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 Post subject: Does the Polywell have a resonance condition?Posted: Thu Oct 20, 2011 9:18 pm

Joined: Tue May 27, 2008 11:14 pm
Posts: 212
Hey Guys,

Just posing a question for you to consider. I have not had time yet to develop it properly. Also, if nobody else noticed, a group from Iran published a basic polywell paper on 10/12/2011.
All the best,

Does the Polywell have a resonance condition?

Assuming the reactor is running at steady state, there are 7 variables inside the Polywell. Set these and you fully describe the experiment. Below these parameters are enumerated, along with the units you measure them in.

1. The injected electron energy [KeV].
2. The injection ion energy. [KeV]
3. The net rate of electron injection. [electrons/second]
4. The net rate of ion injection. [ions/second]
5. The choice of ion to fuse. [cross section, collisional energy, energy generated]
6. The magnetic field strength. [Teslas]
7. The geometry:
a. The number of rings.
b. The diameter of rings.
c. The spacing of rings.
d. The placement of rings.

You also need variables to quantify what the machine produces. These include, but are not limited too:

1. Rate of Fusion [Products/second]
2. Rate of X-Rays [Energy Lost/second]
3. Rate of neutrons [neutrons/second]
4. Rate of yield energy out [Energy/second]

There are several approaches we can take to analyzing this system. We can try to balance mass and energy flow across the reactor. We can look at rates, how fast material and energy moves into different forms around the reactor. We can also use dimensional analysis to try and simplify the problem. This can be a very powerful tool. What if the polywell has a dimensionless number? Like a Reynolds number for fluids. It may be that several already established numbers would apply to this system. Plasma physics already has many, well known numbers. If that were the case we could significantly simplify our variable space. Instead of testing every magnetic field strength combined at various ion energies and electron energies, we would only need to vary one; dimensionless number. We could change, with certainty, the magnetic field ion energy in tandem.

Evidence that a resonance condition may exist:

1. We know that different fusion reactions fuse better, when they collide at a specific energy. For example the D + D -> T + P reaction works best at 1250 KeV. Presumably, the polywell burning DD would try and contain enough electrons to hit that voltage. Therefore, the machine may be “tuned” for the specific fuel being fused.

2. Joe Khachans work indicates that the amount of electrons “caught” inside the polywell peaks at a specific magnetic field strength. He linked this concept to the idea of magnetic mirrors. For a given machine, their maybe an ideal magnetic field strength.

3. More, generally though, the Polywell is a complex system. Increase or decrease one of the variables above and you may get more X-rays and less fusion, or less fusion but better confinement. In such a complicated system, with so many interacting effects, it maybe that the machine has a “sweet spot”. A mode of operation where the rate of fusion peaks.

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 Post subject: Posted: Fri Oct 21, 2011 1:40 am

Joined: Thu Sep 17, 2009 11:18 pm
Posts: 3838
Location: North East Coast
Ahh, that was it. Joe's work. The Iranians did it with their PIC. I knew I'd seen something similar.

In any event, don't forget you can tune for bremstrahlung management. You talked around it, but I was not sure if you realized that it was a key point in tuning.

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 Post subject: Posted: Fri Oct 21, 2011 2:16 am

Joined: Thu Jun 26, 2008 6:52 am
Posts: 2080
On first reflection, using D-D fuel several parameters can be combined. The calibrated neutron counts directly determines the fusion rate, and the known MeV per reaction gives the energy. The only real variable here is the neutron count.

Ion injection ideally will always be as close to zero as you can get it presuming injection is at the Wiffleball border (not deeper in the machine). An alternative might to be to inject the ions from the outside with just enough KE to overcome the magrid repulsion. This would cost more energy but it might have benefits in terms of avoiding electron sinks like a positive ion gun located at the Wiffleball border.

A potential well depth of ~ 1.2 million volts is not desired. While it is true that the D-D cross section continues to increase with increased ion KE, it is not linier. The actual best voltage from an efficiency viewpoint is ~ 15,000 eV. This is where the D-D cross section curve is steepest (a small increase in voltage will increase the fusion rate the the greatest relative amount. If this raw efficiency was the only consideration then this would be the ideal potential well depth- this is what Joel Rogers used for his simulations.

But, there are many other concerns, thermalization issues, Bremsstrulung, arcing, energy output density and thermal loads, etc. I believe Dr Bussard considered all of these issues and decided that ~ 80,000 volts potential well depth in a 3 meter, 10 T machine was the best compromise for D-D fusion.

Consider Bremsstrulung. It scales at the ~1.75 power of the temperature. This means that the Bremsstrulung X-ray losses increases by a factor of ~ 60 for a temperature increase from 100,000 to 1,000,000 eV. Unless the fusion rate increases at a faster rate within this temperature range you are losing ground.

Also, above ~ 1 million eV, other endothermic nuclear reactions become increasingly significant.
http://en.wikipedia.org/wiki/Oppenheime ... ps_process

Also, as the energy of the fuel ions is increased towards the energy of the fusion reactions, unless you have 100% efficient heat to electricity conversion efficiency you are losing ground.
eg: 100KeV fuel ion energy + ~ 3 MeV fusion products energy = 3.1 NeV. That energy converted to electrical energy via a steam cycle (assume ~ 30% efficiency) might yield 1.03 MeV of electrical output. Subtract from this the input energy- even if 100% efficient in accelerating and maintaining the fuel ions without Bremsstrulung losses, etc. , you would yield a net electrical energy of 1.03MeV- 0.1 MeV= 0.903 MeV net gain per fusion reaction.
If the fuel ion was at 1MeV, then the net electrical output would be 3.0MeV + 1 MeV= 4.0 MeV . This fusion output / conversion efficiency of 30% = 1.3 MeV of electrical energy. Subtract the input energy from this: 1.3 MeV - 1.0 MeV = 0.3 MeV. So, not only do you lose ground on the Bremsstrulung issue, but also on the output / input energy ratio per fusion reaction.
This is one area where P-B11 fuel has an advantage if direct conversion is used. There is not as much penalty (at ~ 80% conversion efficiency with direct conversion) for using higher drive energies. The ~ 9 MeV per P-B11 fusion reaction also helps to offset the higher drive voltages needed (still well below a million volts). The need to have excess protons in the mix to minimize Bremsstrulung loses does increase the energy costs for maintaining the mix of particles at ~ 200 KeV, but I suspect the P-B11 mixture would still have an advantage, or at lest less of a disadvantage that would be appreciated without this consideration.

Also, vacuum pumping requirements to prevent charged and neutral particle buildup outside the magrid to levels that lead to potential well destroying arcing will be very challenging. Increasing the voltage too much will compound the problem as the arcing is proportional to the external density AND the voltage.

Dan Tibbets

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