I concur with TallDave. I don't know why ChrisMB is stuck on a constant density. Beta is proportional to the product of the density and temperature (KeV). You can vary each to your harts content, so long as the product produces the same number (within limits set by arcing concerns and wiffleball trapping efficiency).
Concerning ETW machines. I have done a moderate Google search and have found references to the theoretical work by Elmor, Tuck, and Watson. But, I did not find any reference to any published experiments.
I doubt that a ETW machine would have a significantly higher population of electrons (what is significant?). I have the impression that the 1 ppm excess in the Polywell is already pushing the limits obtainable.
Concerning the capacity of the electrostatic potential to contain ions, I guess that there is no theoretical limit, the density could be huge, so long as the density of electrons remains greater by 1 ppm. The trick is to contain the electron density that drives the electrostatic well, as the effect is opposite on them.
The question of collionality also, enters the picture. With low collisonality plasmas (like fusion plasmas (generally in Tokamak conditions)) the global space charges dominates. In the Polywell with several orders greater density, I'm not sure if this still applies to the same extent.
The question is not what potential well is required to contain the average energy ion, but what is required to contain a sufficient proportion of upscattered ions. A. Carlson thought this number was way above the potential well required to contain average ions. I'm guessing that this was due to his instance on treating everything as a thermalized plasma. In a 'monoenergetic' Polywell the average temperature might be 20KeV with small excursions above and below this value (say 1KeV) . In a thermalized plasma with a average temperature of 20KeV, the slued thermal curve might have a few percent of the ions well above 100 KeV, and a rare ion well above a MeV. In one of his papers, Bussard actually discussed the potential needed to contain upscattered ions and he quoted a number ~ 1/2 above the potential well (perhaps ~ 20KV above). I'm not sure if this is before or after annealing adjustments. In any case upscattered ions are encouraged to leave through cusps before they build up so much energy that they compromise the desired conditions inside the Polywell.
Another thing to consider is the magnetic field in a Polywell, that is not in an ETW machine. The average ions are contained electrostatically, The upscattered ions are contained magnetically till they find a cusp. Cross field transport is apparently not a concern over this limited lifetime (a few thousand passes of the upscattered ion before it escapes through a cusp. These ions could still contribute a small amount to the fusion rate, assuming the rate is not dominated too much by confluence, as these ions are less likely to pass through the center. In short, past some limit needed to maintain the Wiffleball trapping factor, any upscattered ions are welcome to leave so long as they do not cost too much energy, which Bussard claims is the case. Hanging around longer would lead to more upside thermalizing of the plasma, which I understand is particularly important when considering the electron temperature and bremsstrulung losses with P-B11 fusion.
Concerning the energy of the injected electrons, there is no free lunch. Weather the high voltage is on the electron guns, or the grid, the electrons steal energy from the electric field to obtain their kinetic energy. In electrical circuits, as the current climbs, the voltage drops, unless you can maintain the potential with a powerful enough power supply. In WB6, I believe EMC2 had a ~ 10-15,000 Volt power supply capable of providing several amps of current. This was way below that needed to establish or maintain a Wiffleball, thus the use of capacitor banks that were charged slowly by the power supply, and discharged rapidly during the experiments.
Incidentally, ChrisMB (or someone) has asked why Bussard used this relatively low voltage when everyone knows levels 3-8 times higher would have been much better. The answer is obvious, due to financial concerns, they could only use what they had available. Either they couldn't get a higher voltage power supply, or they couldn't get the higher voltage capacitors. Also, the design they used for the magrids may not have tolorated higher voltage differentials between the low voltage magnet windings and the high voltage case . The picture of a WB coil before it was welded shut, shows the wire coil protected by only one or a few thin layers of some material like mylar. Failure of this insulation was (I beleive) what lead to the failure that ended WB6's career.
