"Trapped" EM Resonance Modes in a WB-7 Class Grid

[kbaugh]

There have been various descriptions of the "wiffle ball" effect (particularly Tom Ligon's description of the PXL device) that made me wonder if some sort of electromagnetic resonance might be involved.

Specifically, I wondered if it were possible for electromagnetic resonant frequencies to exist in the interior volume of a MaGrid whose wavelengths were too long to effectively radiate out of the holes in the grid. If such modes exist and were excited (for example, by the flow of energetic electrons into and out of the grid), then the RF energy associated with them would be effectively "trapped" inside the grid.

If that were to happen, could it be that the EM fields would tend to "smooth out" the variations in the plasma cloud inside the grid? Someone much more versed in plasma physics will need to weigh in on that, but here is my take on the possible existance of "trapped" EM resonances.

There is a fairly general rule of thumb that states that the number of resonant modes, N, in a cavity of volume, V, having a wavelength greater than lambda is approximately

N ~ 8*pi*V/(3*lambda^3)

So far so good. Tony Barry was kind enough to point me in the direction of the dimensions for WB-7, namely a set of rings whose outer diameter is 307mm, inner diameter is 201mm, forming an assembly of rings that is 393mm tall. The inner volume of the grid is a sphere whose diameter is roughly 370mm, enclosing a volume of 0.0265m.

The largest hole on the MaGrid is the 201mm opening in the face of each toroid (the corner holes look to be 20-30% smaller, but I am too lazy to work through the geometry and estimate the critical dimensions). Any EM field whose wavelength is longer than twice that length would not effectively radiate out of the grid, and would be "trapped". The critical value for wavelength, lambda, is therefore 402mm, corresponding to a frequency of 746 MHz - the highest frequency that can be trapped in the grid.

Now if we plug those values back into the "rule-of-thumb" we find out that there are as many as 3 resonant modes that could be excited in the interior volume of the MaGrid whose wavelengths would be too long to squirt out the holes in the grid. In other words, it is indeed possible to excite EM resonances in a WB-7 class grid system whose energy will be "trapped" by the grid.

There is another way to ask the question: What is the minimum diameter sphere that will support at least one resonant mode whose wavelength is too long to squirt out of the grid? If I plug N=1 and lambda=0.402 into the rull of thumb, I find that a sphere of diameter 246mm might still form a trapped resonance.

So, "trapped" EM resonant modes can exist in a WB-7 class grid system, and can in fact exist even if the resonating cavity is as small as 246mm (about two-thirds of the grid's interior diameter ). What is that cavity? I have no clue, but it could be the "sheath" of electrons that Art Carlson is struggling with in the other threads in the Theory index (the so-called "Carlson Sheath" ).

My next step is to consider whether a resonance mode could be excited by the recirculation of high-energy electrons into and out of the grids, sort of like ringing a church bell by throwing sand at it in just the right rhythm. In order to work that out I need to know the dimensions of the outer grid, and some sort of "geusstimate" for the voltage distributions through the grid system. Any comments or guidance is appreciated.

Regards,
Kevin Baugh
Fairfax VA

[KitemanSA]

There is another way to ask the question: What is the minimum diameter sphere that will support at least one resonant mode whose wavelength is too long to squirt out of the grid? If I plug N=1 and lambda=0.402 into the rull of thumb, I find that a sphere of diameter 246mm might still form a trapped resonance.

The WB-7 is the simplest configuration for the Polywell, not the one with the smallest hole to diameter ratio. If there were 12 magnets rather than 6, would your answer change? If so, then the real answer is "how small do you want it?" There are many possible configurations of polywell, but without your effect, the desire is the simplest, not the smallest whole size to diameter.

[kbaugh]

Actually, I went through this excersize because the holes in WB-7 are rather large relative to the diameter. It wasn't clear to me until I ran through the numbers that a "trapped" mode would exist. If you change the grid configuration to achieve smaller grid openings for the same diameter, the "cut-off" wavelength gets shorter (since the holes are smaller) but you still get "trapped" modes (and more of them than before).

At the moment I am trying to noodle through exactly which modes are excited and then try to make some sort of prediction of what that might lead to in the observable data (if it is ever published).

Cheers,
Kevin

[icarus]

How would the trapped EM modes interact with the electric and magnetic fields from the Magrid?

[kbaugh]

The fields of the trapped EM modes would just add linearly to the static grid fields (the fancy name for that is "superposition"). Even if there were a strong resonant frequency, I would expect the static grid fields to be much stronger than the EM fields everywhere, except of course in the exact center of the grid where the static magnetic fields drop to zero.

Unfortunately, if there is a reasonably-dense cloud of charged particles inside the grid, the EM fields will terminate just at the edge of the cloud. This observation actually suggests one kind of resonant mode in a WB system: a cavity resonance between two concetric spherical shells. That kind of resonance is actually a very simple model for HF propagation through the ionosphere, and I am currently pushing the numbers on the model for WB-7.

What I am more interested in is whether the EM fields can in some sense "smooth out" the random variation of the electrons inside the grid. My intuition says that the presence of a strong enough EM resonance would cause the electrons to stop behaving like individual particles and begin behaving in a more or less collective manner. Is that important? I don't know, but I'm not sure it is something folks on this forum are thinking about at the moment.

Anyway, idle speculation is less useful than coming up with a prediction of what observable effects this could present in the data, so I will keep chipping away at it.

R/
Kevin Baugh