Bussard's bremsstrahlung calculation

[93143]

So how is that supposed to fit together? You've got a maximum in the electron density at an intermediate radius, a maximum in the ion density at a large radius, and electron density very nearly equal to ion density everywhere on account of quasi-neutrality.

Yeah, that's actually been bugging me for a while. I forgot about it...

Perhaps the multiple-well formation noted in that Japanese paper I never read has something to do with it? It shouldn't matter how locally non-neutral the plasma is if it's striated finely enough... gives a whole new meaning to the word "polywell", doesn't it?

Or maybe MSimon's right and it's an oscillating system that stays non-Maxwellian via wakefield acceleration or some such...

EMC2 has quasi-1D simulations, some of them quite old. I know gas kinetics and possess a student copy of Matlab, as well as some elementary skill in C++. Perhaps I should try to sling something together rather than guessing in a vacuum...? No promises, of course...

[TallDave]

Hrm, I hadn't thought of that before. Multiple wells do sort of imply striations, don't they? Makes you wonder what a more detailed picture would look like.

Plus, since it isn't ambipolar there's some region at the edge which is electron rich. Nebel has said we don't know if the cusps are quasineutral, but I suspect they aren't as containment in that situation would be much less... interesting than experiment seems to indicate.

I know it is being very simple minded, but how does it compare to a 5 ball desktop pendulum?

Well, the balls are always gaining entropy. There's no mechanism that reduces it there that I can see. An analogy I like is pushing iron filings off of a field line: you're adding energy to disorder the filings, but the same energy you add ends up being used to reorder them as they move back. Another anology would be shaking a box of different-sized nuts: the nuts tend to end up sorted by size no matter how much energy goes into disordering them, because that's just how the physical laws of different-sized things bouncing around under gravity work out.

[MSimon]

Another source exploring nonthermal plasmas that I have heard counters some of Rider's arguments is Nevins. I'm not sure which spacifically, perhaps the link below is relavent(one of the co-authors is a Carlson- any connection?)

http://adsabs.harvard.edu/abs/1998Sci...281..307C

Also, while the Polywell is quasineutral overall, it is not locally qusineutral. Electrons have to be more concentrated twoards, the center to establish and maintain a potential well- except the very center where some degree of ion focusing creates an opposing but smaller potential anode.


Dan Tibbets

Direct link:

http://www.sciencemag.org/cgi/content/f ... /5375/307a

[Art Carlson]

Another source exploring nonthermal plasmas that I have heard counters some of Rider's arguments is Nevins. I'm not sure which spacifically, perhaps the link below is relavent(one of the co-authors is a Carlson- any connection?)

http://adsabs.harvard.edu/abs/1998Sci...281..307C

Yah, that's me. These are two separate technical comments, one by Nevins and one by me, in response to an article in Science. Both of us cite Rider to support our points, not to counter him in any way.

Also, while the Polywell is quasineutral overall, it is not locally qusineutral. Electrons have to be more concentrated twoards, the center to establish and maintain a potential well- except the very center where some degree of ion focusing creates an opposing but smaller potential anode.

It seems you haven't grasped the concept of quasi-neutrality yet. Electron and ion densities can only differ from each other anywhere by a small amount or over a small volume. You generally need only a tiny difference in the densities to create create potentials. Conversely, you can't have significant differences in the densities without producing outrageous potential differences.

[D Tibbets]

...Also, while the Polywell is quasineutral overall, it is not locally qusineutral. Electrons have to be more concentrated twoards, the center to establish and maintain a potential well- except the very center where some degree of ion focusing creates an opposing but smaller potential anode.

It seems you haven't grasped the concept of quasi-neutrality yet. Electron and ion densities can only differ from each other anywhere by a small amount or over a small volume. You generally need only a tiny difference in the densities to create create potentials. Conversely, you can't have significant differences in the densities without producing outrageous potential differences.

Your right in that my grasp is slippery. Without evolving deeply into the language of mathophysics, I'm left with visual representations that can be innapropiate and dificult to describe.
If the ions are fast in the center (ignoring potential anode forming with good focus) and slow in the periferal regions, I have the image that the ions spend most of thier time in the periferal regions so that they pile up in this region to the extent that the electrostatic interactions allow. This would seem to decrease the density of ions in the center which would be contrary to the idea that these spherical IEC type of devices seem to be good at having high central densities. Perhaps the dynamic nature of the flowing ions and the volumes involved is confusing me. An x number of ions would transit a cm of the core per second, while the same x number of ions would transit the periferal cm in 5 seconds (for example). But, if I look at it with the idea that the ions in a given volume during a set period of time is equivalent throughout the volume then ions would have to be entering and leaving faster in the core compared to the perifery....