By 1959, Elmore, Tuck and Watson5 explored the idea of using Farnsworth's
gizmo backwards to accelerate electrons from the outer sphere (a cathode) to the inner
sphere (an anode). The inner sphere of such a machine is a grid, which forms a
geodesic "potential surface" which the electrons aim for as if it were solid. However,
when they get there, most pass right through and coast in a straight line, converging
from all sides to the center, then they pass out the other side. What results is region at
the center of the inner sphere with a very high density of negative charge, called a
"virtual cathode". This region will attract positively-charged ions, which will tend to
oscillate back and forth through the central region. Provided more electrons are forcefed
into the system than ions, a "potential well" is formed in which the ions are trapped
by excess negative charge. Interestingly, an ion oscillating entirely inside the inner grid
will be trapped almost indefinitely and will conserve its initial kinetic energy remarkably
well, thus theory predicted this device might be a surprisingly efficient ion trap.
However, the electrons had to pass through the grid, which meant eventually most of
them would hit the grid. Depending on the grid's "transparency", an electron might
make 10 to 50 passes before being lost, requiring another electron and the power to fire
it into the system. Because the electrons had to outnumber the ions by a significant
margin, the researchers expected this device could be harnessed to produce only tiny
amounts of fusion, and decided it could never make a workable power reactor. The
Elmore, Tuck, Watson concept is an electron accelerator, or EXL machine (see figure
2).
Dan, I think you're correct that it is impossible to push the electron excess much beyond what PW does -- which is the problem with ETWs. The reason they need an electron excess appears to be that the electron cloud surrounds the anode grid (so the outside electrons aren't accelerating your ions). Polywells solve this by putting a magnetic field on the anode grid and using that B field to keep a large proportion ( >1000:1, this is the GmJ trapping factor) of the electrons confined on the interior.
The thing ETWs apparently do really well is confine ions. I think Bussard saw this and said "Aha! Now I just have to solve the electron loss problem and I've really got something!" and so the Polywell was born.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
If someone puts forward an argument that polywell can achieve EITHER 10T OR beta=1, then I might start paying some attention. If you claim both and you then go on to claim that the ion density in the edge is 1/1000th of that in the centre, then you are claiming densities in excess of STP. If you don't understand that, then you don't understand what beta means. It is a measure of what is, not of what could be. So if you can get beta =1 and you want density 1E20 at the centre, then you only need a 0.0001T field to confine your 1E17 density at the edge.
The problem is, you just don't seem to understand what claiming 10T AND beta=1 means. What it means is that it is almost surely bullshit.
Does anyone know if there's some reason that's physically impossible? Not that we probably need that much ion focus anyway, I'm just curious what would prevent it. I mean, obviously it's very dense, but you would expect that from a machine producing 62.5 billion times more power density than ITER at the core, as chris assumes here.
I haven't actually seen any kind of coherent argument against beta=1 at 10T, although 1000:1 convergence is probably optimistic.
This might be a good time to calculate, based on the ITER comparison, at what size a PW would get to 100MW assuming 10T and no ion convergence.
Dan,
That was Art's question, but I think it was more a question of theory.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
Maybe I am missing the bus here, but is not Beta=1 the balance point of electron kinetic pressure against the confining field as measured at the edge. At this condition (Beta=1) the wiffleball effect occurs, ie.: shrinking of the cusps as the electrons push against the spherical magnetic field?
So who cares if you have a field of 1T or 10T? That merely determines the maximum containable electron kinetic pressure (and corrosponding density). The B-Field is balanced against the plasma pressure, and that is created by how much you inject (drive). Going beyond unity (Beta>1) would inherently create an unstable plasma, as the field applied could no longer contain the electron kinetic pressure at the edges. Thus, the density of the electron plasma is limited to the containing field. Is it not the point to have Beta=1 at the edges in order to achieve Wiffleball? There is more to discuss here relating to what actually happens in the cusps as they shrink, diamagnetic currents, etc. But that is not part of this.
