magrid configuration brainstorming

mattman · Post by **mattman** » Thu Oct 18, 2012 1:29 pm

Hello,

Yes, I have been working on a model in Matlab and I have gotten really far in developing it. Here are the steps that I followed:

1. I used the basic biot-savart law to estimate the field strength at 4 points in the geometry:

A. Ring Center (which technically should be zero)
B. The joint. (where the rings are closest, ~296 Gauss)
C. The Corner (the geometric corner between 3 rings, ~193 Gauss)
D. The Axis (The center of the ring ~197 Gauss)

This is a really simple, first pass estimate but I can use it to check my work as the model gets more complex. I must state that Bussard predicted 70 to 100 Gauss at the corner, but I don't know how he estimated this. Check it the simple math here: http://hyperphysics.phy-astr.gsu.edu/hb ... oo.html#c3

=======
BTW... the rings are SPACED so that the corner and the axis field ARE EQUAL.
This makes electron confinement more uniform. Bussard stated it in his paper. THIS IS A BIG DEAL FOR RING DESIGN.
=======

I pulled two formulas from the 2011 University of Sydney paper and developed 2 more models:

2. The first is in EXCEL. The magnetic field generated by a single ring of current, in polar coordinates. They reference, and I went and found a solution in the book an "Introduction to Electrodynamics" by David Griffiths. This solution used the Complete elliptic integral of the first kind. Excel Has NO Formula for this; I had to go and find a paper on that. I found the paper: "Approximation for Elliptic Integrals" by Yudell L Luke which used the Taylor expansion to estimate it and I had to put that into excel. Here is the formula:

K(M) = 0.125 * PI*[ (1/(sqrt(1-msin^2(0.435*PI())) + (1/(sqrt(1-msin^2(0.3125*PI())) + (1/(sqrt(1-msin^2(0.1875*PI())) + (1/(sqrt(1-msin^2(0.06255*PI()))]

E(M) = 0.125*PI*[sqrt(1-m*sin^2(0.435*pi) + sqrt(1-m*sin^2(0.3125*pi) + sqrt(1-m*sin^2(0.1875*pi) + sqrt(1-m*sin^2(0.0625*pi)]

This will work, unless M gets close to 1. So, the next model I had would estimate the magnetic field at a point relative to a single current loop.

3. The second model uses superposition to add these 6 polar models together to come with a X,Y,Z coordinate model for the magnetic field by the rings. This solution amounted to adding the polar fields that align along the same axis (i.e. X, Y or Z) together. You have to add a small term, when you are converting from a polar system to a Cartesian system, but that is explained. It sort of feels like accounting, adding the correct numbers in the correct columns together. I did this in excel, but it was a big pain. Fortunately, I had my simple math estimate, to keep checking my work. That is critical. You add complexity, but you start with the simplest model first. I completed this in excel.

So now, I have jumped to Matlab and I have made significant progress along those lines. I can get contour plots and vector fields. Except that the direction vectors are not pointed correctly. Here is what I calculated (everything is in Gauss):

Simple Model:
Center: 269.0 **
Corner: 193.8
Joint: 296
Axis: 193.8

Polar Model (Excel):
Center: 269.1
Corner: -625
Joint: -1312
Axis: 197.9

Polar Model (Excel with Taylor Expansion):
Center: 269.1
Corner: -616
Joint: -1198
Axis: 198

Cartesian Model (Excel no Taylor Expansion):
Center: 90x +90y + 90z = 269
Corner: 230x + 230y + 230z = 690
Joint: 399x + 10y + 409z = 819
Axis: 207x + 22y + 22z = 257

Cartesian Model (Excel with Taylor Expansion):
Center: 90x +90y + 90z = 269
Corner: 223x + 223y + 223z = 668
Joint: 322x + 10y + 331z = 663
Axis: 207x + 8y + 25z = 240

** Technical the center field is zero but you can do the field strength from one ring, and then multiply by 6.

I had to leave this problem for the moment to work on other things. Here is what I want to do next:

1. Upload my excel file.

2. Upload a WORKING matlab file.

3. Write up a detailed explanation of all of this (with pictures) so the reader can follow everything.

Also, I would like to do this research professionally.

Randy · Post by **Randy** » Sat Oct 20, 2012 12:01 am

mattman

I have a general idea of where you're coming from now. But what I really need is direct-access to a complete working sample of some of your code/logic.
Is there any way that you can email me one of your work sheets for example?

~Randy

mattman · Post by **mattman** » Mon Oct 22, 2012 1:21 pm

Randy,

I can do that. Here is what I want to know:

How many electrons could Bussards reactor hold?

