Thursday, April 10, 2014

An Argument For Fusion


An Argument For Fusion

If you look at the numbers – in 21 years, many countries will run out of oil and gas [2, 3, 8].  Energy will look like a poker game.  Most international players will be knocked out.  The remaining nations will hold all the chips.  The imbalance in oil and gas will have a big impact.  About eighty percent of the worlds’ energy comes from fossil fuels [9].  What are we going to do?  Bill Mckibbens has argued that we will start a world war over this [11]. No one can predict the future.  But mankind is facing a major energy shortfall.  21 years is not far off.  You reading this; you could be alive then. 

Solutions:

            Everyone has got an energy plan.  We have seen waves of speakers at TED tout their new ideas.  Al Gore and his supports have argued that we can fill the gap with renewables; notably geothermal [10].  We will probably need all of these plans.  Different solutions are needed in different places.  But, everything needs time to develop.  We have to get started now.

Cheap Wins:

            But, we are not doing it.  Ignore the green talk. Use of fossil fuels has been rising worldwide [12].  The reason is money.  If you do not think money runs the world: ask someone with a job.  Fossil fuels are dirt cheap.  They have been since the dawn of the industrial revolution, 250 years ago.  In all that time, through many governments, markets and ideologies - we have burned it.  We still burn it.  Our world is wired for fossil fuels.  It is going to take strong forces, as well as time to wrench us away. 

Wrench Us Away:

These forces could be environmental, political or economic.  An environmental force is when we break the planet, to a point where it becomes unlivable.  I hope this never happens.  We cannot let that happen - but we have already done so much damage.  A political force is when people everywhere decide to ignore the economics and act on Earths’ behalf. Thomas Friedman has pushed for this [1].  I do think it will be fast enough, absolute enough, or permanent enough.  There is not much time.  Political will may work in some countries, but not everywhere.  It may work eventually, but not soon enough.  It may work for periods, but not forever.  This is all due to dirt cheap fossil fuels.  The last option is economic.  We find new sources of energy, and their prices are so low - that it pulls in the entire world.  These must make zero greenhouse gases.  They must scale-up to have an impact. Finally, we need to be able to jockey them into our infrastructure.

Options:

 The field of possibilities is vast.  We can redesign almost everything around energy conservation.  This includes transportation, cities and farming.  There exists as many choices for energy generation.  There is a set of options that Bill Gates has called: energy farming [13].  These are renewables.  They are green, but they lack the energy density, or scale of fossil fuels.  There is a myriad of fission options.  But these are expensive, complex and less safe.  Many options simply mitigate burning carbon: burn less, pollute less or find new sources.  Finally, there is our way of life.  We can, we should, and we must be gentler to the Earth.  It is the only home, we have ever known.

Fusion Trumps All:


   Fusion blows the competition away.  The energy released is - by far - the most mankind has ever encountered.  It should make you think differently about our energy options.  If abused, it could destroy our planet [6, 7].  A good illustration of this, is what one thousand megawatts looks like, in different forms [A, B, C, D, E, F].  This is shown below.  




Fusion, Middle School Style:

On March fourth, Jamie Edwards became the youngest person in the world to fuse the atom.  He is an 8th grader in Lincolnshire, England.  He did this with three thousand pounds, and a principals’ blessing.  His fusor works the same way a polywell does.  This was news.  Over fifty articles reposted the news across the web [4].  Jamie got a letter of congratulations from His Royal Highness, Prince Andrew, the Duke of York [5].   He also got an appearance on the Letterman show [20].  There was even a political cartoon in the daily mirror.



Predictions:

            It is impossible to predict the future.  People have been promising grand things from fusion, for decades.  But this is not 1980 – it is 2014.  Today, we are closer to fusion power than we have ever been.  Today we are more strapped energy, more limited for resources and support more humans than ever before.  Powerful forces are at work.  They are reshaping civilization.  Energy and climates’ sway worldwide is gradually swelling.  The trajectory is clear.  Every nation is going to be looking for energy.  If they have not yet, they will be soon.  Fusion is the most plentiful source known to mankind.  IEC has recently broken away, as a simple, ultra-cheap path to fusion.  The conditions are ripe: interest in this is going to explode - and it cannot happen soon enough.
   
1000 MW Citations:

A.        Oil, coal, uranium and fusion estimates from: Ongena, J., and G. Van Oost. "Energy For Future Centuries Will Fusion Be An Inexhaustible, Safe And Clean Energy Source?" Fusion Science and Technology 45.2T (2004): 3-14. Http://www.ans.org/store/j_464. Web. Mar. 2004. .

B.        Fusion numbers also came from: Lee, Sing, and Sor Heoh Saw. "Nuclear Fusion Energy—Mankind’s Giant Step Forward." Journal of Fusion Energy 30.5 (2011): 398-403. Print.

C.        Solar predictions were from a real plant in India: Jai, Shreya. "India to Build World's Largest Solar Power Plant in Rajasthan." Http://articles.economictimes.indiatimes.com/. The Economic Times of India, 21 Sept. 2013. Web. 08 Apr. 2014. .

D.        Cow calculations were based on:  Otaraku, Ipeghan J., and Evelyn.V. Ogedengbe. "Biogas Production from Sawdust Waste, Cow Dung and Water Hyacinth-Effect of Sawdust Concentration." International Journal of Application or Innovation in Engineering & Management (IJAIEM) 2013th ser. 2.6 (2013): 91-93. Web. June 2013. .

E.        Napier grass were from a real project in Thailand: Vivanpatarakij, Supawat, Weerin Wangjiraniran, Raksanai Nidhiritdhikrai, and Dawan Wiwattanadat. "Potential Study of Electricity Generation 1000 MW with Biogas in Thailand." Advanced Materials Research 622-623 (2012): 1209-212. Print.

F.         Wind calculations were based on a California wind farm: "GE Acquires California Wind Farm, UK Energy Management Firm." Sustainable Business. Sustainable Business, 12 Jan. 2011. Web. 09 Apr. 2014. .

Other Citations :

1.         Friedman, Thomas L. Hot, Flat, and Crowded: Why We Need a Green Revolution-- and How It Can Renew America. New York: Farrar, Straus and Giroux, 2008. Print.

2.         "World Energy Outlook 2013 Factsheet." Www.worldenergyoutlook.org. International Energy Agency, 2013. Web. 7 Apr. 2014. .
3.         "AEO2014 Early Release Overview." E Annual Energy Outlook 2014. Energy Information Agency, 2014. Web. 7 Apr. 2014. .

