Sunday, December 26, 2010

We are now a community.

We are now a community.

        Right now there are thousands of emails registered on Talk-Polywell. Wow. Congratulations polywellers – we are now a community. If we could somehow connect, unify and, organize all these people; we would be a force to be reckoned with. We have come a long way since the Bussards’ video hit YouTube in November of 2006. At that time, if you were a polyweller, there was not very much to connect with.

      I think many of us got started in much the same way. Someone sent us the link to Bussards’ presentation. We watched the video on YouTube. We did not understand it, but we felt we had seen something significant. We were left wondering: what can I do now? Before November 2006, there was not much. At that time there were no polywell blogs, no polywell videos, no polywell group and, polywell did not even exist in wikipedia. This internet community started from basically zero and has grown, person by person, to thousands of people. Great work guys.

How we got here:

       People need to understand that: this did not just happen. This community grew because individuals stood up and made things happen. A few short weeks after Bussards’ speech, Fusor.net and askmar.com both started posting polywell information and M Simon blogged his first post on the polywell. The idea was entered into wikipedia at the end of November 2006. Then, Thomas Ligon republished a polywell article in January of 2007. That spring, the idea was covered by a few news sources. It was mentioned in the New York Times and the Defense News. In March of 2007, a group was started on Yahoo.com. Then, in June, Talk-polywell - the first polywell forum - was set up. In the first two months there were only 59 ardent supporters registered. Some of them went on to contribute greatly to the online Polywell community – including Talldave, FoxRoger, MSimon and KitemanSA. That summer, an Estonian named Indrek, uploaded the first videos simulating the polywell on YouTube.

      While the internet community slowly grew, the experimental world continued moving. Bussard used 2007 to appeal for funding, setting up EMC2 as a charitable research organization. In August of 2007 when Talk-Polywell was only a few months old, the research team got restarted with funding. Unfortunately, that October, Dr. Bussard passed away from cancer. It should be marked as a very sad day for all of us working towards alternative energy. The research team had WB-7 up and running in January 2008 – about the same time that Alan Boyle of msnbc.com wrote his first polywell post. The team, lead by Dr. Richard Nebel, ran tests till late summer 2008. Their results were never published. The team submitted their findings to a review board that fall.

      The internet world continued moving forward. In the fall of 2008 - during the closing months of the presidential campaign – rogersjg submitted a polywell-like idea to Google’s 10 to the 100 competition. Google was giving out 10 million dollars for ideas to help the world. At the same time a polywell presentation was uploaded by CleanEnergyFuture45 on YouTube. In the first weeks of 2009, the cover of Time magazine featured a picture of a compact florescent light bulb with title: “Why we need to see the light about energy efficiency.” Energy was clearly a hot issue. That January, a team of amateur filmmakers interviewed Thomas Ligon, at his home in Virginia. The hour long film that was created, “An Interview with Thomas Ligon on the polywell” was uploaded on YouTube that May.

       Also in the fall of 2008, a thirty year old computer programmer in Brooklyn, NY named Mark Suppes saw Dr. Bussards’ talk and decided he was going to try and build a polywell. That launched prometheusfusionperfection.com a 35 thousand dollar continuing effort to build a working polywell. To date, his blog has received 159,222 hits, over 3,000 dollars in donations and, the volunteer support of many people. He worked through 2009 building a fusor, which produced fusion in mid November of that year. Marks’ effort made world headlines this past June – including a live interview on CNN. Efforts continue to get a working polywell in Brooklyn.

       The wheels of governments turned through most of 2009 trying to secure project funding for Nebels’ team. This was the appropriate balance between analyzing and checking the results as well as moving the research forward. The DOD announced the contract on September 11th 2009. The Navy funded the research for $7.86 million dollars, with a completion date of April 2011 – with an opportunity to secure $4.46 million dollars till October 2012, if things go well. I am sure everyone can agree - we hope things do go well.

What do we do now?

        Regardless of how large our community is, it is still, for the most part under the radar of the mainstream. This is good. We need to prove this idea. We need to prove it in the most sound and legitimate way possible. We need data that says it works. We need theory that says it works. Dr. Nebels’ team can provide the data. I hope the internet community can provide the theory. So that is where my efforts will be aimed at. The established thinking is this is a dead end. We have a 300+ page thesis from MIT that says – regardless of what Mark does in his warehouse, or what Dr. Nebel finds in California – this reactor will never work. I will not accept that judgment until I fully understand why. And I don’t think you should either. This is too important.

“Fusion energy has been 20 years away, for 30 years.”

       I want to say that, regardless of the fusion snags in the past - we have never been here before. In fact, it is because of the past efforts that we are where we are. We have volumes of fundamental fusion data from the 60’s and 70’s, such as reaction byproducts and cross sections. We have a body of work from the 80’s on bulk plasma behavior for a variety of configurations and confinements. We have robust computer models from the 90’s and the 2000’s - code developed for fusion blow back, plasma pressures and temperatures. We have a massive body of work to draw from. Today, we know more about bulk interactions, confinement, injection, power conversion analysis, X-ray production and basic plasma properties, than we ever have before. We should thank the tokamak guys, the laser fusion guys, the national lab scientists, the commercial efforts, the physicists, engineers and mathematicians for making this possible. You should thank them all. They have gotten us here.

      Also, we have something else they did not have. We have the internet - a repository where all this information is accessible to whomever wants it. A tool that allows all of us to communicate, collaborate and put our heads together. Our effort will be mired in the inherent problems of a volunteer, disperse, internet exercise. Peoples’ interest will flare up and then die off a few months later. We will have inherent problems with trust and credibility with each other. There will be mistakes and tangents. Regardless, I think we have the man-power, the tools and the resources to do this. We need to use the web to scrub the best ideas about this machine forward, to educate more people about this machines’ potential and, most importantly, to prove the damn thing will actually work.

       Right now, in our world, there is great confusion. The economy is in a downturn. We are facing global warming. We are facing shrinking energy supplies. We are running out of time. Military, business and political leaders argue and fight about which direction to go in. They don’t know what to do. I know what to do. We have got to build this machine. We have got to commercialize it. We need to get a working polywell in the hands of everyone who needs energy. We have to do it soon.

