Time for a possibly absurbly optimistic prediction

[Art Carlson]

I'm aware the B^-2 result, which as you've shown, is the theory but that doesn;t even begin to address the lack of stability with respect to time. So I would suggest a realistic calculation cannot presume the instantaneous steady state, from which B^-2 derives, but must surely be worse than that because it's, frankly, just plain obvious that as the energy density goes up, stability drops and the B^-2 doesn't include a hint of accommodating stability - I guess??

What sort of stability are you talking about?

Unless people keep trying to turn the thing into a sphere, it should be stable to MHD interchanges as well as any sort of translation or large scale deformation.

Micro-instabilities? Those are usually lumped into transport coefficients.

We are contemplating operation at beta=1, or at least some fixed value, so I don't know why scaling up the energy density should introduce any new instability (like the beta limit in a tokamak).

Unless you have an incredibly dirty plasma, I can't imagine any sort of radiative condensation at fusion temperatures (which may or may not be related to the density limit in tokamaks).

???

[chrismb]

What sort of stability are you talking about?

Unless people keep trying to turn the thing into a sphere

I thought that was the idea!?

Unless you have an incredibly dirty plasma

You mean, like would result with a pile of MeV 3He or 4He particles sputtering the inside of the reactor vessel?? Now I wonder how that could happen!?

[TallDave]

As long as we're being absurd, you might as well toss in 10x density (100x power) for POPS.

[ducks]

On losses we have no handle at all.

Depends how much of Bussard's data you trust. Either way, WB-8 will tell us a lot.

Unless people keep trying to turn the thing into a sphere

I think we agreed on quasi-spherical.

Didn't Dr.B. hve a section on loss mechanisms in his Valencia paper?

Yah. It isn't just theory, according to Bussard.

Tests made on a large variety of machines, over a wide range
of drive and operating parameters have shown that the loss
power scales as the square of the drive voltage, the square
root of the surface electron density and inversely as the 3/4
power of the B fields. At the desirable beta = one condition,
this reduces to power loss scaling as the 3/2 power of the
drive voltage, the 1/4 power of the B field, and the square of
the system size (radius). Since the fusion power scales as
the cube of the size, the fourth power of the B field, and a
power of the E drive energy equal to the E-dependence of
the fusion cross-section (cross-section proportional to E to
the s power), minus 3/2. For DD, s = 2-4, while for DT, s =
3-6 in useful ranges of drive energy. For pB11, the cross
section scales about as s = 3-4 over the system-useful range.

Since WB-8 gets .8T magnets, it should be illuminating.

[TallDave]

Minimal Near break even size reactor:
Fuel D-D
Diameter = ~ 62 cm = ~ 10X size scaling
B -field = ~ 3.3 Tesla = ~ 1,000,000x scaling
Optimization of geometry = ~ 5X scaling
Potential well ~ 100,000 V = ~ 30X scaling

Multiply all of these together and the machine would have a fusion output of ~ 1,500,000 watts. Already near break even.
If the B- field was increased to ~ 6 Tesla, the output would be ~ 18 MW

I'm not sure why you're using 62 cm diameter with 3T magnets.

I did this exercise a while back

.00141 watts from WB-7 at .15m radius and .1T magnets burning D-D

WB-9 - 1.5M radius, 1.8T magnets, burning D-T, higher drive

radius ratio = 10 --> power gain = 10^3
magnet power ratio = --> power gain = 18^4
drive power gain = 10
D-T gain = 68

0.00141*10^3*18^4*10*68 = 100MW

I ignored geometry gains.

If they can get this to work with POPS at 10x density (100x power) as well, we might get 100MW with .4T magnets, which is downright scary.

EDIT: Oops, didn't watch my formulas closely enough. s/b .57T

[D Tibbets]

The numbers I used were arbitarily chosen for convience (rounded numbers). B- fields in the 3 Tesla range because I understand that that is doable with cooled copper (Once magrid crossection volume is large enough to contain alot of windings along with cooling plumbing and insulating structures) To get 10 Tesla, I'm sure superconducters are required. Also, M. Simon's proposal to use MRI magnets are in the 3 Tesla range. Size was chosen to get a round number and to still possibly be squeezed into the current 1 meter vacuum chamber that EMC2 is using, and yet be large enough to possibly get meaningfull size scaling compared to the 30cm WB6 and 30cm (or 35cm?) of WB7.

I briefly considered adding potential POPS gains but I have seen gains mentioned from ~ 4X to a 1000X, so I chose to consider it as frosting on the cake, and not nessisary to develope my optomistic projections. I understand that my numbers are already streaching the engeenering limits of thermal wall loading, vacuum capabilities, etc. Or, even with my nonmaximized numbers, the performance is already limited by engeening concerns, ie- there is alot of wiggle room in the physics ( or as A. Carlson said, lots of room on the pessimistic side of the predictions, but hopefully not to the extent that requirements ballon to such proportions as the Tokamacs need to break even).