4.         "Google News for Jamie Edwards." Google News Service. Google Inc., 15 Mar. 2014. Web. 7 Apr. 2014. .

5.         "Royal Letter of Approval for Schoolboy Who Broke Record." Lancashire Evening Post Website. Lancashire Evening Post, 24 Mar. 2014. Web. 07 Apr. 2014. .

6.         Siegel, RP. "Fusion Power: Pros and Cons." Triple Pundit RSS. People, Plant, Profit, 12 July 2012. Web. 07 Apr. 2014. .

7.         Meadows, Donella H. The Limits to Growth; a Report for the Club of Rome's Project on the Predicament of Mankind. New York: Universe, 1972. Print.

8.         Ongena, J., and G. Van Oost. "Energy For Future Centuries Will Fusion Be An Inexhaustible, Safe And Clean Energy Source?" Fusion Science and Technology 45.2T (2004): 3-14. Http://www.ans.org/store/j_464. Web. Mar. 2004.  .

9.         "Years of Fossil Fuels Remaining." Energy Realities. Energy Realities Project, 2011. Web. 07 Apr. 2014. .

10.       "U.S. Energy Information Administration - EIA - Independent Statistics and Analysis." International Energy Outlook 2013. U.S. Energy Information Administration, 25 July 2013. Web. 07 Apr. 2014. .

11.       Lee, Sing, and Sor Heoh Saw. "Nuclear Fusion Energy—Mankind’s Giant Step Forward." Journal of Fusion Energy 30.5 (2011): 398-403. Print.

12.       Jai, Shreya. "India to Build World's Largest Solar Power Plant in Rajasthan." Http://articles.economictimes.indiatimes.com/. The Economic Times of India, 21 Sept. 2013. Web. 08 Apr. 2014. .

13.       Orchard, Bryan. "Blue Mountain Biogas Plant Turns Pig Manure into Power." - Jan 15 2014 12:00 AM. Pollution Solutions, 15 Jan. 2014. Web. 08 Apr. 2014. .

14.       Otaraku, Ipeghan J., and Evelyn.V. Ogedengbe. "Biogas Production from Sawdust Waste, Cow Dung and Water Hyacinth-Effect of Sawdust Concentration." International Journal of Application or Innovation in Engineering & Management (IJAIEM) 2013th ser. 2.6 (2013): 91-93. Web. June 2013. .

15.       Gore, Albert. Our Choice: A Plan to Solve the Climate Crisis. Emmaus, PA: Rodale, 2009. Print.

16.       McKibben, Bill. Eaarth. New York: Time /Henry Holt, 2010. Print.

17.       Cusick, Daniel. "Fossil Fuel Use Continues to Rise." Scientific American Global RSS. Scientific American, 25 Oct. 2013. Web. 07 Apr. 2014. .

18.       Gates, William, III. "Innovating to Zero!" 2010 TED Conference. TED Conference, Long Beach California. Feb. 2010. Speech.

19.       Vivanpatarakij, Supawat, Weerin Wangjiraniran, Raksanai Nidhiritdhikrai, and Dawan Wiwattanadat. "Potential Study of Electricity Generation 1000 MW with Biogas in Thailand." Advanced Materials Research 622-623 (2012): 1209-212. Print.

20.       "News/education." Jamie Goes from Fusion to Letterman. Lancashire Evening Post, 09 Apr. 2014. Web. 09 Apr. 2014. .

Friday, January 31, 2014

We Have to Try


We Have to Try

“Innovation is what separates leaders from followers.” – Steve Jobs

      Mankind is facing a storm. From shrinking water, energy and resources - we have problems.  Climate change does not help this. Neither does the population boom. To solve this, we must try some new ideas. 

     Fusion power would be a tool; like a hammer or a gun. Like them, this tool can have a big impact. Like them, it can be used to help or to hurt us. Our goal is to get this to mankind. But our other hope is that we use it wisely.


            We need to try it.  We need to act.  The Polywell needs to be developed.  Ultimately, it may not be the tool we seek.  It may fail.  But, the work will move us forward; beyond the unknowns.  It may even usher us into a new age.  The age of fusion.


Summary:

        This post covers work from Convergent Scientific Incorporated.  It has four parts: experimental work, modeling, talk highlights and a conclusion.  Experiment details were imperfect.  CSI trapped electrons for 20 seconds, using: model one.  It is assumed, that this is a wire shaped into a diamond - 14 cm a side with 1,500 amps and held at +500 volts.  This was within a ~0.6 pascal vacuum with four emitters at each corner.  Model one was cooled with a chilling system.  The emitter voltage was varied from -500 to -9,500 volts and a probe measured the resulting trapping.  Results were questioned because the emitters remained on the whole test.  The magnetic and electric fields are mapped using single wire and point charge models.  The excel file is open to the public.  The forces are plotted along the face path of the diamond.  The resulting motion is described.  The effect of sliding or rotating the emitters is explored.  Talk highlights are given.  These include: the impact of pressurizing, moving, shaping and forming structure within the plasma.  The relevant plasma instabilities are mentioned as well as a discussion of structure.  Finally a call for experiments is made, with a list of good reference material.   


Part 1: Experimental Work:

Overview:

       Between October 22nd and December 17th CSI did a number of web talks. Discerning the real tests from the plans was hard. Moreover, CSI did not want to give the details outright. Specific dimensions were the hardest to get. Sizes were extracted from photos and emails. But, the same parameters likely changed between individual tests. Hence, this analysis is not going to be perfect. To circumvent this, ranges are often used. This research is still in the early phases. Early on, it is important to get something that works. This allows you to troubleshoot everything else. The team has not done fusion. They have trapped electrons long-term inside model one. Long-term is subjective. The world record for a tokamak is six and a half minutes [6]. WB6 ran for less than a second [8]. Model one was a low power, low cost and simple device. Despite these limitations, it held in plasma for twenty seconds [1]. The run was limited by the cooling system. If the team had the cash, they could run much longer. Long term trapping is the direction to go in.


Experimental Setup:

      The team is testing model 1. This is a single tungsten or rhodium wire bent into a diamond shape [10]. Attached to it, is a cooling system, power supply and voltage source. This is placed inside a cylindrical vacuum chamber, about the size of a trash bin [6]. Four electron emitters sit around model one [1]. They may align with the device’s corners. There is also a Langmuir probe. The probe may be a simple wire, or a fancy tool with software. The probe is critical. It proves the concept. If everything works correctly, it should measure a negative voltage. The chamber is also connected to a pump and a gas supply. One possible chamber configuration is shown below.