Timeline and Links of Polywell Work:

Bussard’s Video – posted on YouTube Nov 9, 2006 - http://video.google.com/videoplay?docid=1996321846673788606#

Askmar – “Transcript of Should Google Go Nuclear?” - November 9, 2006 - http://www.askmar.com/ConferenceNotes/Should%20Google%20Go%20Nuclear.pdf

Fusor.net – first article November 10, 2006 – www.fusor.net

M Simon’s first Polywell Post - Monday, November 27, 2006
http://powerandcontrol.blogspot.com/2006/11/easy-low-cost-no-radiation-fusion.html

Wikipedia article – Polywell entered on November 27 2006 - http://en.wikipedia.org/wiki/Polywell

Tom Ligon – “The World's Simplest Fusion Reactor, And How to Make It Work” – January 5, 2007 - http://www.fusor.net/newbie/files/Ligon-QED-IE.pdf

New York Times - "Practical Fusion, or Just a Bubble?"- February 27, 2007 – http://www.nytimes.com/2007/02/27/science/27fusion.html

Defense News – “Fighting for Fusion - Why the U.S. Isn't Funding a Promising Energy Technology” - March 5, 2007 – http://www.emc2fusion.org/2007-3-5%20DefenseNews.pdf

Yahoo Group founded March 2007
http://tech.groups.yahoo.com/group/IEC_Fusion/

Indrek’s video – June 2, 2007 - http://www.youtube.com/watch?v=ao0Erhsnor4&feature=related

Talk-Polywell founded June 2007
http://www.talk-polywell.org/bb/index.php

EMC2 Chartable organization - http://www.emc2fusion.org/

Alan Boyle’s First Post - January 9, 2008 - http://cosmiclog.msnbc.msn.com/_news/2008/01/09/4351271-strange-science-takes-time .

Alan Boyle’s second post - June 12 2008 - http://cosmiclog.msnbc.msn.com/_news/2008/06/12/4350196-fusion-quest-goes-forward

Alan Boyle’s third post - August 28, 2008 - http://cosmiclog.msnbc.msn.com/_news/2008/08/28/4350263-fusion-effort-in-flux

Rogersjg’s Google submission - October 19, 2008 - http://www.youtube.com/watch?v=8IJWsXVsAhM&feature=related –

Google’s 10 to the 100th competition - October 20th 2008 - http://www.project10tothe100.com/how_it_works.html

Time Magazine – January 12, 2009 - http://www.time.com/time/covers/0,16641,20090112,00.html

Interview with Thomas Ligon - May 16, 2009 -
http://www.youtube.com/watch?v=1HatEDkNnn8&feature=related

Mark Suppes Work –
http://prometheusfusionperfection.com/



Sunday, October 31, 2010

Explaining the Counter Argument

Hello Polywell Fans,

I have been working steadily since May of 2010 on explaining “A general critique of internal-electrostatic confinement fusion systems”.   This paper was published in 1995 and was written by Dr. Todd Rider.  It is this document, as well as Riders’ thesis, which represent the largest theoretical arguments against the polywell working.  My goal is to explain this paper to you.  We need to see if Riders’ arguments and Bussards’ statements about the Polywell agree or disagree.  

            So far I have explained 70% of Rider’s paper.  Though my work is not yet finished, I feel comfortable releasing the first portion, here on the internet.  It is included below.

Sincerely,
The Polywell Guy.
=============================================

Explanation of “a general critique of internal-electrostatic confinement fusion systems”

Science is a conversation.  One researcher stands up and says: “this is the way it is.”  They do this by writing a paper, filled with evidence which backs up their argument.  A few years and sometimes decades go by and, someone else stands up and responds: “No. This is the way it is.” and so on.  We are in just such a conversation about the polywell; the very early stages.  The first statement - I would call the opening argument - was “The Polywell: A spherically Convergent Ion Focus Concept” published by Nicholas Krall, with assistance from Robert Bussard in 1992.  In that paper, Krall explains the idea of the polywell, and gives an overview of its basic strengths and weaknesses.  This caused a rumbling in the physics community and three years later an answer was advanced.  This came from Dr. Todd Rider, whose 1995 paper: “A general critique of internal-electrostatic confinement fusion systems” gave theoretical reasons against the polywell working.  This paper, combined with Rider’s masters and doctoral theses were often pointed too as the reason the polywell would not work.  Eleven years went by.  In 2006 Robert Bussard responded, in his “should Google Go Nuclear” speech and subsequent “The advent of clean nuclear fusion: super performance space power and propulsion” paper.  The highlights of Bussards retort?  Plasma inside the device behaves differently then expected.  Phenomena such as the Whiffle ball and the virtual anode break Riders’ old assumptions.  There must be something to Bussards’ response, because the Navy gave the team 7.8 million dollars. 

I got a hold of Rider’s ‘95 paper.  It presents a maze of theoretical assumptions and mathematical argument against the polywell.  Rider tackles - one by one - phenomena inside the polywell.  He steals formulas from other situations and applies them to the polywell.  This is about the best one could expect; the polywell was very new idea in 1995.  He makes order of magnitude arguments which both show you how many ways the polywell can fail and, how many ways Rider could have gotten it wrong.  The more I dove into the paper, the more respect I had for Rider.  For one man to tackle such a problem is audacious and the work is certainly scholarly.  However, the topic is so complicated it is hard to imagine the work did not miss something.  For most papers in science, this may not be such an issue.  However the polywell could be a major invention for mankind.  A way to produce cheap clean abundant electricity is not a trivial matter.  In this situation, it is my stance that raw data is needed to verify these claims.  I do not care if the data indicates this idea is a flop.  It is too important to leave up to theory.  

My favorite part of Rider’s paper, is the mass and energy balances.  Rider analyzed energy flow within the reactor; quantifying the amount coming in, going out, and being exchanged between the ions and electrons.  He tried to estimate how fast these energy transfers would happen.  He compared these rates, to the rates of fusion.  The paper also looked at the flow of mass.  How many ions and electrons were entering and leaving the system.  He attempted to quantify ion-ion collision time, calculate how fast ions were lost and how fast the polywell thermalized.  This offers us an interesting and new perspective on the polywell.

What follows is my attempt to explain this paper.  It is very complex - like navigating a maze.  It is not perfect, I am sure I made mistakes.  What you are reading is the result of several months of volunteer work.  What have I learned?  Rider made lots of assumptions.  His work is not solid.  The topic is maddeningly complex – and there is a good chance the analysis is flawed.  It is hard to see how any one man could have account for all the factors in play inside the polywell.  It makes one want to just build the thing and see what kind of results you would get. 

If the polywell works, it would be a major invention, akin to the automobile or the computer.  A cheap, clean way to produce abundant electricity; it would help stop global warming, help stop the energy crisis and make some people very rich.  Not to mention, getting the US out of recession.  This is not something we can afford to leave up to theory alone.  The stakes are too high.  We need data, not complex estimations.  I do not care if the data indicates that the idea is a failure.  I will accept that.  We need to know.  Riders’ paper cannot be taken as a definitive no on this idea, as you will see, he makes many estimations and approximations, stealing formulas from other fusion devices.  It should make you realize how badly testing of this idea is needed.  We need to know for sure.  As the famous physicist Richard Feynman said: “It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.”  Please enjoy this unraveling of Riders paper. 