Concerning Chrismb's concern about sputtered products contaminating the reaction space, so long as the sputtered products are mostly ionized, they would find it very difficult to enter the Magrid (positive ions repelled from the magrid, negative ions tangled up in the collection grid (?)), so contamination will be minimal. The concern would be vacuum pumping of any sputtered or recombined neutrals before they built up to levels which would cause arcing. At these levels the neutrals, even if they penitrated the magrid, would have a density much below (1000X?) the fuel ion density ( due to the Wiffleball traping factor and even without concidering any convergence of the ions to the central core.) The alphas (or P,He3, and H3 fusion products from D-D fusion) could all be slowed to slow speeds while thie energy is harvested, before they hit a wall. I don't know why the different energies would be a show stopper. After all, a mass spectrometer can seperate and collect widely different energy charged particles. Weather this can be done in a Polywell enviornment is debatable, but if almost all of the charged fusion products exit through cusps the engeenering challenge will be simplified.

[EDIT] ps: Is the limit for MHD stability an exactly spherical surface or almost a spherical surface approached from the convex side? I ask because I wonder if I should persue my monople research in order to develope a truely spherical machine like a government official believed the Polywell was claimed to be?

Dan Tibbets

[MSimon]

Tall Dave,

High magnetic fields may be desired even with POPS in order to shield the grids from high energy alphas. You just make the device smaller. Which is very useful in a mobile device. And from a cost standpoint.

[TallDave]

Sure, I was just throwing some fun numbers around. I should probably have figured out how small it could be instead of how weak the magnets could be.

Let's see, with 1T magnets I get 100MW at a radius of .7m. Not bad. That would be pretty cheap.

One nice thing about POPS is that it sounds like it's an extremely inexpensive way to improve density. I imagine the controllers can't be all that expensive.

I suppose I should first be figuring out the minimum magnet size that gives us an acceptable corralling of the alphas. I think Rick was looking at 5T and he said about 1000 passes...

Of course for that I'd have to do the p-B11 numbers instead of D-T. If I'm doing D-T then the size is restricted by the first wall problem.

[TallDave]

Is the limit for MHD stability an exactly spherical surface or almost a spherical surface approached from the convex side?

A spherical plasma is supposed to be MHD-unstable. Art has a post on that somewhere here. I'm still not sure if this works the same for a quasineutral plasma that has an electron-rich edge in which the motion of the electrons is deforming a non-spherical magnetic field into something quasi-spherical.

[KitemanSA]

Sorry to re-hash past discussions, but exactly what was the consequence of this MHD instability? And does that consequence pertain to an electro-statically contained plasma?

[TallDave]

Well, if it's MHD unstable we'd be screwed. Wiser heads correct if I'm wrong here, but I believe the implication is it could only operate at low beta.

http://en.wikipedia.org/wiki/Plasma_stability

But Bussard's thereotical picture of a Polywell seems to be built around something that's at least quasi-spherical in WB mode at beta = ~ 1. IIRC, the problem is the edge annealing picture, for instance, would presumably look a lot different if the plasma's considerably spikier than that little Valencia cartoon posits. Art can probably rehash that argument from memory better than I can.

Maybe Rick will stop by and weigh in at some point.

[KitemanSA]

Thank you for your reference. I did not read it in detail, but I did note one point I thought salient, as follows:

MHD theory is the simplest representation of a plasma, so MHD stability is a necessity for stable devices to be used for nuclear fusion, specifically magnetic fusion energy.

(emphasis added)

This quote seems to imply that MHD stability only applies to magnetic confinement machines, which Polywell ain't. So what is the issue? I must be missing something. In short words an engineer can understand, what is the issue?

[TallDave]

MHD stability applies to any magnetically confined plasma.

It would not apply to things like NIF or the GF "steam fusion" concept or classic IEC fusion, where there is no magnetic confinement.

Where Polywell is supposed to differ is that it has good curvature everywhere -- i.e., the magnetic field increases as you move away from the plasma. It's somewhat difficult to reconcile this with a spherical plasma. Art had an equation describing this in another thread.

[KitemanSA]

MHD stability applies to any magnetically confined plasma.

Again, wikipedia says FRC should be unstable according to MHDs but isn't. So something doesn't apply. Also, as I stated before, Polywell isn't a magnetically confined plasma. It is an electro-statically confined plasma, no? Why would MAGNETO-Hydrodynamics apply to electro-static systems? Something doesn't make sense.

[TallDave]

Also, as I stated before, Polywell isn't a magnetically confined plasma. It is an electro-statically confined plasma, no?

The electrons are magnetically confined. The ions are electrostatically confined. MHD stability still comes into play. This is also mentioned in Valencia:

Thus the device will reach beta = one conditions
when the mean electron energy is about 2.5 keV, in ca. 20
usec. Beyond this point excess electron density will be
driven out beyond the beta = one limit; the field will have
expanded as far as it can within MHD stability limits.

As for FRCs, as the wiki says they appear to exceed MHD predictions due to kinetic effects. A couple papers mention things like two-fluid effects.

[chrismb]

Again, wikipedia says FRC should be unstable according to MHDs but isn't.

It certainly is unstable. Don't mix your language up. It is somewhat more stable than MHD would predict.