impossible, as I remember. At low density the polywell idea did not seem very promising either which is why I moved on to other confinement schemes. Ions simply follow the electrons out of the core. To continue to high density one may have to go to a 1-D code and simply see if polywell is possible in 1-D at all, if not its pretty much a futile effort in 3-D, since the cusps become approximately 1-D problems. In 1-D one can go straight to full-f simulation using the Vlasov equation. At least, that is my suggestion to anyone looking to do serious work on this.

Speaking of Debye length, perhaps you can educate me. Generally, to calculate the Debye length, there needs to be a very, very tiny current to avoid zero in the denominator but otherwise assumes no (or almost infinity small) current flow.. But there is significantly large electron currents (> 40 Amps, and perhaps more than 10 times that if recirculation is considered as current flow) and also significant ion current, at least as fusion ions are leaving the system and being replaced with new fuel ions. How does change the concept of Debye length and it's effect on this plasma.

Dan Tibbets

[kcdodd]

I don't know about that particular assumption. I think the biggie is that the plasma is in thermal equilibrium which means it must have a Maxwellian distribution. There is not really any way to achieve that in any plasma, much less for polywell where it is assumed it is not Maxwellian. Current flow will also necessarily mean it is not Maxwellian. However, interestingly, the conclusion is still very nearly describes most plasmas and so is used as a plasma parameter. I know many like to argue Polywell is exempt because it is not Maxwellian, but the forces at work are the same none-the less and if one messes around with code enough at high density one will see why. It actually becomes worse because Debye shielding assumes there are ions around as background which neutralizes most of the electrons and are immobile. But in Polywell, in the cusps and beyond, one is trying to have zero ions. Which means the effect of the electrons are many times greater (for the same density) and shields the external potential much more. So while the value of debye length is not exactly applicable, it does give, in my opinion, an upper bound, not a lower one, on how far the voltage will penetrate the plasma.

[Joseph Chikva]

I don't think i'm quite ready to actual model a polywell simulation, but at bare minimal, I wanted to model point charges and currents, in a vacuum, in 3D space.

It seems as interesting.
Have you an experience and also computing facilities together with corresponding software for this simulation?