Synopsis of “A general critique of internal-electrostatic confinement fusion systems”
Author: Dr. Todd Rider, MIT
Published: Plasma Physics, June 1995

            Rider opens his paper with a description of electrostatic confinement devices.  These devices make deep electrostatic wells.  Ions are shot into the center of these wells.  The ions fall down the well.  They build up speed and smash together in the center.  They can hit hard enough to fuse.  Here is a graphic of this from Mr. Kralls’ paper:
Figure 1: Mr. Kralls’ diagram describing the polywell.


Mr. Kralls’ paper also suggests that you could “squeeze” the plasma using sound waves.  The idea is by blasting microwaves into the center the plasma would squeeze together.  Riders’ paper will look at both normal Polywells and these, microwave enhanced Polywells.  There are two important polywell properties that Krall and Bussard suggested:

     1. That the material inside the polywell could maintain a sharp energy distribution1,2. The ions would not thermalize or go to a bell curve.  This is shown below in figure two.
     The Polywell will do this.                                     The Polywell will not do this.
Figure 2: A comparison of a non-thermalized and thermalized polywell. 

   2. That polywell could maintain two different ion temperatures2.  For example, if we were fusing deuterium and deuterium -the second easiest fusion reaction- one group of ions could be cold, one group could be hot.  These temperature differences could be maintained. 

Rider is going to look at both these claims.  First, can the material inside the polywell not go to a bell curve?  This is very important.  On this point, there is agreement from Rider, Ligon, Bussard and Krall.  If the material goes to a bell curve, if the polywell thermalizes, it will fail.  Rider starts by figuring out where to look for thermalization: in the center.  Rider models the ions inside the Polywell into three parts: the core, the mantle and the edge.  A picture of this model is below in figure three.  Rider showed that collisional effects were about 100 times less in the edges, then in the dense central core. 
Figure 3: This is a rough sketch of ion distributions inside the Polywell, as modeled by Rider (not to scale).  Some magnetic field lines are shown in green, the magnetics are shown in gray.  Ion density gets higher as you get closer to the center.  Rider broke up the ion concentrations in three zones, the core, the mantle and the edge.  He even assigned rough radiuses to these sizes. The core radius was about 1unit, the mantle radius was between 50 and 80 units, while the edge was about 100 units out.  
Assumptions’ Rider Makes:

These collisional effects lead to the focused ion ball in the center to spread out.  This is degradation of focusing and, is a problem Rider states he will ignore for this paper.  There is good reason to believe that core convergence will rapidly degrade.  By not assuming any degradation of focusing, Rider is assuming that the picture above remains constant throughout all of the Polywell’s operation; a core, a mantle and an edge.  Rider then looks at various effects inside the polywell and notes how some depend on where you are relative to the center, and some depend on the plasma volume and density.


Table 1: This is effects and their dependence on radius, volume and density inside the polywell (for good converged systems).

This means that the size of the core will only slightly change fusion, x-ray cooling, thermalization and ion to electron energy exchange.  This also means it is safe for Rider to compare fusion, x-ray cooling and scattering effects without having to worry about the specific volume or density of the polywell.  I want to point out that these assumptions - are just that - assumptions, not absolute truths.  In reality, fusion rate, x-ray cooling, energy exchange, thermalization and scattering are not absolutely radially dependent nor are they independent of volume and density. 

Rider is going to assume the core as uniform in all directions, with the same energy amounts and temperatures inside the core.  Rider assumes that the fusion fuel is uniformly mixed everywhere with any significant density.  He also assumes the plasma is quasineutral.  Quasineutral means that there is no net charge in volume, the density of negative electrons and the density of positive ions cancel out.  This is shown mathematically below.
(1)
The quasineutral assumption stated mathematically: the density of the electric charge equals the density of the ion charge.

This seems to be one of the most questionable assumptions.  It is a clear fact that to maintain a potential well, there needs to be more electrons than ions inside the polywell.  The polywell cannot work any other way.  If there are more electrons, then only under specific conditions would their densities work out, such that the above expression would hold.  Conditions where the electrons occupied a different volume, the charges worked out or the assumption was for a local volume, not the entire reactor.  Furthermore, if the Whiffle ball and the virtual anode do exist, then there will be regions of the center with excess ions and excess electrons.  There, quasineutrality may not hold.  Below is an example explaining quasineutrality, using DT fuel.
Example 1: working out what the quasineutrality assumption would be for an example polywell reactor.

A. Calculating The Fusion Power Density:

            It makes sense to start by calculating how fast you expect to get energy out of this device.  That way, you can compare this rate to the rates of all these other effects.

(2)
Equation two is the fusion power per volume.  The cross section is the measure of the “fusibility” of two atoms when they smash into one another at some velocity.  Rider applies the quasineutral assumption to this equation, changes the units to cgs -except for energy (eV)- and, rearranges the equation. Looking at the case of deuterium, deuterium fusion, where the fuel densities are the same for all the deuterium ions, Rider can make the following approximation:
(3)

Rider now has the equation in the form he wanted all along; one independent of fuel density.  The above expression estimates the rate of fusion power coming off the reactor in a given volume.

B. Calculating An Ion Lifetime In Device:
Based on this equation above, Rider figures that the time it would take an ion entering the system and getting fused would be.

(4)

This equation works for dissimilar ion fusion (aka A+B fusion) in the case of A + A fusion you divide the above equation by two. 

C. Rate of Energy Transfer Between Two Groups of Ions:
            We have an equation for how energy is transferred from two different clouds of ions.  The guy who figured this out was Lyman J Spitzer, a physics professor at Princeton, back in the ‘50s and ‘60s.  If you are just looking at ion cloud Two being heated by ion cloud One, here is the equation:

(5)


D. Can you keep ions at 2 different temperatures? Case 1

            Rider wants to use equation five above to answer a very important question: can you keep two ion clouds at two different temperatures?  This is a really important question to answer.  Lets’ assume inside the polywell we have cold ions and hot ions.  First looking at the cold ions; we are injecting cold ions and as they get fused they leave.  Also the cold ions pick up energy from the hot ions also flying around in the center.  Given this, Rider gives us the following energy balance:

(6)

Figure 4: Schematic of some of the energy flows analyzed in section D, by no means a complete picture of the energy flows inside the polywell. 