We have seen this experiment before. The 2010 Khachan paper is very similar [9]. A picture of Khachans work is shown below [14]. You spray electrons from an emitter. They enter a device. You see if they can be trapped. The main difference is the trap: a diamond verse a ring structure. If CSI can detect trapping; then it validates Khachans published work.


Vacuum Chamber:

       The vacuum chamber is filled with nitrogen or helium gas [6, 22]. This is common in vacuums. Nitrogen blocks water vapor from entering the chamber [42]. Helium is used to check for leaks [42]. From here, they pump down the chamber. This is done using a turbomolecular pump [10]. It reaches pressures between 1.3 and 0.04 Pascals [22]. This is still thousands of times higher than the WB6 system [6]. There is still gas inside. This background gas, will impact performance. It can create fast moving neutral atoms. It can also be a source of unwanted of positive ions. Both can hurt performance.

Model one:

           Inside the chamber is model one. It is the most unique device in the chamber.  It is shaped like a diamond, shown below.




This is a single wire. With only one pass, a lot of current will be needed. At full power, 1,500 amps flow through this wire; creating a 1,000 gauss field at the corners [22]. This current, heats up the wire [7]. The team tried to re-snake this many times – but the heat still built up [1]. As you will see, heat is a common problem with model one. Hot wires create problems, like arching. Moreover, this problem grows as the device runs “long-term”. Tests could have been longer - if they could just keep the thing cold!



Cooling Issues:

The first version of model one was a bent copper pipe.  Coolant moved inside the pipe, while, current moved in its walls.  This failed.  The copper overheated.  It exploded.  The team wants you to know: do not use melting copper.  They switched to a tungsten or rhodium wire.  Both are very hard materials, with high melting points [12, 13].  Tungsten will be used for modeling [10].  Unfortunately, a wire does not have a cavity for coolant.  The team tried an outside ring of coolant - but this behaved poorly [1].  Finally, Model one was merely arranged to touch a chilling system [10].  Heat was conducted away.  This is a mediocre solution.  Better chillers would allow longer runs.  

Chilling System:

     The chilling system is rather elaborate. The first cooling loop uses a Fluorinert. This is a liquid, often used to cool electronics. The fluid does not conduct; lowering its negative impacts on electric conduction [1]. The fluid moves in a closed loop: from the pump, near the device, and into a heat exchanger. The exchanger moves heat into a second water and glycol loop. This flows into a giant open tank. A sketch and model of the cooling system is shown below [7]. This coolant system can pull about six kilowatts of heat from model one [5]. Estimates (using joule heating) show that this is probably more than they need.



The Fields:

      Model one is kept cold so that it can generate an electric and magnetic field. The device needs to attract, affect and trap electrons. Negative electrons are attracted to a positive object. Model one must be biased positive. The team used a transformer to put it at a positive 500 volts [1]. When everything is turned on, model one makes a web of electric and magnetic fields. These are shown below.



Electron Emitters:


        CSI examined three ways to make electrons [1]. The first is field emission. Electrons can spontaneously leave metals in a vacuum. This can happen at room temperature and may have happen inside CSI’s chamber [2]. However this can easily avoided by engineering. The effect amplifies as the temperature rises. This is known thermionic emission. If you heat the wire, more electrons will leave. CSI purposely used four heated nichrome wires to do this. Nichrome is a common emitter [3]. In addition, these wires can be part of a proper electron gun. This was CSI third method [1]. The company altered an e-gun design from the Sydney team [10]. A schematic and picture of their electron gun is shown below [14].


CSI’s design may have been as simple as: a heated wire next to a positive disc, with a hole in it. The disc focuses the electrons in a beam [4]. All the tests used at least four emitters [1]. They had a voltage placed on them. Using a transformer and a Labview program, the team could vary the emitters up to a negative 9,500 volts [23]. The combined positive model one and negative emitters - made a hill for the electrons to roll down. They fell into model one. Their flow was constant; emitters ran throughout the runs [5].


Operating Procedure:


      CSI ran experiments from January to late summer 2012 [5]. Many tests were done. These included: several geometries, various emitters and even a fusor/polywell hybrid. Tests meant several steps. First, the vacuum chamber was prepared. The chamber was filled with helium, to check for leaks. Once sealed, nitrogen was pumped in. Next, they pumped down the chamber. It reached pressures between 1.3 and 0.04 Pascals [22]. The next step is turning on the coolant system. This makes the chamber, low pressure and cool. Next, the voltages are applied. From here the test can start. The device and emitters are turned on. Runs typically lasted for 35 seconds [1]. CSI states that for 20 of those seconds, it measured a steady, constant voltage drop.


Experimental Results:

The company ran three tests.  In each test, the drive voltage was changed.  This is the drop between the emitters and device.  The device was always at a positive 500 volts; but the four emitters were set at lower voltages.  Each time, the probe measured a negative voltage in the center. This meant that electrons were present.  Gausses’ law gives a rough estimate of how many electrons (multiply by 5.5E7). 


The company would not provide results for the third test (1,500 volts).  These results prompt some questions.  First, why were the emitters left on throughout the test?  How does the company know it measured trapping – and not electrons merely streaming past?  There are many good practices that need to be followed here, such as control tests and checking equipment.  We must assume CSI abides by these rules.  Despite these questions, the work is commendable – it took years to get this data.  

Part 2: Modeling

Device Geometry:

      The magnetic and electric fields need to be modeled. They create a Lorentz force which guides the electrons in. CSI gives some of specifications of model one. It lists the plasma volume as 1.4E-3 cubic meters [5]. If this is the total volume, than model one is fourteen centimeters per side. We take the current to be 1,500 amps with a 1,000 gauss field at the corners. The electrons modelled as flying into the face of the diamond. The emitters are 30 centimeters from device center. This is the geometry to simulate.



Simple Models:

       The best kind of models, are always the simplest. The fields can be estimated using material from high school physics. For instance, the magnetic field made by a straight wire - can be used to map out the B-field [15]. The device is twelve straight wires in a diamond. This was used in a previous post to look at how the magnetic fields change with geometry [11]. That analysis yielded three rules. First, as the diamond gets bigger, its’ field strength drops exponentially. Second, the field rises linearly with higher current. Finally, the highest fields were at the device corners. This model is shown below. The key length to find is the distance to the wire, as the electrons fly in. The magnetic force is a cross product between the velocity and the magnetic vector. This creates problems. The magnetic force is very sensitive to the angle between the vectors. The force can vary as much as ten thousand fold! For this work, an angle of less than 5 degrees is assumed.


