Derivation of radius of the potential well and ion density.

[laksindiaforfusion]

Hi,

First I would like to thank Joe for adding me into this forum.


Now let me get right to the point. The theoretical basis of the "virtual anode" and the derivation of the radius of the potential well:
Process:
1) The MaGrids are turned on
2) electrons are injected
3) electrons have suffecient density to form wiffle ball, creating a non thermal distribution inside the diamagnetic ball because of a potential well formation.
4) The potential well limits the natural energy modes according to the Schrodingers equation for spherical potential well.

Here is how we can arrive at the math for a collisionless regime:
prelim1) Find the radius and potential well(Vp) depth and dimensions (Rp) for the electron concentration at the center, in terms of the magnetic field, assume complete vacuum and an initial electron density.

1) Find the state equation of a charged particle inside a spherical potential well with potential Vp(r) for |r|<Rp and 0 elsewhere. They should be either Hankel or Bessel functions or could even be sinusoids.

2) The above would give us a discrete set of energy states called modes (100s of KeV hopefully) and their probabilities of existence inside the well for each discrete (i.e. quantum) states. The natural mode ideally should look like a spheical cosine (or Bessel) (with a big bulge at the center of the sphere and something that evens out towards the end). The subsequent mores would be better if they are cosines of the fundamental frequency. I need to work out the quantum mechanics, will get back to you after that :).

3) Refer: http://quantummechanics.ucsd.edu/ph130a ... de224.html
and especially
http://quantummechanics.ucsd.edu/ph130a ... de230.html
According to Dr. B, there should be a LARGE concentration of the ions right in the center of the potential well. I am trying to derive that mathematically using quantum mechanics of the spherical well, will update you as and when i get there.

4) Because of the large ion concentration at the center of this potential well, we have the Columb Radius going down and the chance that ions interact very high also the mean free path would become smaller and smaller due to higher density(correct me if i am wrong here). Causing fusion. Reasonable assumption BUT, a lower ion density at the center can cause lesser fusion and hence lesser power defeating the purpose.

5) Dr. B suggest that to have enough Ion density we need a larger machine which suggesting that there is a relationship between the following: the ion density inside the potential well, the potential well, the magnetic field causing the potential well, the current causing the magnetic field, and the electron density. The side effects being B loses dude to cusp issues and arcing. And therefore larger density == larger machine (lower cusp loses and arcing) and higher current.

6) Dr. B has not provided the equations, even in the steady state which is unfortunate. But i guess the steady state equations are not that difficult to work out, I can do them in around three- four months. I am brushing up on quantum mechanics.

7) Collisions can be accounted in this way:

7a) Collision with energy loses, ions fuse with electrons: change of particle properties and hence effects the potential of the potential well, need to account that in the equations

7b) Collision without loses: ions with ions, electrons with electons, ions with electrons without fusing. This does NOT change the energy content of the potential well, it does change the energy distribution in the particles.

7c) Collisions due to energy inputs: when energy is added into the potential well, it gets redistributed into the particles effecting the potential. Hence we should make sure that the "absorbable" energy added thru fusion + the energy injected thru the magrid == the energy lost thru B loses (hope we can get the arcing to stop completely). The unabsorbable energy of fusion (hope it is greater than 80% generated) is then extracted thru grids.

8) We need very sensitive control systems and transducers to achieve the above balance, too much ion injection can cause potential well destruction, too much electron injection can cause B-loses. Too much magrid pressure can change the other two (and increase ohmic loses if we are lookinig at non-superconductors)



Request: if any of you are interested in collaborating please contact me and also let me know if you have any equations on the ion densities in the potential well center.

My initial thought about this reactor was "CRACKPOT!!", especially I started going thru the materials, which I must say are presented rather shoddily (which made my mind almost confirm that this dude was a "crackpot!!!") But now I have come to the conclusion that this thing has a good chance to work. Hope someone gets their hands into making those papers look standard. I mean, i could not believe that the IAC paper that Bussard had published really did not have one formatted equation and was full of typos. Even the Em2fusion.org site has typos (look at the caption under the right most pic)

However the people who came up with the idea of the potential well confinement must be freaking geniuses, combine that with Dr. Bussard's ingenious wiffle-ball magrid idea and i guess you should have a working Fusion Reactor.