This energy balance, equation six, is also shown schematically in figure four, which shows the flow of energy inside just the ion cloud.  I have a few questions here.  I can think of a few other sources of heat, I do not know if Rider did not include them because they are insignificant, or if they cannot be a mechanism for heating.  Some suggestions would be: heat transfer from the electron cloud, annealing from the potential well, radiation from the walls, and x-ray heating from within the cloud.  Electron heating of the ion cloud is an easy thing to ignore; an electron is about 1,836 times less massive then an ion. Also the fusion products leaving have lots of energy, and they will re-heat material as they bump into ions on their flight out (for DD fusion this is about 3.64 MeV, loads of energy).  Incidentally, they will probably not incite other fusion reactions, though the products of DD fusion can, in theory, undergo a cascade of other fusion reactions.  Rider now works out two equations: the ion to ion heating rate, and the ion cooling rate.  The ion cooling rate is solely due to the replacement of hot fused ions with cold ions coming in from outside.
(7,8)

He is looking specifically at the ion two, population.  He balances the two expressions and integrates over space and density, coming to this expression for the cold ion’s temperature.
(9)
Where the Ln() term is the Coulomb logarithm.  The Coulomb logarithm is a way to find the mean free path for an ion in a big cloud of ions.  Lets say you have a cloud of ions.  You know the density, the charge, the temperature of this cloud.  You throw in a test ion.  The coulomb logarithm is a way to tell how for that test ion could go without smacking into other ions.  The Z is the atomic number it would be 1 for deuterium and 1 for tritium. By including Z, Rider has made his nice equation work for lots of fuel combinations.  From this Rider calculates that the cold ion temperature would be within 5% of the hot ion temperature.  If that were true, then Rider argues you could only keep the two cloud temperature separated by a maximum of 5%. 

D. Can you keep ions at 2 different temperatures? Case II

            Rider looks at another method of maintaining two different temperatures, a hypothetical case.  Assume you keep the cold ions cold, artificially; how much cooling would you need to pull this off?  To figure this out, Rider needs to know the velocity of the collisions between the ions.  He assumes all collision velocities are
(10)
This is an estimation based on the statistics for such a case.  There will certainly be collisions at much higher and lower energies.   If this is true then all the energy transferred from the really hot ions to the really cold ions will be via collisions.  Rider can then use his ion to ion heating equation, equation seven.  Is Rider missing any energy flows?  I do not know.  Rider divides the energy transfer rate by the fusion power rate to arrive at equation 11.

(11)
What Rider is actually doing by this is comparing how fast we can fusion energy out, to how fast energy would transfer from one cloud to the other.  The idea is, if one cloud can be heated, would it lose energy to the cold cloud faster, than fusion energy comes out of the reactor?  In addition, there is another rate to consider: the rate it takes to heat the hot cloud in the first place.

It is important to point out that Rider’s analysis do contain some simplifications.  First of all, there are the assumptions on collision velocity and his estimation on the Columbic logarithm value.  These are somewhat reasonable.  Next, Rider is only looking at two rates, ion to ion energy transfer and fusion rate.  There are, electron to ion energy transfers (albeit small), x-ray heating and cooling, ion annealing, Cyclotron radiation and fusion products reheating the cloud; just to name a few other phenomena which could effect ion temperature.

Rider is correct that if one could maintain a temperature difference this would vastly improve Polywell performance.  For instance, in the P-B11 reaction, the reaction everyone wants to do, it is helpful if we keep the borons cold and the protons hot.  Ideally we would maintain this temperature difference and run the reaction at 620,000 eV - to take advantage of the peak cross section for the reaction.  I have read5 that the optimum voltage for pB11 was 550,000 eV; this needs to be figured out.  Rider plugs in the numbers for this situation, into his equation and comes up with this comparison.
(12)

 

This argument makes a Polywell operating like this: an energy loser.  What he is saying is: in this case you would always need to put in energy faster then you can get it out.  This is, of course, a hypothetical case.  Based on these calculations Rider will, from now on, assume all clouds of ions have the same average temperature.  Rider accurately points out that even if you had a big cloud of ions in the center, in which each individual ion was at the same temperature, not all the ions would collide correctly.  It is these kinds of calculations that make me want actual, real, data about polywell operation.

Wednesday, September 1, 2010

The Debate Over Electron Behavior.

        There are a number of different ideas and theories about what is exactly happening to electrons inside the polywell. Here is a summary of these ideas:

1. Electron recirculation – Where are they travelling?
2. Electron recirculation – When are they moving fast? When are they moving slow?
3. The magnetic mirror line - Where do the electrons turn around?
4. The Whiffle ball – Are the electrons creating their own magnetic field?
5. Are the electrons mutually repulsive in the center?
6. Are electrons packing in the cusp points?

This is a very complex topic. I am also no expert. What is presented here are ideas that have developed in discussions with former employees who worked on the Polywell, physicists, papers, online information and, forum discussions. From all these interactions, I have attempted – here - to cobble together a picture of what the electrons are doing inside the polywell. This is hard to do with no data. This is also all volunteer.

We need data. We need hard proof of what is and is not happening inside the machine. As you start to think, plan and read about the Polywell you see that the topic is maddeningly complex. There is a good chance most theoretical analysis of the polywell is flawed. It is just hard to see how any one person, group, computer program or theory could catch all the factors in play inside the polywell. It makes one want to just build the thing and see what kind of results you would get.

If the polywell works, it would be a major invention, akin to the automobile or the computer. A cheap, clean way to produce abundant electricity; it would help stop global warming, help stop the energy crisis and make some people very rich. Not to mention, getting the US out of recession. This is not something we can afford to leave up to theory alone. The stakes are too high. We need data, not complex estimations. I do not care if the data indicates that the idea is a failure. I will accept that. We need to know. The discussions below will start to give you a taste of how complex the electron picture is alone. It should make you realize how badly testing of this idea is needed. We need to know for sure. As the famous physicist Richard Feynman said: “It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.”

1. Where are the electrons recirculating?

       Here is the setup: we have a polywell filled with ONLY electrons, NO IONS. We know the electrons will recirculate, from the center along the magnetic cusp lines. There are 14 cusps; Six for each side, and 8 for each corner. We know this because of Indrek's - electron only - polywell simulation and, because Bussard presented this in his Google presentation. Watch 52 minutes, 35 second in4. You can see Indrek's simulation here:

http://www.youtube.com/watch?v=ao0Erhsnor4&feature=related



Figure 1: Two Images from Indreks’ simulation showing electrons flowing to and from the cusps. Notice the electrons are CORKSCREWING along the magnetic field lines. They ride the cusp lines like a roller coaster, out and back into the middle.

2. When are the electrons moving fast? When are they moving slow?
      Imagine we had a magnetic field in a square. The top of the square is dense, the bottom is light. The top of the square has a dense magnetic field and the bottom has a light magnetic field. We set an electron on the square. Below are statements that can be made about this simple example.



Figure 2: A scenario discussed below, two electrons placed in a high density and, a low density electric field.

   A. The electron will align itself. All free floating electrons spin. This spin creates a diamagnetic moment, or a mini magnetic. The electron will act like a mini magnet. It will align its’ magnetic field with the external magnetic field; it will turn.

    B. The electron will not move. This is because of the Lorentz Force1. The Lorentz force is the force that all electrons experience in a magnetic field. The force is given as: Force = charge*(velocity vector X Magnetic Field). With no starting velocity, the velocity vector is zero, therefore the force is zero, therefore the electron will sit there. It will not move.

