# Polywell

The polywell is a type of nuclear fusion reactor that uses an electric field to heat ions to fusion conditions. It is closely related to the magnetic mirror, the fusor, the biconic cusp and the high beta fusion reactor. A set of electromagnets generates a magnetic field which traps electrons. This creates a negative voltage, which attracts positive ions. As the ions accelerate towards the negative center, their kinetic energy rises. If the ions collide in the center, they can fuse.

The polywell is one of many devices, which use an electric field to heat ions to fusion conditions.[1] This branch of fusion research is known as Inertial electrostatic confinement. The polywell was developed by Robert Bussard, as an improvement over the fusor. His company, EMC2, Inc., developed the initial devices for the U.S. Navy.

## Mechanism

### Fusor

Main article: Fusor
Farnsworth–Hirsch fusor during operation in so called "star mode" characterized by "rays" of glowing plasma which appear to emanate from the gaps in the inner grid.

A Farnsworth-Hirsch fusor consists of two wire cages, one inside the other. These are often referred to as grids. This structure is placed inside a vacuum chamber. The outer cage is charged positively against the inner cage. Nuclei are injected as ions into the system. The most common fuel used is ionized deuterium gas. Because the ions are positive they fly towards the negative inner cage. If they miss the inner cage, they will fly right through the center of the device at high speeds. They can fly out the other side of the inner cage. As the ions move outward, they feel a Coulomb force which directs them back towards the center. Over time, a core of ionized gas can form inside the inner cage. They continue to pass back and forth through the core until they strike either the grid or another nucleus. Most strikes with other nuclei do not result in fusion, but occasionally the strikes are sufficiently energetic that fusion results. Grid strikes raise the temperature of the grid and lower the energy of the plasma.

In fusors, the potential well is made with a wire cage. Because most of the ions fall into the cage, fusors suffer from high conduction losses. Hence, no fusor has ever come close to break-even energy output.

This is an illustration of the basic mechanism of fusion in fusors. (1) The fusor contains two concentric wire cages. The cathode is inside the anode. (2) Positive ions are attracted to the inner cathode. They fall down the voltage drop. The electric field does work on the ions heating them to fusion conditions. (3) The ions miss the inner cage. (4) The ions collide in the center and may fuse.[2][3]

### Polywell

A plot of the magnetic field generated by the MaGrid inside a polywell. The null point is marked in red in the center.

The problem with the fusor is that the inner wire cage conducts away too much energy and mass. The solution, suggested by Robert Bussard and Oleg Lavrentiev,[4] was to replace the negative cage with a "virtual cathode" made of a cloud of electrons.

A polywell consists of several parts:[5]

• A vacuum chamber
• Inside the chamber, a set of positively charged electromagnet coils are arranged in a polyhedron called the MaGrid. The simplest MaGrid and the most studied so far is the truncated cube, composed of six ring-shaped coils arranged like the six faces of a cube. The six magnetic poles are pointing in the same direction toward the center. The magnetic field vanishes at the center by symmetry, creating a null point.
• Electron guns facing ring axis. Once inside the MaGrid, the electrons are confined by the magnetic fields. Those gaining enough energy manage to escape through the magnetic cusps, but are retained by the electric field and tend to slow down and return inside the MaGrid along the cusps, away from the grid, avoiding surface contact and losses. Most of electrons are trapped in the middle of the device. The electrons act as a virtual cathode, a negative electric potential well attracting the positive ions.
• Gas puffers at corner. The cold gas puffed inside the MaGrid ionizes when it reaches the electron cloud. Ions fall down the potential well, building up speed, slamming together and fusing in the center. Ions are electrostatically confined so densely that they increase the fusion rate, releasing more energy.

The magnetic energy density required to confine electrons is far smaller than that required to directly confine ions, as is done in other fusion projects such as ITER.[6][7][8]

## Behavior

This is an illustration of single electron motion inside the polywell. It is based on figures from "Low beta confinement in a polywell modeled with conventional point cusp theories" but is not an exact copy.

### Magnetic mirror and cusp confinement

Almost all simulations and experiments with polywells involved low-beta plasma regimes (where β < 1).[9] In such configurations, the plasma pressure is weak compared to the magnetic pressure. The electron recirculation and losses occur through the magnetic cusps. The electron cloud in the center is confined by cusp confinement, as an improvement over the simpler magnetic mirror confinement in biconic cusp experiments.[10]

The biconic cusp consists of two opposed ring-shaped electromagnetic coils, spaced apart the diameter of the ring. The losses in this mirror device come from two point cusps, each located at the center of the rings; and one linear equatorial cusp between the rings.[11]

The truncated cube polywell is an improvement over this design because it moves the magnets closer together, thus narrowing the problematic line cusps, while still preserving the internal volume of the reactor. The MaGrid has six point cusps, each located in the middle of the rings; and two highly modified line cusps, linking the eight corner cusps located at cube vertices. The key is that these two line cusps are much narrower than the single line cusp in the traditional magnetic mirror machines, so the net losses are less. The two line cusps losses are similar to or lower than the six face-centered point cusps.[12]

### Wiffle-Ball confinement

In 1955, Harold Grad theorized that a high-beta configuration coupled with a cusped magnetic field would dramatically improve plasma confinement.[13] Following this idea, Bussard repeatedly claimed that at β = 1 the central electron cloud would become diamagnetic and would push the magnetic field lines back, out from the center; almost closing the cusps through which electrons can escape, increasing the number of electrons being trapped inside.