I think of it like a cup. We fill the cup up with water. How much water is in there at the end? The U of Sydney paper has given us the model and the mathematical requirements for containment. Bussards paper has given us the specific details about his machine (2.25” diameter thick rings, 10” in diameter, 4,000 amps running through each). Apply the model to the machine and you have a computer generated field you can work with. Then I want to do an energy density analysis.

What is great about this equation is it accounts for electric AND magnetic fields, together. The electric fields can be estimated by treating the center electron cloud like a sphere of uniform charge - a decent first estimate. Then you solve for the energy density. The energy density map is like a mountain range. To occupy a "high peak" the electron will need a corresponding amount of energy. We can treat the energy distribution of the electrons (~2E12) like a bell curve, with an average of 100 eV of energy (based on Bussards estimates).

It is an interesting problem and it may take some time, but I think it might be solvable.

Randy · Post by **Randy** » Fri Oct 26, 2012 4:03 am

mattman,

My program renders magnetic field lines (streamlines). I only posted the program source code to provide a general reference for people seeking to quantitatively determine the general shape and magnitude of magnetic field lines surrounding their magrid designs. I specifically designed it to allow both visual and quantitative inspection of the nature of point and line cusps present in any general magrid design.

I mistook your interest as related to this aspect of my program.

I've thought about your last post for several days and have decided that what you suggest is simply out of my league. At your current stage of understanding, you are simply too far ahead of me for me to be of much help to you. Dude, I’m no plasma physicist. You’re welcome to examine the source code of my program if you think it may be of any help to you.

In relation to calculating 3D magnetic field lines, the most important module in my program is: “modNDSolve.bas.” This (ASCII text) file contains the basic procedure I use to calculate the endpoints of each sequential streamline segment – everything else is just 3D support code.

~Randy

Randy · Post by **Randy** » Fri Oct 26, 2012 6:22 am

Download link to my Magrid 1.0 3D magnetic field line rendering program:

http://www.planet-source-code.com/vb/sc ... 7&lngWId=1

Hope this works

~Randy

D Tibbets · Post by **D Tibbets** » Sat Oct 27, 2012 6:26 pm

Again, I don't know where the 4000 Amps comes from. WB6 results did show a current of thousands of amps , but this was during the arcing terminal stage= where current waqs clowing from the magrid to the wall/ supports- ie: while the machine was shorting out. The actual e-gun (headlight filaments) current waqs about 45 amps during the stage where the Wiffleball and deep potential well was maintained.

Also, I have seen mention of a electron density of ~ 10^13 electrons per cubic cm. This would be 10^19 electrons per cubic meter. I believe this is above the "Brillian" limit and is a whole different discussion.
When you are talking about the net charge, you are talking about the difference in the positive and negative charges. Using the 1 ppm charge limits. In WB6 the charged particle density may have been ~ 2 *10^13 charged particles per cc. This would mean there was ~ 1.000000 *10 ^13 deuterium ions and 1.000001 *10^13 electrons per cc.

And remember the injected electron numbers are somewhat different when talking about gas puffer vs ion gunned versions.

Dan Tibbets

mattman · Post by **mattman** » Mon Oct 29, 2012 2:40 pm

Dan,

I double checked. You are right. I am sorry about this - I am not perfect, nor am I getting paid to do this work.

What is the correct number? So It can be listed on the blog?

Here is where I got the 4,000 amps, from "The Advent of Clean Nuclear Fusion: Superperformance Space Power and Propulsion "

The overall result is that a deep potential well is provided in
a few tens of usec, and the ions formed by ionization are
trapped within this well, heated by the fast e- injection to
well depth energy, and thus yielding fusion. However, the
cap drive current ran away as the internal puff gas supplied
leaked out into the volume around the machine and led to
external arc shutdown. The arcs were from feedthrough
leads into the main vacuum tank and the tank walls, and had
nothing to do with the machine or its containing cage/shell.
This took place over 0.5-2 msec after puff-gas actuation, so
little time was available for true Polywell operation. The cap
drive current to the test system then ran away to over 4000 A
to this external feedthrough arcing, as the Polywell formed
and fusions occurred. This destroyed the well depth (due to
drop in drive voltage). However the system did run at
emitter currents (to the machine) of 40 A for about 0.3-0.4
msec, proving the basic concept. Figures 17 and 18 show
data from these tests.

=============
Randy,

I downloaded your VB file. Over 1,300 downloads! Congratulations! You are having an impact!

I am slammed at work (and by Hurricane Sandy) and cannot seriously devote time to this (cleaning up the excel file) until after November 7th. By then, your analysis may be ahead of me.