    C. The electron sitting high magnetic field is more energized. That electron has more potential energy. This is from the equation for energy density2. Energy Density = e0/2*(electric field density)^2 + 1/2*u0 *(Magnetic field density)^2. So if the field lines are denser, then the energy density is higher. Energy goes up by B squared. Therefore the electron sitting in the higher density field has more potential energy. To restate, the setup is two electrons, one high energy and one low energy. They are both not moving and, both aligned.

     D. Now kick the electrons. The one in the high field moves faster. This is because of the Lorentz Force. Force = charge*(velocity vector X Magnetic Field). If the Magnetic field is higher, the force is higher (assuming each electron gets the same kick). So, if you have a higher B field, you have a high energy, you have faster moving electrons. We also know that the electrons move along the cusps.

Figure 3: Magnetic field lines inside the polywell, taken from Indreks’ simulation6. Electrons will move faster in the denser field, so recirculation occurs faster along the sides of the polywell and the cusp corners, then in the center. Some believe that electrons stop movement in the center.

E. We know that there is a higher magnetic field at the cusps, or the corners of the polywell. This can be seen above, in a picture of the magnetic field lines, taken from Indreks’ simulation. It seems reasonable then to assume then that these recirculating electrons would move faster at the corners of the device and slower in the middle. Some believe that they come to a complete standstill in the middle. This Picture is not universally agreed upon. Therefore, our picture of electron re-circulation looks like this:


Figure 4: Hypothesized picture of electron recirculation inside polywell. Note electrons are moving from the center to the corners and recirculating back. The picture is somewhat simplified because the actually electrons would be corkscrewing instead of moving in straight lines. The big question is speed. The electrons should move faster in the denser field, so they will move faster in the cusps then in the center of the polywell.

3. The magnetic mirror line - Where do the electrons turn around?

      As the electrons travel up the cusp lines they move faster. They reach some point where they turn around. This U-turn point is where the electron hits a magnetic mirror. I will explain magnetic mirrors as best I can, borrowing from a lecturer from the University of Texas at Austin5. These notes look at both the electric and magnetic field effects on the particle. Therefore I would imagine this scenario is more comprehensive then the energy density and Lorenz force arguments I was using above. Since both are approximations anyways, both can shed light on electron behavior inside the polywell.

 Figure 5: This is a picture of an electron in some fictitious electric and magnetic field.

     Let us assume this that the fields are not varying with time. It just sits there. The above particle has some energy. If the magnetic field remains unchanged, and the particle does not move, then the energy of the particle remains constant. The equation that gives the particles total energy, is shown below



Unfortunately, I do not know what the U and Ve is specifically referring too. The U is most likely the part of particle’s velocity which runs parallel to the magnetic field lines. This is the velocity we care about, since it would be about the speed at which the electrons ride the magnetic field lines inside the polywell. The Ve is probably the velocity of the particle relative to the electric field. Here are some statements that can be made about electron behavior in such a field.

1. If the field is constant with time, the particle gains or loses no total energy as it moves around the field. This is the ideal case. No process like this can occur without losing some energy, or it would break the 2nd law of thermodynamics. Ideally, energy would just be transferred from kinetic to potential and back as the electron moves. As the particle speeds up, kinetic energy increases, potential energy decreases and total energy remains constant. The opposite happens when the particle slows down. The particle loses kinetic energy – transferring it to potential energy.

2. You can rearrange the above equation in a field that is constant in time. In this case, the author was interested in the velocity parallel to the magnetic field lines.

From this equation the author determines there are three mathematical cases for a magnetic mirror.



Case 1:
In this case the electrons can move in any direction. Up or down the magnetic field lines. They DO move “up” the magnetic field lines due to the Lorenz force described above. The Lorenz force is the force an electron experiences due to a magnetic field.

Case 2:

In this region, where the above mathematical statement is true, the electrons are prohibited from going. Essentially what this is stating is that the electron energy is not high enough to overcome the “containment” energy.

Case 3:
This case, represents the line between the two regions. It represents the mirror point, the point where the recirculating electrons would have to turn around. A nice analogy can be made using a marble in a bowl. This analogy is shown graphically in figure Six.



Figure 6: A simple analogy explaining magnetic mirrors: a marble in a bowl. The highest the marble can reach as it rolls around in the bowl is the blue line. This is the 3rd case, where the total energy of the electron matches the containment energy at that point. The lid of the bowl is the maximum energy the system can contain. Any electron with a total energy higher than that maximum, would fly out of the system.

      Here is an important point. This containment is magnets containing electrons. The magnetics are creating magnetic mirror lines, which the electrons cannot cross. There are no ions in this picture. It seems there would be a completely different potential well for the ions. One created by the electrons. Below is a fictitious drawing of what these magnetic mirror lines might look like inside the polywell.


Figure 7: A possible magnetic mirror line picture adopted from Indreks’ simulation6. Originally, this picture was a 2D image of the magnetic field lines (shown in blue), from some plane cut across the polywell. The magnetic field intensity is represented by the different colored regions. You can see the cusps very well in this image, there are cusp lines running out at each corner. There are also cusps at each side. A fictitious black line has been drawn representing the turn around point for the electrons. I did this arbitrarily.


Figure 8: Electron recirculating picture, complete with magnetic mirror lines.

4. The Whiffle Ball Theory – Are electrons creating their own field?

The Whiffle ball hypothesis is a very critical part of the polywell. It can be explained as followed. All electrons have a diamagnetic moment. This is created by their spin. This moment behaves like a small magnetic. When a strong external field is applied, it can align the moments of the electrons in an object against the field. This creates a repulsive magnetic field. Thomas Ligon does a good job describing it, from “An interview with Thomas Ligon” on YouTube. He states the following:

“In that region, there is essentially next to no magnetic field. Everywhere else, where there is a magnetic field, electrons are passing through in small populations. These electrons will behave classically, following electromagnetic theory, the right hand rule and all the other stuff they normally do. In principal, Dr. Bussard believed that if you got the electron current inside the machine up high enough the cloud of electrons itself starts doing things to the magnetic field that one would not gather from studying a single electron. He believed that they would go diamagnetic and exclude the magnetic field and push it back.”

This is shown graphically below.


Figure 9 & 10: The first figure shows graphically how electron moments can align against an external magnetic field. This cases the electrons to create their own magnetic field in response. In materials, this means that something can behave like a magnetic, when a strong magnetic field is applied to it. An example of this is shown above, where a frog behaves like a magnet, and floats in response to about a 16 Tesla external field. This is believed to be happening inside the polywell. The some of the electrons in the cloud are aligning their moments against the external magnetic field. They are making their own field. This is supposed to push back the external field and help contain the electrons. This is the Whiffle ball effect. As of this writing, it is only a theory.


5. Are the electrons mutually repulsive in the center?
6. Are electrons packing in the cusp points?

      Both these were comments made about electron behavior from Thomas Ligon’s interview.