I think this thing should work. If not we will make it work ::)

[pstudier]

2) The above would give us a discrete set of energy states called modes (100s of KeV hopefully) and their probabilities of existence inside the well for each discrete (i.e. quantum) states. The natural mode ideally should look like a spheical cosine (or Bessel) (with a big bulge at the center of the sphere and something that evens out towards the end). The subsequent mores would be better if they are cosines of the fundamental frequency. I need to work out the quantum mechanics, will get back to you after that .

Quantum mechanics do not apply here. From http://en.wikipedia.org/wiki/Electron_diffraction we find that the wavelength of an election at 10keV is 1.2 x 10 ** -11 meters, or 0.12 angstrom which is much smaller than the dimensions of the device.

[laksindiaforfusion]

Agreed on the electron part, it is indeed very small.

The objective here is to analyze how a particle would behave in a potential well and how a lot of them would behave and how can we induce fusion. The only answer that i know of is the quant. mech that i did some 10 years back

There are two behaviours we can look at, corrections welcome
--> Potential well is a local minima of potential energy

1) Non Quantum mech way: How does a particle behave in it.

2) Quantum mech way: How does a particle behave in it.

Either ways here is how we can derive a lot of things in this

1) There are solutions on the work done to bring a charged sphere together. (which would be our initial energy expended)

2) One can calculate the "charge induced" pressure at the surface of the electron Wiffle Ball for a given radius with a given electron density.

3) That would give the amount of electro magnetic pressure required to hold the WB of a given radius and electron/charge density together.

4) That would give the size/power/geometry required for the electro magnets.

5) Derive the state equations for a non-collision regime for an ion in a potential well, in this case a sperical potential well. Quantum or non quantum way , i will do some more elementary physics reading and would decide, till then forgive my stupidity and correct my mistakes.

6) The equations SHOULD show a high ion concentration at the center of the electron sphere. If it does not, we screwed up somewhere with the assumptions/calculation or we have the rare chance that Dr. Bussard was wrong

Please let me know if this is do-able. or atleast a solution is possible in a simulation way.

[scareduck]

Wow. Just, wow.

[laksindiaforfusion]

Wow. Just, wow.

Dont know if you meant compliments or sarcasm ,

but yes i am "trying" to startup. And we have some initial products in mind... polywell not one of them for now.. this is my interest Biometrics/embedded systems is my bread and butter

And thats why you have a rag-tag site.. which needs a lot of work

[scareduck]

Major buzzword overload.

[laksindiaforfusion]

Major buzzword overload.

Heh, the aim is to confuse the people till they give us their business and trust its a major item in our businessplan . every sales executive is given a buzzword confusion checklist, they need to make sure that the client is confused and then only shall we discuss the price of our services or products.

Sarcasm/jokes apart:

Has anyone got the mathematics.. or tried to derive it. I dont want to re-invent the wheel

[MSimon]

Has anyone got the mathematics.. or tried to derive it. I dont want to re-invent the wheel :)

Try drmike on the Virtual Pollywell thread:

viewtopic.php?t=203&start=270

[scareduck]

Heh, the aim is to confuse the people till they give us their business and trust

Nobody will trust you if you are so plainly trying to blow smoke up their dresses. 1999 has come and gone.

[laksindiaforfusion]

Heh, the aim is to confuse the people till they give us their business and trust

Nobody will trust you if you are so plainly trying to blow smoke up their dresses. 1999 has come and gone.

true, thats why we have prototypes of what we are trying to sell. i pretty much lived thru what was left in 1999, and i know that no VC would give me money on promises. We do have protoypes with measured performance metrics, and we are talking with a few knowledgeable VCs. The site is just my idea, none of my partners worry about it for now. They would the day we get funded.

I was being joking the earlier comment.. no offense meant though. I am assembling a team of people who know way more web designing, customer relations management etc than i do

Thanks for the comments

[laksindiaforfusion]

Ooops, I was complaining about there not being one equations:

As everyone might know http://askmar.com/Fusion.html has all the equations neatly formated.

Should have dug in more. Too much excitement is not great fun