Well, you get the idea of my confusion. My basic concept (using a capaciter analog) though is that there is charge seperation like in a capaciter (even if it is only ~ 1 ppm) except the 'dielectric' is represented by the inertia of the particles. The system is in transition as the inertial motions of the particles will quickly average out (thermalize and reach a neutral or quasineutral state on both large and small scales). Because the ion/ electrons in the plasma are dismal dielectrics, the 'capaciter' is kept charged by the constant input of energy via the high energy electron beams.


Dan Tibbets
(my head hurts)

[Art Carlson]

Actually, Dan, I'd say your grasp of the physics of mono-energetic particles in varying potentials is right on. The trouble is that proponents talk about mono-energetic particles, and potential variations, and quasi-neutrality, but these can't all be true at the same time. To be fair, if the ion motion is primarily radial, then there are convergence effects that can play a role, but I have good reasons to believe that radial ion motion will not be maintainable. I believe that the potential in the polywell will be approximately flat. Any "action" will occur near the edge, probably on a scale determined by the refueling physics.

[Roger]

I have the image that the ions spend most of thier time in the periferal regions so that they pile up in this region to the extent that the electrostatic interactions allow. This would seem to decrease the density of ions in the center which would be contrary to the idea that these spherical IEC type of devices seem to be good at having high central densities.


Dan Tibbets
(my head hurts)

Question, whats the ratio of "ion turn around at the periphery time" to "ion cross thru the potential well transit time"?

If turnaround time is less than transit time, then I could understand how these spherical IEC type of devices seem to be good at having high central densities. No?

Thanks.

[D Tibbets]

A prepublication paper by Nevins from 1995. He discusses IEC possibilities for net fusion power. He concluded it was not pratical. He mentioned the Polywell so I assume he was aware of the Wiffle Ball claims, but this was well befor WB6 so it does not take into consideration those claimed gains. On page 8 of the pdf he says keeping the ions radially orentated for sufficient times was possible, but it required 10 times as much recirculating power (power in?) to do so, compared to the fusion power out. Also, I believe he said that keeping the ions monoenergetic was possible but less important (?). In the subsequent pages he dives into the math (of which I of course ignored).
Bussard repeatedly stressed that the input efficiencies were inadiquit in all his efforts untill the recirculation breakthrough of WB6. Does this breakthrough (along with the scaling claimes) push the system over the edge based on Nevins then arguments?

http://www.osti.gov/bridge/servlets/pur ... /41400.pdf



Dan Tibbets

[MSimon]

A prepublication paper by Nevins from 1995. He discusses IEC possibilities for net fusion power. He concluded it was not pratical. He mentioned the Polywell so I assume he was aware of the Wiffle Ball claims, but this was well befor WB6 so it does not take into consideration those claimed gains. On page 8 of the pdf he says keeping the ions radially orentated for sufficient times was possible, but it required 10 times as much recirculating power (power in?) to do so, compared to the fusion power out. Also, I believe he said that keeping the ions monoenergetic was possible but less important (?). In the subsequent pages he dives into the math (of which I of course ignored).
Bussard repeatedly stressed that the input efficiencies were inadiquit in all his efforts untill the recirculation breakthrough of WB6. Does this breakthrough (along with the scaling claimes) push the system over the edge based on Nevins then arguments?

http://www.osti.gov/bridge/servlets/pur ... /41400.pdf

Dan Tibbets

I was doing some BOE calculations based on WB-6. Given A WB with 1 m diameter coils and 3 T field, power output is most likely in the 400 watt to 4 Mw range for D-D. Depending on assumptions.

Mine for high power: Density outside the core 1E-6 torr. Density multiplication of 1,000 due to WB confinement.

[D Tibbets]

I was doing some BOE calculations based on WB-6. Given A WB with 1 m diameter coils and 3 T field, power output is most likely in the 400 watt to 4 Mw range for D-D. Depending on assumptions.

Mine for high power: Density outside the core 1E-6 torr. Density multiplication of 1,000 due to WB confinement.

Are your density numbers comparing the core to the periferal wiffleball area, or to the space outside the magrid? Or, the density in the Wiffle Ball in general (average) versus the density outside the magrid? I'm guessing , based on discussions about arching, that the 1E-6 is the density outside the magrid as that is the density that approaches the external arcing limits. If the core density is 1000 times that, then what is the density in the periferal Wiffle Ball? IE- how much convergence/ focusing are you assuming?


Dan Tibbets

[MSimon]

I was doing some BOE calculations based on WB-6. Given A WB with 1 m diameter coils and 3 T field, power output is most likely in the 400 watt to 4 Mw range for D-D. Depending on assumptions.

Mine for high power: Density outside the core 1E-6 torr. Density multiplication of 1,000 due to WB confinement.

