Another Rider Paper From 1997

[mattman]

Hey All,

I had not seen this paper before.

Title: "Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium" from 1997.

Abstract: Analytical Fokker–Planck calculations are used to accurately determine the minimum power that
must be recycled in order to maintain a plasma out of thermodynamic equilibrium despite collisions.
For virtually all possible types of fusion reactors in which the major particle species are significantly
non-Maxwellian or are at radically different mean energies, this minimum recirculating power is
substantially larger than the fusion power. Barring the discovery of methods for recycling the power
at exceedingly high efficiencies, grossly nonequilibrium reactors will not be able to produce net
power. © 1997 American Institute of Physics. @S1070-664X~97!01404-3#


Has anyone dug into this paper before? Is this any different from his thesis? Or his 1995 paper: "A general critique of internal-electrostatic confinement fusion systems"

[hanelyp]

Those sound like familiar arguments.

A point to consider for the polywell is that while the plasma at any given location may be out of thermal equilibrium, the plasma as a whole is, by my understanding, supposed to be in thermal equilibrium. Near the edges the electrons are hot with a spread narrow for their energy, and the ions reverse. Towards the center these energy roles are reversed.

[D Tibbets]

I'm not sure that is an accurate description of the plasma.
The plasma is in thermal equilibrium (the ions) at the edge. This is an inevitable consequence of the logarithmic increased Coulomb collisionality at low temperature and energies on the top of the ion potential well;
the key is that the thermal spread is tiny at these low energies relative to the energy at the botom of the potential well. Thus the ion plasma is in thermal equilibrium only at this low energy edge. This has the effect that the "monoenergetic" properties are reset on each pass of the ions. In the mantle region the MFP is longer than the distance traveled so very little thermalization happens here per pass. In the core, provided there is some significant amount of convergence, the density increases considerably with corresponding shorter MFP. Here some thermalization may occur on each pass, but I think full thermalization is not reached (?). Certainly core collisions,being at the near center of a sphere produces little increase in angular momentum, so the radial vectors are mostly maintained.

http://www.askmar.com/Fusion_files/EMC2 ... etimes.pdf

http://www.askmar.com/Fusion_files/EMC2 ... %20Ion.pdf

http://www.askmar.com/Fusion_files/EMC2 ... ration.pdf

Ignoring edge thermalization (annealing), there are papers on Askmor that concludes that ions do not thermalize (fully) overt heir lifetime before they fuse and leave the system. The question of electron thermalization is another issue. If the electron lifetime in terms of distance traveled (the number of passes) before escape is near the ion lifetimes, then at the same average energy and almost the same density the thermalization times should be ~ the same as the ions (I think). Because the electrons are traveling roughly 60 times faster the time of thermalization verses the confinement time should match the ions. At 10,000eV (peak energy)the electrons are traveling ~ 10 million M/s and the ions are traveling at ~ 200 thousand M/s. The corresponding dwell time or confinement times with an equal number of passes for both species being ~ 0.25 ms for the electrons and ~ 10-20 ms for the ions, the degree of thermalization (without annealing) should be roughly the same. I don't know how accurate the ion thermalization times are in the system, but the numbers are consistent . This simple comparison may not very applicable. One of the papers linked above goes into electron thermalization analysis.

As the machine diameter and the density increases the charged particle MFP/ dwell time will decrease and thermalization will be more prevalent. This will be off set somewhat by the anticipated increased temperature, up to ~ 100 KeV for D-D. Here annealing may be required on each pass to prevent ion thermalization. The electrons in the larger, higher B field machines is another issue. Does central electron annealing occur to any significant extent?

Dan Tibbets

[D Tibbets]

There is a counter argument to Rider's paper. I think the root of the different conclusions is that the Fokker–Planck calculations were not ideal for modeling the system. As pointed out on this forum before, a paper by Dolan may be more relevant.

http://www.askmar.com/Fusion_files/Magn ... nement.pdf

Dan Tibbets

[mattman]

Dan,

Yes - Rider probably had it wrong. Please formally publish that and make every physicist worldwide be aware of this.

[D Tibbets]

There is a counter argument to Rider's paper. I think the root of the different conclusions is that the Fokker–Planck calculations were not ideal for modeling the system. As pointed out on this forum before, a paper by Dolan may be more relevant.

http://www.askmar.com/Fusion_files/Magn ... nement.pdf

Dan Tibbets

Actually, I think I mentioned the wrong author. It s should be Chacon. And it is not my opinion or expertise (or lack thereof) that applies but the paper that was published and referenced by R. Nebel.

rnebel
Post subject:
PostPosted: Thu May 01, 2008 10:07 am
Offline

R. Nebel post

Joined: Sun Dec 23, 2007 6:15 pm
Posts: 144
JMC and MSimon:
Actually, you need to click on “read more” under the design section, then “main parameters” then on the “more” button. What you will find is that the average density of ITER is ~ 1.0e20/m**3. If you use the formula I sent you for the Polywell, you will get a density ~ 2.5e22/m**3. The upshot of this is that the Polywell has a power density that is ~ 62500 times bigger than ITER EVEN IF THERE IS NO ION CONVERGENCE! Thus, a Polywell should far outperform a Tokamak even with a constant density Maxwellian plasma. Even if Rider and Nevins were correct (which Chacon has pretty clearly shown they aren’t) this isn’t a show stopper. It has a lot more significance for Hirsch/Farnsworth machines that have low average densities than it does for the Polywell.
The best analogy that I can think of is that the wiffleball mode is the jet engine and the ion convergence is the afterburner. The 2.5e22/m**3 density is what the Polywell should have on the edge, and then it hopefully goes up a few orders of magnitude as it goes into the interior. I don’t mean to imply that ion convergence isn’t important. This power density boost is what enables the Polywell to be built in small attractive unit sizes and to easily use advanced fuels.
However, the wiffleball mode is essential and the ion convergence simply makes things better. If we can’t get the wiffleball, then we can kiss our behinds goodbye. That’s why we are focused on achieving the wiffleball and we aren’t paying any attention to Rider and Nevins. They’re just a distraction. Does this kind of make sense?

The important portion for this discussion is "Even if Rider and Nevins were correct (which Chacon has pretty clearly shown they aren’t) this isn’t a show stopper."

Dan Tibbets

[D Tibbets]

PS: I'm depending mostly on the hear say from Nebel. I'm uncertain of the actual paper. Listed below though are two links of ~ the proper time frame. And the third is a more recent paper abstract.


http://www.ipp.mpg.de/1525287/Chacon.pdf


http://www.physics.ucla.edu/icnsp/PDF/bromley.pdf



http://arxiv.org/abs/1101.3701

Dan Tibbets

[Ivy Matt]

Is this the paper?

L. Chacón, G. H. Miley, D. C. Barnes and D. A. Knoll, "Energy gain calculations in Penning fusion systems using a bounce-averaged Fokker–Planck model" (Physics of Plasmas, Dec. 2000)

[D Tibbets]

Thanks, that may be the most pertinent paper. It does have both Rider's and Nevin's papers in the bibliography (#4 and #10). It also includes differences in Q that might be expected. The first link in my previous post may have more simulation details. At least it is 3 times longer (if that is any indication of content ).

Dan Tibbets