Electric Field:

        The electron starts at the emitter. This emitter is biased as negative 500 volts [10]. The electron is repelled from this; and moves towards the positive device. We do not know how far away the emitter was placed – so a range was picked. This was 30 to 50 centimeters; center to center. The electric field was modeled using simple point charges [16]. The three wires were represented by three points. These are like piles of positive charge. The emitter became a heap of negative charge, at one point. This is shown below. A key parameter was finding the amounts of charge at each point. To do this, it was assumed that halfway between the wires and emitter – there was no electric field. This provided a nice check. From here, it was easy to find the amount of charge.


Electron Worldview:

       These models were put into excel. The sheet can be downloaded here. The velocity is modeled using newtons’ equations of motion. There are several points of interest along this path.



        The first is next to the emitter. The electron starts here with no velocity. But immediately, it feels a strong repelling force. This is because it is next to a large negative charge. It speeds away, building up velocity. Very soon, the magnetic force overtakes the electric force. When this happens, the electron starts to corkscrew. It spirals along the magnetic field line [17]. It reaches a halfway point between the device and emitters. Here, the electric field is zero: the device and emitter fields cancel out. The electron is now being tugged towards the positive device. Despite this, the magnetic force still dominates the electric. It peaks as the electron pass through the face of the diamond. The electrons enter a magnetic “cup”. Ideally, they oscillate around inside this field. These forces are plotted below. To truly measure trapping – the probe must detect them after the emitters are off. This raises questions about the CSI test. The four emitters were on the whole time. Did the probe merely see electrons as they streamed past - or did it see trapped electrons?


Electron Motion:

      We know how electrons move under such forces [17]. When the electric force dominates; particles move in a straight line. When the magnetic force dominates; the electrons spiral. As the magnetic field rises, electrons spin in a tighter corkscrew. The stronger force should prevail. This is critical inside model one. The negative electron is surrounded by positive wires. The magnetic must overpower the electric field; otherwise the electron would hit the wires. This would drive up conduction losses. It would kill trapping. Hence, the particles should follow the B-fields inside model one. An example of what this motion might look like is shown below.

The motion of a beam is wildly different than one electron.  Electrons in a beam interact.  They ricochet off one another, vary the surround fields and shift the forces. Hence, beams are modeled differently than one electron [19, 20, 21]. Also, the fields change once electrons fill the device center.

Changing The Geometry:

      Excel shows what happens as the geometry changes. For instance, what happens when the emitters are moved backwards? If the electron has farther to travel, it has more time to accelerate. This raises its velocity. That creates a stronger magnetic force. Previous posts have shown the same idea [18]. The electric force also rises, but for different reasons. We assume that there is a zero voltage - halfway between the emitter and device. This underpins the model. If the two are farther apart, it takes more charge to get zero. Excel creates stronger point charges, as the emitter moves away. This creates stronger electric forces. This is shown below.
There was no time to look at the other path into model one. Here, the particles enter through the corners of the diamond. They reach the device sooner, and pass through the biggest magnetic field possible. This occurs at the tiny gap between the two wires. After this, they see a very sharp decline in the field. The sharper field should improve containment [5]. Based on this knowledge, a rough sketch of the force plots is shown below. Between these two paths, there is a sense of the fields inside model one.




Part 3: Talk Highlights

October Talk:

           The company’s first talk: physics of IEC devices will not clarify their experiments, like this post. The details listed above were from emails with CSI. The talks cover the issues they have found, after doing the tests. Lets’ assume the tests worked - and CSI can trap electrons. The next question is how to confine them. Here, the tokamak world can help. Plasma has been confined magnetically for many decades. There is plenty of literature that CSI can use.

Talk Highlights:

            The rule for magnetic confinement is this: as the machine gets bigger, the confinement gets worse. Nobody understands why this is (in all cases) [5]. But, we have some tips to avoid problems. Devlin mentions four:

1. Pressurize It.  The plasma is held in by a magnetic field.  The higher the field, the better the hold.  This is the approach Lockheed martin is taking [41].

2. Keep It Moving.  It helps to keep plasma moving.  Especially on the outside edge.  The easiest way to do this is to spin it.  You can do this by applying a revolving current.  Once, a team stabilized a tiny amount of plasma for weeks this way [24].  Both tokamaks and stellarators spin material for stability [38].  People have also tried collapsing or converging it [40].  You can also oscillate it in a wave, as LANL tried a few years ago [39].

3. Make Structure.  Riders argues that if you merely had a hot blob of plasma (unstructured, thermalized, isentropic, uniform) that you cannot expect net power [29, 30, 31].  Hence, anything you do to move plasma away from a blob - helps.  This means forcing any structure, through steep fields or steep density changes inside the cloud [5].  It also means using clouds which are mainly positive or negative.

4. Shape it.  We like big plasma volumes - with small skin areas [5].  The best example is the sun.  It is a big sphere.  It has a tiny surface-area to volume ratio.  Hence, the polywell improves as it gets bigger.  It also improves if the cusps are pinched off; and the plasma balloons into a sphere [8].  

A key question is: which of these effects trumps the others? Does having a high beta number trump a high velocity? If an expert wants to weigh in here, we would appreciate it.



Structure verses Instabilities:

       There are two trends working within plasma: structure and instability. For every structure, there is normally instability there to wreck it. The growth or suppression of these is well understood. Marshall Rosenbluth was the instability king [22]. He sorted out many of the instabilities known today. CSI mentions two:


1.  Weibel instability.  When a beam enters plasma, there is a chance that it can break up into filaments [49].  This is the due to the fields that it generates during its motion.  This has been studied extensively.

2.  Diocotron instability.  When two sheets of plasma move past one another, eddies form.  This represents an energy loss mechanism.

CSI also hints at a structure within the cloud. Specifically: an edge and a core region. This is a bit controversial. Critics would argue the cloud lacks that level of detail. Supporters have opposed this. Now, we have some data. Khachans’ 2013 paper measured electron densities inside the cloud [48]. The results hint at different density in center verses the edge. CSI want these densities to be vastly different, but, so far they have only found a 5 or 10 times difference [5].