Once ions are introduced, they are attracted to the core(big minus) and they orbit<oscillate> with an intensity directly related to the percieved well depth. And for sure, if you introduce too many Ions (+), you will overcome the electron density (-), so this would be a "knob". In the currently used operating condition (maximum electron density based on Beta=1), would not the effect of increasing the B-field mean that you are going to increase the ability to have a higher well depth (electron pressure/density), a good thing, and also eventually compress the ion gyro radius (also a good thing)? And with that, eventually you will have more ions orbiting tighter in the center and in turn possibly have more fusion events? I think this is outside the proposed operating realm of the PW. I would think that there is a point that for a given size of machine, with given drive potentials, that scaling up the B-Fields does nothing but a: waste power and b: compress gyro radius which is not neccessary, and this point is essentially Beta=1. If you increase the B-Field, you have just moved the point at where Beta=1 for that machine.
The Beta=1 regime is what Bussard has operated at on every test machine. It is how he tested for Wiffleball Effect. I do not understand where one would say that Beta=1 has not been achieved. The increasing of the B-Field merely sets the upper operating limit for a given machine configuration, the maximum electron kinetic pressure containable, and in turn, density and well depth, which in turn determines just how energetic the ions will be as they accellerate for the center, which in turn is hopefully enough to cause fusion when they collide (at whatever angle). After all, the higher the energy of the Famous Flying Ions, means the greater the collision angle range over which they still retain enough ompf to fuse.
The MAGRID is all about electron confinement, minimizing electron losses and increasing electron lifetime in the machine. This is the Well.
Ions are introduced to take advantage of the electron created virtual cathode (Well). They care not about the Magrid, they care about the virtual cathode in the middle and the Super E(-) they think lives there but can't find. They also care if they will live long enough to thermalize or not before they fuse.
Raising the magnetic field only increases the operating potential of a given machine. I do not see this as a chicken and the egg issue.
Last edited by ladajo on Fri Jul 09, 2010 11:15 pm, edited 1 time in total.
OK... ITER helpfully gives me a plasma volume of 837 m^3 so I'm going to smush that into a sphere to calculate a Polywell radius... from V = 4/3pi*r^3 I get r = (3/4V/pi)^(1/3) and that gives me a radius of 5.846271089... someone tell me if I did something horrible there; it appears to work in reverse though.
Now things get a little crazy. If PW has a 62,500 power density advantage, that means at the plasma radius above, with no ion convergence, we'd get... 31.25 million MW. That'll be useful later when we want to build a Dyson sphere, but for now let's try for something more practical in these primitive days of 2010. Let's conservatively assume PW machine radius is twice the plasma radius. At 1m radius I get, from r^3 scaling down, a power ratio of 1600 and a power (again, no convergence) of.... 19,549 MW. Um.
Did I do something wrong here? Or is ITER's power optimistic or something? Otherwise Rick has a lot of room for error.
I don't get to 100MW till radius is around .2m.
Oh wait... ITER is giving D-T numbers aren't they? brb...
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
...ok, power density of D-T to D-D is 68:1. Let's run through that again...
So, with D-D, ITER makes an amusing 7.35 MW, and instead of 31.25 million megawatts, with D-D PW starts with a mere 460,000 MW at ITER's volume (maybe we'll just make a ringworld). So, for 1m radius PW (machine, .5m plasma), ratio is still 1599 and we get a power of (drumroll please)... 287MW.
Now we're looking pretty reasonable, and in fair agreement with our WB-6 extrapolations. But this is still without any ion convergence.
Next, we should look at WB-8 numbers.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
I really do wish I could keep out of this, but it is all a bit cringe-worthy to watch, without corrective inputs.
D-D to D-T 'conversion' is accepted to be x200.
The max empirical power from toks appears to be around 0.5W/cc with DT.
Yes, ladajo, you are right and have, again, understood what my original point was. "I would think that there is a point that for a given size of machine, with given drive potentials, that scaling up the B-Fields does nothing but a: waste power and b: compress gyro radius which is not neccessary, and this point is essentially Beta=1. If you increase the B-Field, you have just moved the point at where Beta=1 for that machine." This was the point I was making above. I am, clearly, not entirely incomprehensible!
