Where's the beef?

Art Carlson · Post by **Art Carlson** » Mon Jul 21, 2008 8:19 pm

kcdodd wrote:I guess I just don't get your math. To start, what is debye length even supposed to mean when talking about a pure electron sheet. That would mean the thickness of your pure electron sheet would *decrease* with higher densities. That makes no sense to me.

Then plug in the electron gyroradius. That is the width of the cusp loss hole. I only converted to the Debye length for mathematical convenience.

lambda_D^2 = (epsilon_0*kT) / (n_e*e^2)
= 4 * ( (m_e*kT) / (e^2B^2) ) * ( B^2 / (2*mu_0*2*n_e*kT) ) * (epsilon_0*mu_0)*kT/m_e
= rho_e^2 * beta^-1 * 4kT/(m_e*c^2)

I used 2*n_e in beta to account for the ions. beta is (said to be) one. With kT~100 keV, the last term is also about 1, so we see that rho_e is at least very nearly equal to lambda_D.

kcdodd · Post by **kcdodd** » Mon Jul 21, 2008 8:55 pm

Ok, I'm not sure if Im doing this right:

gyroradius:
r_g^2 = m_e^2*v_perp^2/(q^2*B^2)

Velocity perpendicular:
(1/2)*m_e*v_perp^2 = 2*(1/2)*KT (2 degrees of freedom)
=> v_perp^2 = 2KT/m_e

Beta condition:
beta = 2nKT*mu_0/B^2 = 1
=> B^2 = 2nKT*mu_0

plug in:

r_g^2 = m_e^2*(2KT/m_e)/(q^2*2nKT*mu_0) = m_e/(n*q^2*mu_0)

I seem to lost all dependence on temperature, but at least I see that the thickness decreases because of the beta assumption.

TallDave · Post by **TallDave** » Mon Jul 21, 2008 9:14 pm

Why do you think the density ratio will have this value

Because Bussard and Nebel both stated it does.

but I contend that the electron density in the sheet will be comparable to that in the interior for a significant distance

How relevant is that to the overall force, though? Shouldn't it be a Gaussian distribution?

"the Magrid is pushing back on any ions that far out": If "that far out" is within the magrid radius, then there is no field from the magrid doing anything to the ions. (Faraday cage and all that.)

My understanding is there's a gradient from the positive charge on the Magrid to the bottom of the well, Faraday effect or no. Anyways, I'm not sure the Faraday effect applies here; the charge is on the grid itself, not external to it.

Actually, now that I think about it, if the Magrid is a Faraday cage then the ions won't see any force from the electrons outside it, making it even less likely they could pull ions out.

You can pick a hole in my calculation, or you can offer a calculation that leads to a different conclusion. In the face of a calculation that contradicts your intuition, the way things "seem" to you doesn't carry much weight.

Shrug. I don't believe your calculation carries any more weight than my intuition. I haven't really bothered to look into the calculation because throwing math at an ill-defined problem just gives you ill-defined math. We don't have enough data for anything more than throwing around competing theories.

Art Carlson · Post by **Art Carlson** » Tue Jul 22, 2008 9:36 am

I love it.

TallDave wrote:
Why do you think the density ratio will have this value
Because Bussard and Nebel both stated it does.
In the face of a calculation that contradicts your intuition, the way things "seem" to you doesn't carry much weight.
Shrug. I don't believe your calculation carries any more weight than my intuition. I haven't really bothered to look into the calculation ...

I think I better go back to real life now. I'm willing to make an investment to do physics, but I don't have time for hearsay and speculation.

tonybarry · Post by **tonybarry** » Tue Jul 22, 2008 12:39 pm

Hmmm. I'll back a calculation over an intuition any day. The calculation is at least tangible, reducible to components which can be tested and checked by others, and discussable by those interested. Intuition is perilously close to religion (God said it is this way, I believe it, and that settles it).

If Art's calculations cannot be refuted in the theoretical realm, then they stand; either as an issue with the polywell which is addressed through experiment, or a fact which allows us to realise that the polywell concept cannot work as stated.

I for one will thank Dr. Carlson if he does so provide such an refutation, providing that it is in fact a reasonable expression of physics. Since my personal knowledge is inadequate to comment further, I shall close here.

Regards,
Tony Barry

TallDave · Post by **TallDave** » Tue Jul 22, 2008 2:58 pm

I'm willing to make an investment to do physics, but I don't have time for hearsay and speculation.