Part 4: Conclusion



“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.” - Richard Feynman



Modeling is for wimps:

No model is a substitute for data.  This could be an excel worksheet, a matlab program or a vast FORTRAN code.  This became clear - in 2012 - when NIF failed to get ignition.  Vast teams of experts used models to predict success.  Their models were flawed.  For example, excel shows that CSI has met a condition for the mirror.  Does this mean the device traps?  Hell no.  Only data can prove trapping.  The model only helps you get a sense of the physics.

Theory is also for wimps:

       Also, theory is no substitute for data. When it comes to theory; one must admit human frailty. The body of physics literature is vast and constantly growing. No one can stay abreast of all of it. There is theory work arguing against the polywell [29, 30, 31, 32]. There are also papers arguing for it [8, 34, 35]. However, none of that matters if the data turns up something unexpected. That said; here are some sources which have been helpful. Feel free to comment below. For magnetic mirrors, there are several.  Richard Post developed the mechanics of magnetic mirrors in the sixties [26]. Francis Chen and Richard Fitzpatrick have good notes on its’ effect on bulk plasmas [27, 45]. Also, Peter Catto did nice work on reflections for any ratio [28]. These mirrors have holes in them (cusps). Thomas Dolan wrote a great review of confinement in cusp geometries [36] and Harold Grad modeled the behavior of the particles that dwell inside them [42, 43, 44]. Lyman Spitzer’s book gives the rate equations for different plasma effects [37] (this text underpins Riders work). Also, Tim Thorson wrote the best explanation of fusors I have ever read [33]. Finally, William Barr was the guy nearest to direct conversion [46, 47, 25]. Each represents a part of this great scientific conversation. Our hope is, the debate continues. Our hope is, this leads to changing the world.

Work Cited:

1. "Some Questions about Your Work." Interview by Devlin Baker. Email 16 Jan. 2014: n. pag. Web. 17 Jan. 2014.

2. "Field Electron Emission." Wikipedia. Wikimedia Foundation, 22 Jan. 2014. Web. 28 Jan. 2014. .

3. "Nichrome Wire." EBay. EBay Inc, 30 Jan. 2014. Web. 28 Jan. 2014. .

4. "Electrostatic Lens." Wikipedia. Wikimedia Foundation, 21 Dec. 2013. Web. 28 Jan. 2014. .

5. Physics of IEC Devices. Perf. Devlin Baker. Convergent Scientific Inc., Oct 22, 2013. http://sproutvideo.com/videos/1c9bd8bd171be4c994

6. "ITER - the Way to New Energy." ITER - History of the Tokamak. ITER, 2012. Web. 28 Jan. 2014. .

7. "Joule Heating." Wikipedia. Wikimedia Foundation, 13 Jan. 2014. Web. 28 Jan. 2014. .

8. Bussard, Robert W. "The Advent of Clean Nuclear Fusion: Superperformance Space Power and Propulsion." 57th International Astronautical Congress (2006). Web.

9. Carr, Matthew, and Joe Khachan. "The Dependence of the Virtual Cathode in a Polywell™ on the Coil Current and Background Gas Pressure." Physics of Plasmas 17.5 (2010). American Institute of Physics, 24 May 2010. Web.

10. "Some Questions about Your Work." Interview by Devlin Baker. Email 20 Jan. 2014: n. pag. Print.

11. "The Serious Need For Data." The Polywell Blog. Blogspot, 6 Jan. 2014. Web. 28 Jan. 2014. .

12. "Tungsten." Wikipedia. Wikimedia Foundation, 19 Jan. 2014. Web. 28 Jan. 2014. .

13. "Rhodium." Wikipedia. Wikimedia Foundation, 16 Jan. 2014. Web. 27 Jan. 2014. .

14. Cornish, Scott, and Joe Khachan. "The Use of Microchannels as an Electron Source for the Polywell." 2011 US-Japan IEC Workshop (2011): n. pag. Poster Presentation. Web. Oct. 2011. .

15. Nave, R. "Magnetic Field of Current." Magnetic Fields of Currents. University of Georgia - Physics Department, n.d. Web. 27 Jan. 2014. .

16. Nave, R. "Electric Field of Point Charge." Electric Field of Point Charge. University of Georgia - Physics Department, n.d. Web. 28 Jan. 2014. .

17. "Electron Cyclotron Resonance." Wikipedia. Wikimedia Foundation, 19 Jan. 2014. Web. 28 Jan. 2014. .

18. "Taking A Stab At Simulation." The Polywell Blog. Blogspot, 6 Feb. 2013. Web. 28 Jan. 2014. .

19. Down, Adrian. "Beam Instability." Duke Texts (n.d.): 1-5. Web. 9 Apr. 2007. .

20. Bharuthram, R. "Electron-acoustic Instability Driven by a Field-aligned Hot Electron Beam." Journal of Plasma Physics 46.01 (1991): 1. Print.

21. Robinson, Guy. "9.3.3 Electron Beam Plasma Instability." 9.3.3 Electron Beam Plasma Instability. Parallel Computing, 1 Mar. 1995. Web. 29 Jan. 2014. .

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23. "Response to Comments." Interview by Devlin Baker. Email 29 Jan. 2014: n. pag. Print.

24. X.-P. Huang. "Steady-State Confinement of Non-neutral Plasmas by Rotating Electric Fields." PHYSICAL REVIEW LETTERS 78.5 (1997): 875-78. Print.

25. Rosenbluth, Marshall. "Generic Issues for Direct Conversion of Fusion Energy from Alternative Fuels." Plasma Physics and Controlled Fusion 36 (1994): 1255-268. Print. 79.

26. "Mirror Systems: Fuel Cycles, loss reduction and energy recovery" by Richard F. Post, BNES Nuclear fusion reactor conferences at Culham laboratory, September 1969.

27. Fitzpatrick, Richard. "Magnetic Mirrors." Magnetic Mirrors. N.p., 31 Mar. 2011. Web. 06 Sept. 2012. http://farside.ph.utexas.edu/teaching/plasma/lectures/node21.html

28. Catto, Peter J., and Xing Zhong Li. "14. Particle Loss Rates from Electrostatic Wells of Arbitary Mirror Ratios." Physics of Fluids 28.1 (1985): 352-57. Web.

29. “Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium” by Dr. Todd Rider, MIT, 1994.

30. Nevins, W. M. "Can Inertial Electrostatic Confinement Work beyond the Ion–ion Collisional Time Scale?" Physics of Plasmas 2.10 (1995): 3804. Print.