Davids' presentation from the IEC conference indicates he may have already done what I wanted to do – applied the Syndey model to Bussard’s reactor.

http://www.aero.umd.edu/sedwick/present ... tation.pdf

===========

All,

What is the deal with this $146,725 Grant from NASA to University of Maryland on September 7th 2012? Check it out (at the bottom of the page):

https://www.fpds.gov/dbsight/search.do? ... r&start=30

Anyone know about this?

ladajo · Post by **ladajo** » Mon Oct 29, 2012 2:54 pm

Yes, the surge was the result of a shorted margrid winding wire rubbing at a feedthrough. 4000 amps is not normal by any means.

ladajo · Post by **ladajo** » Mon Oct 29, 2012 2:56 pm

Yes, I have seen this. And no it has nothing to do with Polywell.

The land surface responds to climate variability and also modulates the climate through the exchange of energy, matter and momentum. It is well known that the response and modulation largely depend on land cover and plant functional types and their properties. The synergy of the AVIRIS and MASTER data with high spatial and spectral resolutions provides us an unprecedented data resource to study the spatial variability of the land-atmosphere exchange of water, carbon and energy at the ecosystem scale. Scheduled multiple transects at different seasons outlined in the ROSES2011 call for proposals and the high temporal refreshing frequency of the future HyspIRI data will enable us to study the temporal dynamics of such land-atmosphere exchange. We propose to use the HyspIRI-like airborne measurements resulting from the planned campaigns in FY2013 and FY2014 to 1) map the following surface radiation and energy budget components from both AVIRIS and MASTER data: insolation/photosynthetically active radiation (PAR), albedo, net radiations, and evapotranspiration (ET); and 2) quantify the changes in the land-cover-dependent surface radiation and energy budget under varying climatic conditions. We have developed the corresponding algorithms for the multispectral remotely sensed data in the recent years. In this study, these algorithms will be refined and extended to hyperspectral data, and extensively validated using the AVIRIS and MASTER data at many field stations where surface measurements are available. These products will be mainly used for addressing scientific questions in this proposal, but also provided to other investigators for many other applications. They can also be scaled up for validating other coarser resolution radiation energy products. This is a research proposal responding to A26 calling for proposals that ¿utilize AVIRIS measurements, MASTER measurements, or both to address one or more of the HyspIRI science questions¿. The scientific question we will try to answer is CQ4 ¿How do species, functional type, and biodiversity composition within ecosystems influence the energy, water and biogeochemical cycles under varying climatic conditions?¿ All these algorithms developed in this study can be potentially used for generating the operational surface radiation and energy products from the VSWIR and TIR data of the HyspIRI mission in the future. Since the proposed efforts build on our algorithm development from the previous NASA projects, it is a cost-effective strategy for refining the algorithms and generating the needed products for analysis.

mattman · Post by **mattman** » Tue Oct 30, 2012 3:44 pm

That is too bad.

Curiousfusor · Post by **Curiousfusor** » Tue Nov 13, 2012 4:59 pm

I know this threads been down for a tad, but I have a question that I'm just itching to get out there: is there any electromagnet setup that allows for one pole to face in and the other out, but not a series of magnets facing in to allow for one pole in and out (resulting in field cusp), but instead a steel spherical globe lined/ wraped on the inside and out with copper, forming the electromagnet? It'd be like taking one torus extending out and warping the sides up and around to a small point. Resulting in two small cusp at the top and the bottom to inject deterium into. Would this work or another hair brain idea, and could maybe even these two cusp be completely closed in. Essentially doing what a Tokamac does in a sphere instead of a torus? If there's no cusp there's essentially no electron loss (losses through the cusp that is) wouldn't this extend the electron lifetime significantly?

ladajo · Post by **ladajo** » Tue Nov 13, 2012 5:06 pm

Have you looked at the spherical Tokamak concept?

Curiousfusor · Post by **Curiousfusor** » Tue Nov 13, 2012 5:44 pm

Yeah I thought about spheromacs and spherical tokamacs but the thought is unlike a spheromak in that the center is completely hollow. It's completely feasible that a spherical tokamak could be used to contain electrons instead of ions, and then radialy accelerate ions like a polywell, but tokamacs don't rely on particle speed for fusion, so the center spine of a spherical tokamak would have to be removed, because it be a stuctural target. Can this be done? There has to be an arrangement where cusp are removed, I mean tokamacs dont have field cusp right.

D Tibbets · Post by **D Tibbets** » Wed Nov 14, 2012 6:57 pm

ladajo wrote:Yes, the surge was the result of a shorted margrid winding wire rubbing at a feedthrough. 4000 amps is not normal by any means.