“Lets assume you do not have any ions in here and you fill this machine up with all the electrons it will hold. The neat thing is, the electrons are mutually repulsive in the center here and they actually lose kinetic energy going into the center. The depth of the potential well occurs, when the center is space charge limited. Electrons are losing energy to the point where they basically come to a standstill. The electrons in the middle of this machine are not hot. They are nearly cold. They are lukewarm at best. When they get trapped, the electrons lose kinetic energy in here. Now if you start putting boron, or if you start concentrating ions in here, the ions themselves are positively charged and they will partially counteract the tendency of the electrons to repel each other. So you start getting whets called a virtual anode. It is a structure in which the ions themselves allow the electrons to come in with a little more kinetic energy.”
Is this true? We need data to verify this.


Figure 11: Hypothetical picture of electron behavior inside the polywell. This includes electrons moving faster at the cusps then in the center. It also includes packing at the edges, and a magnetic mirror line (in red) which shows where the electrons would turn around.

Sources:

1. http://en.wikipedia.org/wiki/Lorentz_force

2. http://en.wikipedia.org/wiki/Energy_density

3. http://en.wikipedia.org/wiki/Electron_magnetic_dipole_moment

4. "Should Google Go Nuclear" 52 minutes, 35 seconds in

5. http://farside.ph.utexas.edu/teaching/plasma/lectures/node22.html#e2.75

6. Mandre, Indrek. "Ephi - the Simple Physics Simulator." Web. http://www.mare.ee/indrek/ephi/.

7. “An Interview with Thomas Ligon” Web. http://www.youtube.com/watch?v=1HatEDkNnn8

Monday, July 5, 2010

W.W.W.D. What Would Widgets Do?

Oil spills – yuck. Its one of many, many problems I hear about each day in the news. I normally turn off CNN when they start their reporting. It is getting so bad a guy can’t enjoy the Sunday paper without seeing headlines on coal mines, the economy, the Middle East or, pollution. I just want to read the Sunday comics. There are allot of problems we face, and it is hard to see how most of them are connected; and how they could all be solved together. That’s right America, together. Here is my solution: the Widget.


What are Widgets, you say? Widgets produce cheap, clean, abundant, green electricity. A Widget costs five million dollars, is about the size of a gas station and runs on water. I am going to build one next year - just so I can go back to reading the Sunday comics in peace. I plan to make a fortune selling and servicing my Widgets. I am going to build a big factory in your town and hire all you unemployed workers out there, to make my Widgets. We’ll put Widgets in every city in America. Those big coal fire plants in Texas - shut them down, we got my Widgets. We’ll put a big Widget in New York City, right next to the Brooklyn Bridge. We’ll put a Widget at the foot of the Space Needle in Seattle. We’ll even put a Widget inside the superdome in New Orleans. Yes, my Widgets are going to sell.

Now, I know what your thinking… won’t that put people out of work? No fear, I will hire all you people to operate my Widgets. Work for an oil company? Come work on our Widgets. Widgets will single handedly end coal mine accidents. No need for coal - we have my Widgets. Three Mile Islands will be a thing of the past, now that there are Widgets. Widgets can make so much electricity, that electricity will be as cheap as dirt. Pretty soon everything will run on electricity: stoves, grills, snowmobiles and, cars. I mean, if a gallon of electricity is 8 cents, who would want to use gas?

Imagine a fleet of electric cars running on Widget power. We could put Exxon out of business. Of course, I will hire them all for Widget work. We will definitely still need oil for lots of other things, but I’ll bet the Sunday comics, we will need a lot less of it. Think of it. No more oil spills. No more drilling in Alaska. No more strip mining in Alberta. No more drilling in Kazakhstan. Also, if we stop having to buy oil then we will stop sending money to mean people in the Middle East. A dictator cannot hurt his people, with no money to spend.

I bet my Widgets could stabilize the region. Not only that, I bet my Widgets could make clean water. That’s right America: clean water. A Widget can make lots of energy and, hooked up to a desalination plant, can churn out cheap, clean water. We will put desalination plants across the Islamic countries. We will pump clean, cheap water into Cairo, Mexico City and, Tel Aviv. Widgets will solve California water problem, end the shortages in Phoenix and, stop the draining of the Colorado River.

While we on it, I will license my Widgets across Africa. The UN will install small Widgets in African villages across the continent. Widget electricity will raise the standard of living. It will give many people something better to do, rather then fight each other. I bet you Africans will stop cutting down so many trees for fuel too. When you can create cheap, clean, abundant energy, you can power all kinds of changes.

All of these changes will make America the wealthiest, cleanest and most respected nation on Earth, end global warming and solve the energy crisis. Widgets can do it! So my friends - look for my Widgets next year. I am going to get right on that and, maybe some of you will join me. Then, hopefully, we can all get back to enjoying the Sunday newspaper in peace.

Sunday, May 16, 2010

Transcript of Polywell Film

Hello,

     There is a film on YouTube which covers the Polywell. The title of this 56 minute film is: "An Interview with Thomas Ligon On the Polywell" You can start watching it here:

http://www.youtube.com/watch?v=1HatEDkNnn8&feature=related

However, the audio on this film is pretty bad. For some time now, people have been asking for a transcript of the film. This has finally been finished. This document is much to long to be put here on the blog, but a copy can be downloaded from www.askmar.com. You should check it out. Here is the link:


Below is an excerpt from the 27 page document...
=========================================

What form do you see this research taking? Do you expect it to be publicly funded, government funded research or, do you see it going to private funding?

I can envision an angel stepping in and funding this thing and, I know there are a couple people with some money who have expressed some interest. But it really ought to be government funding. This is the type of program that we have governments for. It is for everybody’s good, it should be kept for everybody’s good. It should be done as a government program to save the world, to save the United States but also to save the world. That is the way it ought to be done, wither it will or not, well, so far the funding has been almost exclusively government.  If Dr. Bussard had dreamed this thing up, instead of the Riggatron, we might be there by now. But his comment to me was, you do not go out looking for angels, you don’t find angels, angels find you.

So you can see this design applied to a nuclear power plant, that does not require a cooling tower, that’s much smaller than the tokamak and if, IF, it can burn PB11 and do direct conversion, and then it will have high efficiency? As a power plant?


Very high efficiency. Theoretically, assuming you can not recover the bremsstrahlung radiation the limit is about 95 percent, good luck reaching it. Because the energy spread on the alpha particles is so tight, you should be able to come up with a grid structure that even a very simple, single electrode means of recovery could approach 85% efficiency. That is high. Nothing else is much more than 33%, no steam cycle. I guess maybe the theoretical limit might be around 40%, nothing gets much above 33% efficiency.


Assuming that the major technical challenges were solved, assuming that this concept works, can you give us a sense of what this machine might end up looking like?