I really do wish I could keep out of this, but it is all a bit cringe-worthy to watch, without corrective inputs.
Oh please , you've induced as many cringes as anyone.
D-D to D-T 'conversion' is accepted to be x200.
What's your source for that? The power density relation is given as 68:1 here. Is there another factor that enters into the power density? If so, what?
Hmmmm, 200 does make it come out very nicely to 98MW (again, before convergence). I like this # if I can find an excuse to use it.
The max empirical power from toks appears to be around 0.5W/cc with DT.
Roughly the same as the number ITER gives, but thanks for sharing.
This was the point I was making above. I am, clearly, not entirely incomprehensible!
Sometimes I think you're trying to make sense, then you write things like this. If your point was just that density/temp increases with B at beta=1, then you've successfully stated something fairly obvious, which we all agree with. Earlier, your point seemed to be that B=10 and beta =1 were incompatible, an argument for which you gave one fairly ridiculous reason (MeV plasmas) and one reason (density) for which you have given no explanation, as of yet, as to why it's problematic, which makes me begin to suspect you may not actually have one but are merely being obstreperous.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
For WB-8, I'm going to assume machine radius of .5m, plasma .25m (anyone so disposed should feel free to refine my simplistic 2:1 ratio of machine radius to plasma radius).
So... (10/.8 )^4 = 24414 as the ratio of power between a 10T and a .8T machine, all else being equal, I get 36 MW at .5m at 10T which gives us... 1471 watts of fusion from WB-8. Interesting.
I'm tempted to ask Simon where that starts to be a rem hazard. If Rick gets ahold of some tritium the lab boys may need lead aprons at 100KW.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
To Chris MB, I admit the dynamics of the electron and ion flows within the Polywell are complex. If the plasma is considered to be like a fluid, then pressure/ density would be the same throughout the containment area. This is what is derived in the model presented by Joel- equal ion density throughout the Wiffleball. This does not mean the ions have the same energy throughout. The ions converge towards the center if there is some convergence/ focus of the ions. The ions speed up as they approach the center(assuming elliptical potential well, and before the ions are slowed by any vertual anode. As the ions transit this central zone they are concentrating into a smaller volume, but they spend less time there than they do in the outer regions , but the outer regions have a larger volume. I don't know if the opposing actions cancel out so that the measured density is the same everywhere in the Wiffleball, but I suspect this is the case as it would satisfy the hydraulic pressure picture. The comparison to opposing beams would imply a multiplication of the density where the beams intersect. The picture is foggy for me. Therefore Joel's model is simpler and the results he got was based on this condition. I believe his calculations gave a breakeven radius of 1.3 meters. In this case the complications of considering density gradiants within the Wiffleball can be ignored and this gives a baseline for predicting minimal performance under various size, B field, density and energy conditions.
The additional complications of bunching, like with POPS or other effects would complicate the picture even more.
TallDave wrote: I hope we can get some FAQ answers out of this at least. I look forward to someday answering 99% of questions from noobies by telling them to go FAQ themselves.
TD,
Any time you provide a "Q & A" for the FAQ and get general buyin from the folk here, I would be MOST pleased to post it at the FAQ. Better yet, please get posting priveleges there and you can do it yourself!
Last edited by KitemanSA on Fri Jul 09, 2010 11:16 pm, edited 1 time in total.
Thanks, did that a couple weeks ago actually. Today I added that tidbit from MSimon about the current limits of first-wall materials (thanks, Simon!) so hopefully now I can stop asking him that again every few months.
I should really try to add a few a week. There's bound to be a flood of interest if WB-8 confinement results are good. I was thinking of one for "What are the advantages/disadvantages of PWs relative to toks?" I think we covered some good ground on that this week. I feel like I understand that topic a lot better now. The WB-8/100 extrapolations might be good too.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
, you've induced as many cringes as anyone.