Are your desity numbers comparing the core to the periferal wiffleball area, or to the space outside the magrid? Or, the density in the Wiffle Ball
in general (average) versus the density outside the magrid? I'm guessing , based on discussions about arching, that the 1E-6 is the density outside the magrid as that is the density that approaches the external arcing limits. If the core density is 1000 times that, then what is the density in the periferal Wiffle Ball? IE- how much convergence/ focusing are you assuming?

Dan Tibbets

Yes. 1E-6 outside the grids.

I made no assumption about density gradients/focusing except that they would be the same as WB-6. In other words my assumptions were based on scaling alone.

Density
External/Internal Density multiplication
Volume

The density scaling is reasonable i.e. a 30X B field gives a density scaling of 900 IIRC.

Now one thing for sure is that there is bound to be a lot of noise in the numbers. I might be off as much as a factor of 5 in either direction. Although a factor of 2 is a lot more likely.

[TheRadicalModerate]

The electrons are fast at the edge, and fairly slow in the core. They are slowest at the bottom of the well, which is not at the centre of the reactor but rather at some finite radius, where the ion focus begins to dominate the potential distribution and the virtual cathode starts to give way to the virtual anode. The electron density should also have a maximum very near this radius, because of the 'traffic-jam' effect of the slowdown.

The result is a region with low energy, high density, and high cross section, just like the edge region for the ions.

So how is that supposed to fit together? You've got a maximum in the electron density at an intermediate radius, a maximum in the ion density at a large radius, and electron density very nearly equal to ion density everywhere on account of quasi-neutrality. Your logic is OK, it's the picture we're getting from Bussard that has a problem somewhere.

I'm wondering about the max ion density at the edge of the machine. Consider a spherical shell at some distance R from the center of the machine. I'd think that the ion density would be proportional to (relative time to traverse the shell) / (volume of the shell). The kinetic energy of an ion is proportional to 1/R, which means that the time spent in a shell is proportional to sqrt(R). And the volume of the shell is 4*pi*(R^2)*dR, i.e. proportional to R^2. So density is proportional to R^(-3/2), or denser in the center than the edge, isn't it?

[Art Carlson]

I'm wondering about the max ion density at the edge of the machine. Consider a spherical shell at some distance R from the center of the machine. I'd think that the ion density would be proportional to (relative time to traverse the shell) / (volume of the shell). The kinetic energy of an ion is proportional to 1/R, which means that the time spent in a shell is proportional to sqrt(R). And the volume of the shell is 4*pi*(R^2)*dR, i.e. proportional to R^2. So density is proportional to R^(-3/2), or denser in the center than the edge, isn't it?

The analysis is OK, but why would the kinetic energy be proportional to 1/R?

If you can maintain an anisotropic velocity distribution, then there are focusing effects. A flat potential and a density ~R^-2 is consistent with purely radial velocities of both species. It would be interesting to try to find consistent profiles for other assumptions, e.g. radial ions and isotropic electrons.

[TheRadicalModerate]

I'm wondering about the max ion density at the edge of the machine. Consider a spherical shell at some distance R from the center of the machine. I'd think that the ion density would be proportional to (relative time to traverse the shell) / (volume of the shell). The kinetic energy of an ion is proportional to 1/R, which means that the time spent in a shell is proportional to sqrt(R). And the volume of the shell is 4*pi*(R^2)*dR, i.e. proportional to R^2. So density is proportional to R^(-3/2), or denser in the center than the edge, isn't it?

The analysis is OK, but why would the kinetic energy be proportional to 1/R?

What's the proper value? I was on shaky ground with that one and assumed that the kinetic energy had to scale the same way as the potential did. (I fell and couldn't get up trying to convert between time-based parametric equations and position-based force values.) Either way, it still looks like the assertion that the ions are denser at the edge is not correct (i.e. that they're denser in the center, despite moving at maximum velocity).

If you can maintain an anisotropic velocity distribution, then there are focusing effects. A flat potential and a density ~R^-2 is consistent with purely radial velocities of both species. It would be interesting to try to find consistent profiles for other assumptions, e.g. radial ions and isotropic electrons.

If you can prove that the ion velocity distros are isotropic and not radial for a polywell, then I think we can all pack up and go home, can't we? Focusing is everything, and is the second half of the edge annealing argument. Bussard was asserting that not only did the radial velocity components cluster, but that the transverse velocity components were effectively removed completely. Without that, the machine simply won't work.

As for the electron velocity distro, seems like it's bi-modal: you've got isotropic behavior inside the wiffle-field boundary, but the cusps should preferentially select for purely radial electrons to escape the field.

Which brings me to my next point of confusion: We keep saying that the core electrons are cold. If we're injecting them into the center and therefore increasing the electrostatic potential of the virtual cathode, doesn't all of that injection energy wind up heating them up? Seems like they want out of that containment awful bad...

[MSimon]

The analysis is OK, but why would the kinetic energy be proportional to 1/R?

Electric field?