31. Rider, Todd H. "A General Critique of Inertial-electrostatic Confinement Fusion Systems." Physics of Plasmas 2.6 (1995): 1853. Print.

32. “Is There a Better Route to Fusion?” April 1rst 2005. Presentation.

33. Thorson, Timothy A. Ion Flow and Fusion Reactivity Characterization of a Spherically Convergent Ion Focus. Thesis. Wisconsin Madison, 1996. Madison: University of Wisconsin, 1996. Print.

34. Krall, Nicholas A., M. Coleman, and K. Maffei. "Forming and Maintaining a Potential Well in a Quasi Spherical Magnetic Trap." Physics of Plasma. American Physical Society, 6 Oct. 1995. Web

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37. Spitzer, Lyman. Physics of Fully Ionized Gases. New York: Interscience, 1962. Print.

38. Maarten De Bock. "Understanding and Controlling Plasma Rotation in Tokamaks." PhD Thesis: Technische Universiteit Eindhoven January 22 (2007): n. pag. Print.

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Monday, January 6, 2014

The Serious Need For Data


 The Serious Need For Data

Introduction:

            For many years, this blog has aspired to give accurate information clearly.  It has not been perfect.  But, it has been fun.  Posts have answered key questions, explained obscure references and offered context.  The quality is high.  Some posts took months to compose.  You should read them. 

            However, we are reaching the limits of mere theory.  We need to build it.  We need to test it.  The Polywell has not failed or worked - yet.  We just don’t know.  We need a body of data - from a big machine.  The Navy could save us some hassle by publishing.

            The Polywell is a real plasma system.  It will face real problems; like energy loss, power balance, instabilities and control issues.  No one knows if these problems can kill the polywell.  We have to try it. 

News:

            Events around the polywell continued to move forward, in the last half of 2013.  In June, NBC news spoke with Taylor Wilson about his homemade fusion reactor [30].  His fusor is similar to a polywell.  NBC’s Brian Williams call Taylor: “incredible”.  This press is exciting.  It should help fund fusion research.  Also that month, the first polywell doctoral thesis was published [28].  At the core of this work, was data of trapped electrons inside a polywell.  The work is strong; but it is limited to small, low power devices. 

            In October, the University of Sydney published again [29].  The team simulated electrons inside the polywell.  The group wanted to know how long electrons would be confined – and where they were.  Variables were then changed: the current, ring radius, and starting particle energy.  Simulations revealed that the devices’ behavior improved as it got bigger [29].  But, simulations are still not data.  This work was presented at the 15th annual IEC conference in Kyoto, Japan [33].  In October, a polywell startup: Convergent Scientific Incorporated did its first investor call.  They claim to have measured electron trapping, built a fusor/polywell hybrid and have numerical simulations running.  This post examines some of these claims.  The company wants to raise a million dollars for non-breakeven devices. 

            In November, the Polywell was included at the MIT co-lab conference [34].  Thanks to Dennis Peterson for making this happen.  The following week, polywell work was presented at the 2013 APS conference in Denver, Colorado [35].   Jeff Kollasch - a new graduate student at Wisconsin - presented Vlasov-Poisson simulations of the polywells.  Hopefully - this work will become another science publication. Also in November, a second polywell novel by William Flint: “To fly from folly: saving the polywell” went live on amazon [36].  In December, Dr. George Miley published the first IEC textbook [33].  This is a milestone - the field has its first textbook!  Miley has been busy.  His autobiography was also published in June [32].  The book documents his life and over five decades of fusion research.

            In addition, two organizations have joined polywell/fusor space.  The first is the North West Nuclear Consortium.  Carl Greninger - a manager at Microsoft; has a created a high school physics class on fusors [37].  A group of 18 students and 4 instructors meet every Friday to do real nuclear fusion at Mr. Greningers’ home [38].  This has generated a lot of press and awards at science fairs.  The other is Radiant Matter Research.  This pair of Dutch students has the equipment and is on the path to building a polywell.  This activity is exciting; but it is no substitute for real hard data.

Executive Summary:

      This post examines a new design from Convergent Scientific Incorporated. The case for an open effort is made - by examining the result of a closed effort. CSI was founded in 2010, in Washington State. Presentations in the fall of 2013 offered some insight into their work. CSI is simultaneously doing CUDA simulations and running multiple experiments. For income, their goal is to make and sell medical isotopes. They have built an octahedron confinement grid: model one. Good magnetic design is discussed including: field uniformity, continuousness, symmetry, low curvature and non-intersections. The strengths and weakness of a “single-turn” cage are also mentioned. The geometry and magnetic field is examined at the corners, center and cage surface. A device - 14 cm a side with 1,500 amps and a 1,000 Gauss field at the corners – is assumed to be model one. Analysis reveals that the field strength falls as size increases, the field rises linearly with current and the corner field is sensitive to the shape of the bends. Finally, an ideal geometry for a uniform field is mentioned.

A History Lesson: 

         In 1999, a man named Alex Klein got an idea. His idea was to internally reflect ion beams [13]. The reflection was based off of magnetic mirror work from Israel [10]. Beams bounce around inside, collide and fuse. Klein worked on his idea for 10 years – getting a PhD, publishing and pitching it to a venture capitalist [11]. He saw this idea as having great value - so he strove to hide it from the public. After raising 3 million dollars, building a company and his reactor - it failed. The problem [11] was: “…the ions slowed down in the mirrors, wasting time there, leading to high losses…” Unfortunately few people knew about this effort. When the company folded, no one was trying to duplicate Kleins’ work. Worst still: some people have purposed to repeat his idea. In fact beam schemes had already been patented in the eighties [18, 19, 20].

A Call for Openness:

            Fusion is hard.  No one has a solution for it yet.  A common mistake people make, is thinking that they have the solution.  They often try and hide it, patent it or conceal it.  We argue: that this is a mistake.  After working for ten years on a solution - only to hit a brick wall – if the work has not been made public, then it has been wasted.  It is critical that these efforts are open.  Only an open effort can be taken seriously by the public.  Openness means explaining ideas, problems and failures.  It means admitting if this fails.  It also means educating a supporting community.  It limits repeating bad ideas and helps create a market.   Being open means explaining everything in simple English and correcting mistakes when they are found.  Hiding behind an NDA, IP, jargon and obscure references is not being open.
 