A sphere, maybe, 6 meters or so in diameter, with some supporting equipment. The sphere might contain a mag grid it might be made up of 12 magnets instead of 6. It would have some supporting cryogenic equipment to operate the super conducting magnets. It will have some cooling load, because we are going to have some fusion products. I hope we have enough fusion products hitting the mag grid that we have to do some thermal shielding of it. If it is a DD burn it is going to have to have some kind of a neutron absorbing blanket to generate the heat, in which case, you would have steam components. It would look like any other power plant that has steam. I am hoping that it would simply have a bank of DC to AC power converters sapping energy straight off the PB11 reaction at 85% efficiency and feeding it out the power grid.


Sunday, April 4, 2010

Conversations and updates on the Polywell

Hello,

For those of you out there who have not been following the Polywell research recently, the group at the Navy have come out with their next generation design for a test reactor, WB 7.1. WB 7.1 looks to be a duplicate of WB 7 with some improved diagnostics. They have also put a nice picture of WB-7 in operation. MSNBC did another blog post on the machine. I sent out links to let people know about the developments. A good friend had some questions and comments about all this. Below are the answers to his questions from my own research and from M. Simon of Talk-Polywell. The answers are included here with links and the pictures for your enjoyment.

Photos:





Links:

MSNBC article

Questions/Answers:

1. What are the pieces that touch the vertices of the loops?

The metal loops are connected by a very strong insulator. The blocks are white, so I am guessing they are probably Beryllium Oxide. Beryllium is a very nasty thing to work with. It is transparent to X-rays, which is why we like it. The stuff is ~$105 per pound; those blocks in there might be ~300-400 dollars.

2. Why are there so many freaking holes in design 2?

The holes are for the vacuum pumps, electron guns, Ions guns, and Neutron counters. As long as we fuse DD or DT we are making neutrons. We count the neutrons to determine how well we are doing. Neutrons can also cook the reactor, destroying the rings and making them radioactive. The holy grail of fusion, however, is fusing PB11, a much hard thing to fuse. If that were to happen there would be low amounts of neutrons, low amounts of radioactivity.

The holes are for diagnostics. A production reactor would not need so many. pB11 would reduce neutrons by a factor of about 1E3 to 1E6. This is caused by side reactions. The Hydrogen used in the reactor would need to be purified as much as possible in order to eliminate Deuterium.

3. This is designed to heat water as a means of energy exchange?

I do not know about the DD & DT energy exchange. There is probably a steam cycle in this scheme. I believe you can catch neutrons in a blanket of Lithium (~$300 per pound). If we fuse PB11, there is a great way to get the energy out: direct conversion. PB11 fusion generates alpha particles or hydrogen nucleus, when these strike metal they can draw a current. The theoretical efficiencies on this process are very high.

D-D and D-T would probably use a steam cycle. However, alpha collection may be worthwhile even in those cases. It would be an engineering/economic question.

4. Does this thing still only cost $200k to build?

No. I think $200K was a guess at the final commercial price. It is still allot cheaper than NIF (~$4.2 billion) and ITER (~$1.23 billion for US). The beauty is in the size and the scale. As of right now, you do not need exotic technologies to get this to work. The e-gun is pre-WWII, a very mature technology. The modern ion gun is late 70's. The rings could be superconductors, which could create cooling issues.

$200K would be for a small pulsed experiment. My estimate for a production reactor is about $.50 to $1/watt. The experimental net power machine (100 MW) is estimated at $200 million. That would include a reactor building (for shielding).

5. 100MW.....holy crap.

Bussard showed that the fusion rate increases with the 7th of the radius. He showed that the net power out increases as the 5th of the radius. He also showed that increasing the rings increases confinement which makes it work better. EMC2 inc. is assuming he is right, and that is why they are calling the 20 ft x 20 ft x 20 ft device a 100 MW machine.

Power is a function of R^3 (volume) and B^4 (magnetic field). Net power will be less (to account for losses). The R^7 is for copper coils. For superconducting coils the scaling needs to be separated into its components due to limitations on maximum field of the super conductors.

Monday, January 4, 2010

A very simple model for the polywell to spark discussion:

Imagine we had a population of 50 ions and 50 electrons inside the polywell. Now we spilt up the ions into two groups, half have enough energy to fuse and half do not. This is analogous to an ion population with a Boltzmann distribution illustrated below.



Now there are a couple of reactions that we can model. Fusion reactions are high energy ions hitting high energy ions. We will call these H ions; H is for high energy. When H and H hit they should fuse creating an F. F is for a fusion product. Assume that F’s leave the system. We will call the other ions L; L stands for low energy. When an H meets an L, we would assume they would both leave with equal energy. We do not care what this energy is; suffice to say they both now lack enough energy to fuse. Bremsstrahlung reactions (or X-ray reactions) are electrons hitting either of these types. Anytime an electron whizzes past an ion, an X-ray can be made. Assume this reaction would drop H ions into L ions. Assume that the electron population remains constant; we feed in enough electrons to compensate for losses. If you move along this line of thinking, then you can setup six possible reactions. These are illustrated below.



Since we have a population of 100 electrons and ions, then we can figure out what the probability of each of the above reactions is. We can do this by applying basic statistics. For example the total number of reactions in a population of a 100 where it is just two things hitting one another, is 100 choose 2. Mathematically this is shown below.



The same method is used anytime a reaction involves something hitting itself; for example H and H reactions. In other cases, you multiply the size of the two populations. Using this process we can calculate the likelihood of each reaction inside the polywell.




Note that the fusion reactions are only 6% of all possible reactions. With all the possible reactions of the system enumerated and their probabilities laid out, the next step is to factor in the energy. If one looks at deuterium, deuterium reactions very quickly it becomes clear that H+H  F is a serious oversimplification. Here is a list of all the possible deuterium reactions from “Physics of Fusion Fuel Cycles”.




Fig 2: The two DD reactions, with two possible side reactions and the energy produced in millions of electron volts. Listed is the total energy released by reaction followed by the subset of that energy trapped in the hot neutron.


For our model, we want a simple amount of energy to assign to the H+H reaction. The number we will use will be positive 10.8 MeV. For a description of how this number was decided upon, please see the appendix. The average amount of energy an x-ray can have is between 12 eV and 12 KeV. We will assign negative 11 KeV to the E+H reaction, and negative 3 keV to the E+L reaction. This again is an oversimplification; the reader can refer to the NRL plasma foundry for a much better treatment of x-ray cooling. We can assume all the rest of the reactions are elastic. Based on this, below are the energies of each reaction.




From this, one can see why fusion is so energetically desirable. Given all that has been outlined above it becomes possible to track material and energy into and out of our system. For a DT reaction, ions need about 10 keV to fuse together. The reaction we are treating is DD. Assume the H ions 16 keV and L ions 5 keV, so we can track the total energy across the system. Details on this calculation and the energy assignment can be found in the appendix. Therefore an energy balance across the system in MeV is:



Model:

Using this construct, one can create a little model in excel. This was done, using a random number generator, and the probabilities to choose which of the six reactions take place. Graphs of material and energy balance from a given run are presented below.