No, this was a separate issue. The shorting during normal WB6 testing was the ~ 12,000 volts supplied to the magrid metal surface by the capacitor bank and which shorted (arced-glow discharged) to various structures outside of the magrid. The short that developed during the last test that involved the magnetic windings was a breakdown of the varnish insulation on the wires , the intervening mylar (?) insulating sheath, and the metal of the magrid case. This connected the thousands of amps of low voltage magnet wire current to the different potential of thousands of volts on the magrid surface. I'm not sure which way the current flowed- both systems had thousands of amps available. The magrid surface supplied by the capacitor bank, and the magnet wires from the bank of batteries. In any case the insulation breakdown spot became a powerfull arc welder. The resulting heating probably made a fused mess of local magnet wires and burned a hole in the casing before the system shut down. The magrid assembly probably did not look much different afterwords, but the damage was catastrophic from a functional stand point.

The expected arc breakdown between the magrid surface and other structures- feed throughs, Faraday cage, etc. did reach thousands of amps and this power was supplied by the capacitor banksand would have continued untill the capacitor bank was drained or the switch was opened. The conductor for this current was the plasma. Look up Pashin arc breakdown, the conductivity of a plasma is exponential once a minimal preswsure is reached. As mentioned by Bussard, this limit was reached quickly after the gas puff due to neutral gas leakage ooutside of the magrid. This gas (and it's ability to be be quickly ionized by the electron guns, etc. produced the relatively high conductivity- the short. In the WB6 report this was illustrated by the graphs, and was catastrophic in terms of maintaining the internal potential well. This gas puffing / ionization internally and externally process allowed for a brief "steady state" potential well, but then quickly broke down in the small machine. Larger size, better shilding of external strutures, more attention to minimizing sharp angles and better vacuum pumping may allow for much extended steady states (hours to months).
The important point is that during the deep potential well, near Beta=1 "steady state" conditions of ~ 0.2 mS the electron current from the E-guns nessisary to maintain that condition was ~ 40 Amps. This multiplied by the accelerating voltage on the magrid surface results in the ~ 480,000 Watts of input power in WB6 This ignores the magnet wire power and the pumping power, both of which are trivial- with superconducting magnets.

As a check, Bussard's claim of a Q of ~ 1/100,000,000 for WB6 works out as ~ 1 mW (one billion D-D fusions per second) of fusion power / ~500,000 Watts in = 1/500,000,000 Q. So an input current of ~40 Amps is reasonable.

Dan Tibbets

D Tibbets · Post by **D Tibbets** » Wed Nov 14, 2012 7:46 pm

Curiousfusor wrote:I know this threads been down for a tad, but I have a question that I'm just itching to get out there: is there any electromagnet setup that allows for one pole to face in and the other out, but not a series of magnets facing in to allow for one pole in and out (resulting in field cusp), but instead a steel spherical globe lined/ wraped on the inside and out with copper, forming the electromagnet? It'd be like taking one torus extending out and warping the sides up and around to a small point. Resulting in two small cusp at the top and the bottom to inject deterium into. Would this work or another hair brain idea, and could maybe even these two cusp be completely closed in. Essentially doing what a Tokamac does in a sphere instead of a torus? If there's no cusp there's essentially no electron loss (losses through the cusp that is) wouldn't this extend the electron lifetime significantly?

I don't think so. This sounds like an attempt at a functional monoplole. There are two polar cusps, but the leakage through these may be small (comparable to a face centered central point cusp in the Polywell(?)). The problem is building the system. Each magnet will have cusps between the next magnet, so using a lot of magnets only increases the number of cusps- unless you can find a real monopole. Also, the geometries of these cusps are critical, all have to be convex towards the center, otherwise macro instabilities can occur, and these apparently are a very bad loss mechanisms.

I suppose you might construct a quasi monopole confinement scheme by assembling many magnets into a sphere, and if the magnetic fields are strong enough that the cusp B fields related openings are much narrower than the gyroradius of the electrons, they may act as a quasi spherical surface with very small leakage (this ignores the scattering effects that lead to the spacing of the WB6 magnets). Perhaps a thousand Tesla field with 50 KeV electrons(?). Theoretically possible(?) but practically impossible with the many tiny electromagnets.

In the EMC2 patent application, it is mentioned that some tried to assemble a confinement system of many magnets arranged with opposite poles facing inward, but this did not work.

The Polywell is theorized to operate better by increasing the number of magnets to more closely approach a quasi spherical shape. The improvement may be ~ 5X (also, more and smaller magnets would reduce the distance to the center of the individual coils and thus decrease the face point cusp leakage- apparently more so than would the increased sum leakage of the point cusps. But, the engineering difficulties go up rapidly. That is why the minimal truncated cube design is what has been used thus far.

Dan Tibbets