Convergent Scientific:

             Convergent Scientific was founded in 2010, in Washington State.  The company has two physicists behind it: Devlin Baker and Dr. Joel Rogers.  Each has deep roots in this field.  Devlin started out building his own fusors in 2001 [1].  Dr. Rogers has been studying nuclear physics at a national laboratory his entire career [1].  Joel has presented at every single IEC conference since 2008 and was in contact with Dr. Bussard while he was still alive [2, 3, 4].  



Devlin seems have done most of the experiments, while across the border, Joel is assisting from Vancouver [7]. The tests mainly happened in 2012. Now, the focus has shifted to simulations [6]. Unfortunately, CSI has yet to get a patent.  Convergent has been in a legal fight with the U.S. Patent Office since 2008 [7, 5].  The paperwork is ugly.  Dr. Rogers tried to patent a power plant design with only simulations as supporting evidence.  Naturally, the examiners do not believe him.  One examiner explained [8]: “…Energy production though fusion reactions have not been achieved to date, let alone at the time of filing, despite a world-wide fusion energy research program…”  CSI needs data, to get a patent. 

Investor Call:


In the fall of 2013, Convergent Scientific did its first investor call.  This consisted of web presentations posted online.  These are: “The physics of IEC devices”, “Numerical simulations of IEC plasmas” and “Commercial applications of IEC devices.”  These talks are intense.  Mr. Baker had to cover a great deal of material in a very short amount of time.  Overall, the presentations felt jerky.  He spends plenty of time on boring subjects, but breezes through topics of interest.  It is also codified in technical language that is hard to follow.  It appears the company is following a two pronged strategy: building machines and simulating polywells.  They have assembled a serious lab space.



Field Redesign:

            People have long wondered about redesigning the containing magnetic field.  They argue that the magnetic mirror effect is independent of direction.  The mirror will reflect particles when they move into denser fields [10].  This happens only under certain conditions; but it will happen regardless of if the field points one way, or the other [23].  Redesigning has been a source of much speculation.  At last check, over 850 posts online debated different designs [15, 9].  Endolith, an electrical engineer, has argued for the new design of an 8-sided spherical cage [16].  Alternative designs have even been patented - going back to the 1980’s [18, 19, 20].  Some examples are shown below.


  
Keys to “Good” Fields:

In reality, many of these designs will fail.  They look good on paper, but in reality will fail to hold in particles.  Failure hinges on the structure of magnetic fields inside.  We do not understand everything about magnetic containment.  However, there are some principals that can be used to gauge good designs:

1.    Uniform Strength:  Electrons in the center should see uniform field strength in all directions.  This is like water held in a pool.  The walls of the pool must be the same height.  This was the driving force behind WB6– the ring location forced the corners and the sides to have equal field strength [24]. 

2.    Continuous Fields:  None of the fields must run into a metal surface.  This drives up conduction losses and was the reason for HEPS failure. 

3.    Not Intersecting:  Fields which stream particles past one another - lead to counter-streaming, two stream and sheet-sheet instabilities [27].

4.    Low Curvature: Bent fields, fling plasma outward, leading to conduction losses [26].  This effect worsens with tighter curvature. 

5.   Symmetry:  Symmetry has been true throughout most of magnetic confinements’ history.  In polywells, this means that the same fields cannot butt up against each other.  An inward pointed field cannot be next to another inward pointed field.  This is shown best with two simple geometries: six rings in a cube and an eight sided diamond.  See blow.  Notice that no red surfaces meet.  Each design can be expanded by adding more rings or loops.


You can see why the Tokamak is so celebrated - its' design follows these principals.  Ideally, we want another magnetic configuration that works.  Bussard first patented that diamond shape, in 1989 [21, 22].  The document show a prominent figure of an octahedron.  CSI has built this. They say they have run current through it and, trapped electrons within it [17]. 

Model 1:

          This design is known as model 1.  It is very odd looking, when compared with the ring structure.  First, it is made only by one wire; it is a “single turn” magnet.  The change has trade offs.  It hurts the device, because it requires hundreds of times more current to get the same fields.  But, it helps the device, because it reduces the amount of extra surfaces (struts, connectors, feed lines) in the center.  The wire bends are notable.  It is likely - that the most interesting and problematic physics occurs there.


CSI has said that several experiments were attempted.  These included several materials for the wire, such as copper, tungsten and Rhodium[6].  They had problems excess heat, so some designs included cooling tubes inside [14].  It is also possible that geometries beyond the octahedron were attempted.  In addition, a polywell/fusor hybrid was also tested.  The company will not disclose the exact dimensions of model 1.  However, from the parameters provided in their presentations [6] and on their website [23], we can discern a range of sizes.

Basic Math:

            You can define the geometry with four variables.  The first is the length of one side of the diamond.  CSI lists the plasma as having a volume of 1.4E-3 cubic meters [23].  If this is the total volume inside the cage; then model one is fourteen centimeters per side.  Alternatively, they give an average confinement radius of 16 centimeters [23]. If this is the average distance from cage to device center then model one is twenty-six centimeters per side.  The next two variables describe the bend.  The first is the length of wire involved in the bend.  The second is the smallest gap between two bent wires.  It is this gap which drives the magnetic field at the corner.  The last parameter is the thickness of the copper wire.  With these four variables, we can completely define the geometry.


With the geometry defined, analyzing the magnetic field around the diamond is easy.  Analysis is done by applying the Biot-Savart law to different locations [25].  The strongest field occurs at the corners.  At the corner, two wires come very close together.  This is similar to the joint in normal polywells.  CSI gives the strongest field as 1,000 Gauss, at 1,500 amps [22].  Using this, the bend variables can be found.  The next location is device center.  The field here is generated by twelve wires.  The weakest field is located on the surface of the diamond.  The field here is created by three wires.  A comparison of these three locations is plotted below.



Field Design:

            These equations say plenty about how to design the perfect field.  A big issue with the diamond grid is that it is a single wire.  It may be possible to snake many wires together inside the grid; but if it remains “single turn”, low field strength should be a concern.  These equations say much about getting around that problem.  First, as the diamond gets bigger, the field strength drops exponentially.  Next, the field strength rises linearly with current.  Finally, the highest field is at the corners - and here, it is very sensitive to the shape of the bends.   The corner field varies wildly.  This gives designers a lot of flexibility.  Their goal could be to get the surface and corner fields equal.  This was the principal used in designing WB6 and may significantly help containment.  The optimum geometry for this is when the face distance is 1.5 times the corner distance.  This is design is shown below.  Finally, by assuming a current direction - we can quickly determine the vector field.  This is also shown below.