Fig 3: material overtime generated by model.



Fig 4: Energy within model over time.
Conclusion:

The point of this model is to make the reader think about the polywell from a rough engineering standpoint. It is by no means complete, nor does it claim to be. Many of the assumptions in it are weak. There are many effects that it does not take into account. Based on Bussard’s work, a reasonable estimate is that there was about 1.4E12 electrons and about 1E6 fewer ions inside the WB-6 device (see appendix). One interesting conclusion from the model is only 6% of the reactions would be fusion reaction. This percentage should change for Bussards WB-6 test. From Bussards’ WB6 work these amounts would presumably be 1.4E12 electrons, 7E11 L and H ions and 2.8E12 total things in the system. Bussard also estimated that electrons have about 100,000 re-circulations before they hit a metal surface and leave the polywell6. This loss was not accounted for. The model also oversimplifies the energy of the ions, into two H and L ion groups. This assumption has been shown to be critical to the Polywell working. It has been shown that a population of ions with a bell curve inside the polywell will kill the device14. Bussard also claimed that his WB-6 experiment did deuterium-deuterium fusion with a 10 kilovolt potential well6. These claims now seem reasonable. If it takes about 10 KeV for DT fusion, Bussards reactor would be in the right ballpark for deuterium fusion.


Appendix:

Assigning Energy to the H+H reaction:

This is an estimate at best. One way to do this is to assume that all the reactions that can occur do occur. Then calculate the number of times each reaction occurs and the energy produced with each reaction. You can then get the weighted average energy. Assume that 16.66 deuterium ions go into the first round of fusion reactions; that means there are 8.33 pairs. You can calculate the probability of each of the first fusion reactions by the ratio of their energies.




Next, assume that all the T and He fuse with the all remaining deuterium. There is no probability here because T reactions do not compete with He reactions. Assuming this, 16.67 total reactions took place across the whole system. Then you can find the weighted average energy for our model for fusion reactions.



This means that the average energy for every H+H interaction is 10.80 MeV.



Assigning Energy to the H and L Ions:

The easiest type of fusion is deuterium tritium fusion. This is based off measurements where one ion was smashed into other ion. Researchers fired different ions at one another at various speeds and measured the amount of fusion reactions that occurred. This is quantified in a fusion reactions’ cross section. Cross sections are area measurements in units of barns or 10-28 meters2. Cross sections for various fusion reactions are plotted below12.



This cross section is used to calculate the rate of fusion for large thermalized clouds of ions. The normal way to measure fusion within these clouds is some variation on the equation below.



Where, F is fusions per second per volume, n is ions per volume, v is the average velocity of the ions in the cloud and sigma the average cross section of the reaction.

One can also calculate the energy it would take to fuse just one deuterium and one tritium ion. The ions need to overcome the columbic repulsive forces, and come close enough together to where the nuclear force can take over. The nuclear force binds nucleouse together. This process is made easier by quantum tunneling. Quantum tunneling arises out of the wave-particle nature of protons. A proton, acting like a particle could not tunnel across a barrier; but if it acts like a wave it can. The effect lowers the energy needed to fuse DT. The energy is about 10 kiloelectronvolts4. Based on this, you can estimate what the temperature of a thermalized cloud of pure deuterium would need to fuse. You have to assume all the ions have an average temperature is 10 KeV.



One reference cited a temperature of 120 million kelvins4 for a DT cloud this is compared to our estimate of 92 million kelvins for a D cloud. For DT, one would imagine a cloud split between the ions. The temperature of this cloud could not be estimated because the heat capacity of tritium could not be found. In any case 10 kiloelectronvolts is a good estimate for what is needed for fusion for DD.


Calculating the amount of Ions & Electrons in the WB6 Test:

If you accept that one can form a Whiffle ball; then a number of conclusions naturally follow from that. For basic analysis, we can treat the Whiffle ball like a point charge. From a general physics textbook we can find the follow equation for a point charge:







For my analysis, I assume 20 cm there is no charge. Bussard claimed there was a 10 kilovolt well in the center, from a 12.5 kV drive voltage. Applying the above equation, this means there are about 1.4E12 electrons in the Whiffle ball. Bussard claimed that the electron density in the Whiffle ball was 1E13 electron/cm^3. This means the Whiffle ball would be 0.6 cm in diameter, about five one millionths of the total volume.

***** 4-21-2012 Edit:  20 cm is too close to assume that there is no charge.  Hence the number of electrons (1.4 billion) predicted here, is probably a low estimate.****

Calculating the amount of Electrons needed for a Diamagnetic Whiffle Ball:

The “Whiffle ball” is a theory. It is not necessarily happening. It also may not be needed by the polywell for it to produce power. The idea is if you jam enough electrons together and subject them to a strong magnetic field, they behave diamagnetically. They push the field back. Diamagnetism is when something that is not a magnet, acts like a magnet. The example used in the film is a frog which becomes magnetic. It took about 16 Teslas to make the frog fly. In Bussards Valencia paper we can find the quote describing conditions in WB-6. "If all the electrons were still at ca. 100 eV, … at B=1000 [Gauss]." Let's assume that the magnetic field was 1000 gauss or 0.1 teslas and the electrons have energy of 100 eV.

Electrons spin. Their spin creates a magnetic moment, like a tiny magnet. A quick and easy way to find out if the Whiffle ball is possible is to see if 1.4E12 electrons would have enough magnet strength to match the 0.1 teslas external field. This is an easy estimate to make.




It appears they would have enough magnetic strength.



Works Cited:

1. http://en.wikipedia.org/wiki/Sun

2. http://www.fusor.net/newbie/files/Ligon-QED-IE.pdf

3. http://en.wikipedia.org/wiki/Nuclear_cross_section

4. http://en.wikipedia.org/wiki/Nuclear_fusion

5. "Should Google Go Nuclear?" by Mark Duncan, 12-4-2007, www.Askmar.com

6. "The Advent of Clean Nuclear Fusion: Super performance Space Power and Propulsion" Bussard R.W. 57th International Astronautical Congress (IAC 2006)

7. "Coulomb law, electric potential and Biot-Savart law differentiations for tricubic interpolation" Indrek Mandre, http://www.mare.ee/indrek/

8. http://www.ru.nl/hfml/research/levitation/diamagnetic/

9. “Physics of Fusion Fuel Cycles” JR McNally, Jr. Nuclear Technology/Fusion, August 3, 1981.

10. “Feasibility of advanced fuels” Hiromu Momota, APR. 1995, Transactions of fusion technology, 27, 38-31.

11. http://en.wikipedia.org/wiki/Bremsstrahlung

12. http://www.kayelaby.npl.co.uk/images/p548.jpg

13. http://en.wikipedia.org/wiki/Deutrium

14. “Fundamental limitations on Plasma Fusion Systems not in thermodynamic equilibrium” Todd Rider, Thesis, MIT, June 1995.