Heh, well, what did you think you were doing? Without the data, there is necessarily a lot of speculation involved. And I have pointed out several potential problems with the assumptions that went into the calculation, as you requested, which would make the calculation irrelevant.

Also, if you're going to dismiss the WB trapping factors as "hearsay" and assume they're wrong, thus eliminating any possibility of the device working in the first place, then whether the ions go out the cusps seems of trivial interest.

tony,

All else being equal, so will I. But when you don't know whether you're dealing with a sphere or a pyramid, doing the math to calculate the volume isn't especially useful.

Munchausen · Post by **Munchausen** » Tue Jul 22, 2008 4:01 pm

Because Bussard and Nebel both stated it does

Luke 21:14-15

14Settle it therefore in your hearts, not to meditate before what ye shall answer:

15For I will give you a mouth and wisdom, which all your adversaries shall not be able to gainsay nor resist.

TallDave · Post by **TallDave** » Tue Jul 22, 2008 4:30 pm

Heh, well one hopes they based that on experimental data rather than divine inspiration.

scareduck · Post by **scareduck** » Tue Jul 22, 2008 5:53 pm

Jesus and the gyroradius! I think I've heard it all, now.

ravingdave · Post by **ravingdave** » Tue Jul 22, 2008 6:51 pm

scareduck wrote:Jesus and the gyroradius! I think I've heard it all, now.

If I understand his point correctly, he is slapping us supporters. (deservedly so.)

The other side would prefer to see some equations backing up our points or refuting theirs. Other than Dr. Nebel, our side seems to be a little weak, prefering to regard the statements of Dr. Bussard as "ex cathedra". And of course there is always that lifesaver, "Wait for the Experiment! " While we secretly hope it comes out our way.

David

MSimon · Post by **MSimon** » Tue Jul 22, 2008 7:25 pm

I have been waiting almost two years (since Nov 006) for experimental results. A few more weeks isn't going to hurt.

Back when I started the hope was small that anything could be done. Now it is just a matter of time.

Patience grasshopper.

icarus · Post by **icarus** » Tue Jul 22, 2008 7:37 pm

These are some of the facts that make it less than a pseudo-science as painted by some not so charitable slurs.

To prove that it will not work 'a priori' by calculation Art needs to spell out ALL his assumptions (and justify them), right back to first principles and follow the calculations through thoroughly.

Or at least to a level that Dr. Bussard has done to prove that it will work.

Bussard has a history of designing and building nuclear reactors that work (KIWI).

The tokomaks, FRC projects etc have an extended history of promising much by the way of "trust us we have done the calculations".

scareduck · Post by **scareduck** » Tue Jul 22, 2008 8:23 pm

icarus wrote:Bussard has a history of designing and building nuclear reactors that work (KIWI).

But not yet fusion devices. Bussard previously made rather elaborate claims for commercially viable fusion devices that turned out to be baseless, something I unearthed earlier. It's fair to say that Bussard was an optimist, but a stable full of sh*t does not guarantee the presence of a pony.

kcdodd · Post by **kcdodd** » Wed Jul 23, 2008 9:02 am

I think the fields generates by any electron sheet, even if it is large, is more radial than you think. At first glance we could put 6 infinite planes of charge each with their uniform field produced along the normal. They would divide the divice into 1/24 sections. Looking at, say, the section pointing along the +z, +x direction, the normals (all divided by sqrt(2) to normalize) of the planes would be (1, 0, 1), (-1, 0, 1), (0, 1, 1), (0, -1, 1), (1, 1, 0), and (1, -1, 0). Summing together you get (2, 0, 4) for the field in that section. Hmm, the field points approximately along the +z, +x direction as well (ie, nearly radial), not conclusive.

Of course, the planes are not closed, they do not pass along the axial directions because the line cusps are interrupted by adjacent coils. So, we really need to get a numerical solution to see what effect all these fans have even if they could get larger in magnitude then the core.

MSimon · Post by **MSimon** » Wed Jul 23, 2008 9:34 am

scareduck wrote:
icarus wrote:Bussard has a history of designing and building nuclear reactors that work (KIWI).
But not yet fusion devices. Bussard previously made rather elaborate claims for commercially viable fusion devices that turned out to be baseless, something I unearthed earlier. It's fair to say that Bussard was an optimist, but a stable full of sh*t does not guarantee the presence of a pony.

I think some one pointed out in another thread that when he found his previous preferred method for fusion unworkable he abandoned it.

So the worst you can say (with some confidence) is that he did not find a problem with Polywell before he died.