Work Cited:

1.            Baker, Devlin. "Convergent Scientific Inc." Https://gust.com/c/convsci. Gust LLC, Dec. 2013. Web. 4 Jan. 2014.

2.            Rusi, Toni. "Fusion with Space Related Aspects Thread." Fusion with Space Related Aspects Thread. NASA, 4 June 2007. Web. 04 Jan. 2014.

3.            Rogers, Joel. "IEC2008 10th US-Japan Workshop on Inertial Electrostatic Confinement Fusion - Uji, Kyoto." IEC2008 10th US-Japan Workshop on Inertial Electrostatic Confinement Fusion - Uji, Kyoto. Kyoto University, 9 Dec. 2008. Web. 04 Jan. 2014.

4.       Rogers, Joel. "Steady State Polywell Fusion Device Designed Using 2D Simulation." The 10th Annual US-Japan IEC Conference. Kyoto University, 4 Dec. 2008. Web. 04 Jan. 2014. .

5. Rogers, Joel. Application: Modular Apparatus for Confining Plasma. Patent 2010/0284501. N.d. Print.

6. Physics of IEC Devices. Perf. Devlin Baker. Convergent Scientific Inc., Oct 22, 2013. http://sproutvideo.com/videos/1c9bd8bd171be4c994

7. Pair database. http://portal.uspto.gov/pair/PublicPair Rogers, Joel. Application: 12/141,644 Modular Apparatus For Confining A Plasma. Patent 2010/0284501.

8. United States of America. US Department of Commerce. Patent Office. Final Rejection 12/141,644. Page 6. By Johannes P. Mondt. Washing DC: USPO, 2013. Print.

9. "Talk-Polywell.org." Magrid Configuration Brainstorming. Talk Polywell, 9 Nov. 2007. Web. 04 Jan. 2014.

10. Allen, Ronald J. "A Demonstration of the Magnetic Mirror Effect." American Journal of Physics 30.12 (1962): 867. Print. http://www.beamfusion.org/technology/index.html

11. "Discussion MIX and Marble." Interview of Dr. Alex Klein. 30 Apr. 2013. Interview.

12. “MARBLE-1 the Multiple Ambipolar Recirculating Beam Line Experiment” Alex Klein Poster presentation, 2011 US-Japan IEC conference.

13. Devlin baker, private communication, 1-2-2014

14. "Talk-Polywell.org." Magrid Configuration Brainstorming. Talk Polywell, 9 Nov. 2007. Web. 04 Jan. 2014. .

15. Endolith. "Would an Octahedral Magnet Work as a Magnetic Bottle?" Plasma Physics. Stack Exchange, 20 Aug. 2013. Web. 04 Jan. 2014. .

16. Numerical Simulations of IEC Plasmas. Performed: Devlin Baker. Convergent Scientific Inc. Nov 5, 2013.

17. Converging Beam Fusion System. William Jarnagin, assignee. Patent 4202725. 13 May 1980. Print.

18. Apparatus for Colliding Nuclear Particle Beams Using Ring Magnets. John P Blewett, assignee. Patent 5034183. 23 May 1989. Print.

19. Method for Forming Magnetic Fields. Stephen A Whitlock, assignee. Patent 5517083. 21 Dec. 1996. Print.

20. Should Google Go Nuclear?" R.W. Bussard. Google Videos. 9 Nov. 2006. 20 Feb. 2009.

21. Method and Apparatus for Controlling Charged Particles. Robert Bussard, assignee. Patent 4826646. 29 Oct. 1989. Print.

22. Blair, Clarke. CSI Overview. Bellingham Washington: Convergent Scientific, 2013. Print.

23. "Mirror Systems: Fuel Cycles, loss reduction and energy recovery" by Richard F. Post, BNES Nuclear fusion reactor conferences at Culham laboratory, September 1969.

24. "The Polywell Blog." The Physical Basis for the Polywell. The Polywell Blog, 30 July 2012. Web. 04 Jan. 2014. .

25. "Biot–Savart Law." Wikipedia. Wikimedia Foundation, 01 Mar. 2014. Web. 05 Jan. 2014. .

26. L. I. Rudakov and R. Z. Sagdeev, DAN SSSR 138, 581 (1961), Soviet Phys. Doklady 6, 415 (1961). Nuclear Fusion, Supplement 2, 1962, p. 481.

27. Bittencourt, J. A. Fundamentals of Plasma Physics, Third Ed. 2004 Springer-Verlag, New York.

28. Carr, Matthew. Electrostatic Potential Measurements and Point Cusp Theories Applied to a Low Beta Polywell Fusion Device. Diss. University of Sydney, 2013. Sydney: University of Sydney, 2013. Print.

29. Gummersall, David. "Scaling Law of Electron Confinement in a Zero Beta Polywell Device. “Physics of Plasmas 20.10 (2013): 102701-02701-7. Print.

30. Williams, Brian. "19-year-old Hopes to Revolutionize Nuclear Power." NBCNews.com. NBC/Universal, 14 June 2013. Web. 05 Jan. 2014. .

31. Miley, George H. Life at the Center of the Energy Crisis: A Technologist's Search for a Black Swan. Washing DC: N.P., 2013. Print.

32. Miley, George. Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications. Illinois: N.P., 2013. Print.

33. “Towards a virtual cathode for inertial electrostatic confinement.” Joe Khachan, 15th annual 2013 US-Japan IEC workshop, Kyoto University, October 6, 2013.

34. Petersen, Dennis. 2013 MIT Co-Lab Conference Proposals. 2 Nov. 2013. It's the 21st Century. Where's My Fusion Reactor? Massachusetts Institution of Technology, Boston.

35. Kollasch, Jeff. Vlasov-Poisson Calculations of Electron Confinement times in Polywell Devices Using a Steady-state Particle-in-cell Method. Proc. of 2013 APS Division of Plasma Physics Conference, Marriott Hotel, Denver. Denver: APS, 2013. Print.

36. Flint, William. To Fly from Folly: Saving the Polywell. San Francisco: Amazon, 2013. Online.

37. "Mr. Fusion Helps Students Build a Nuclear Reactor." Mr. Fusion Helps Students Build a Nuclear Reactor. Microsoft Inc., 17 Aug. 2011. Web. 05 Jan. 2014. .

38. "Personal Interview." Interview of Carl Greninger. 17 Dec. 2013.