WiffleBall confinement in a Polywell: magnetic field lines are expelled and cusps narrowed inside MaGrid due to the high-beta diamagnetic cloud of electrons in the center.

Cusped confinement was explored theoretically [14] and experimentally.[15] However, most cusped experiments failed and disappeared from national programs by 1980. Bussard later called this type of confinement the Wiffle-Ball. This analogy was used to describe electron trapping inside the field. Marbles can be trapped inside a Wiffle ball, a hollow, perforated sphere; if marbles are put inside, they can roll and sometimes escape through the holes in the sphere. The magnetic topology of a high-beta polywell acts similarly with electrons.

Evolution of magnetic topology inside a Polywell from magnetic mirror to WiffleBall confinement. B = constant and I = variable.

For many decades, cusped confinement never behaved experimentally as was predicted. Sharply bent fields were even used by Lawrence Livermore National Laboratory in a series of magnetic mirror machines from the late sixties to mid eighties. After investing hundreds of millions into the program, the machines still leaked plasma at the field ends. Many scientists shifted focus onto looping the fields making the tokamak. it was thought the cusped confinement effect did not even exist. Until June 2014, when EMC2 published a preprint[16] provide strong evidence that the effect is real.

According to Bussard, typical cusp leakage rate is such that an electron makes 5 to 8 passes before escaping through a cusp in a standard mirror confinement biconic cusp; 10 to 60 passes in a polywell under mirror confinement (at low-beta) that he called cusp confinement; and several thousand passes in Wiffle-Ball confinement (high Beta).[17][18]

In February 2013, Lockheed Martin Skunk Works announced a new compact fusion machine, the high beta fusion reactor, closely related to the biconic cusp and the polywell, and working at β = 1.[19]

### Particles motion

Inside the MaGrid, single electrons travel straight through the null point, due to their infinite gyroradius in regions of no magnetic field. Next, as they head towards the MaGrid, they experience a Lorentz force which causes them to corkscrew tighter and tighter along the denser magnetic field lines.[9][20] Their gyroradius shrinks and when they hit a dense magnetic field they can be reflected using the magnetic mirror effect.[21][22][23] Electron trapping has been measured in polywells with Langmuir probes.[8][24][25]

A visualization of the electron flow in a polywell has been made in 3D simulations by Indrek Mare.[26]

The polywell attempts to confine the ions and electrons through two different means, borrowed from fusors and magnetic mirrors. The electrons are easier to confine magnetically because they have so much less mass than the ions.[27] The machine confines ions using an electric field in the same way a fusor confines the ions: in the polywell, the ions are attracted to the negative cloud in the center. In the fusor, they are attracted to a negative wire cage in the center.

### Electron recirculation and thermalization

The space between the MaGrid and the vacuum chamber must be sufficient for the electron recirculation through all cusps of the machine, so that cusp electron flow is not a loss mechanism to structures.[28][29]

According to Bussard, the plasma is nonthermal in the sense that it does not reach Maxwellian thermalization statistics; and not that ions and electrons have different average temperatures. Questions have been raised about the ability of the polywell to maintain a quasi-monoenergetic energy distributions among the ion and electron populations, which are driven by the continuous injection of new electrons in order to recover from their loss to structures, and because an excess of electrons is needed to maintain the negative potential well.[5]

If the electrons lifetime is too long in the polywell, electrons could become thermalized, and develop high energy loss distributions. But this has been proven not to be the case, because the potential wells for the ions and the electrons are in opposite directions, so the Coulomb collisions varies so greatly across the system:

• at the edge, ions are slow whereas electrons are fast with a small Coulomb cross-section;
• at the center, ions are fast whereas electrons are slow with a high cross-section, but they occupy a small volume for a short fractional time of their transit life in the system.

This variation is sufficient to prevent energy spreading in the electron population before the electrons are lost by collisions with walls. Similarly, for ion-ion and electron-ion collisions before ions can fuse vary so greatly across the system that fusion reaction rates dominate the tendency to energy exchange and spreading.

Since the electrons are slower in the center where fusion reactions occur, the Bremsstrahlung is less in this core region. This is why Bremsstrahlung may be less that predicted by Rider.[30] As of 2014, whether the electrons are thermalized and the plasma is thermal or not remains to be demonstrated experimentally.

## Considerations for net power

### Fuel type

This is a plot of the cross section of different fusion reactions.

Nuclear fusion refers to reactions in which lighter nuclei are combined to become heavier nuclei. This process changes mass into energy which may be captured to provide fusion power. Many types of atoms can be fused. The probability of a fusion reaction occurring is controlled by the cross section of the fuel,[31] which is in turn a function of its temperature. The easiest nuclei to fuse are deuterium and tritium, and their fusion occurs when the ions have a temperature of at least 4 keV (kiloelectronvolts) or about 45 million Kelvin. The polywell would achieve this by accelerating an ion with a charge of 1 down a 4,000 volt electric field. The high cost, short half-life and radioactivity of tritium made it difficult to be used by Bussard's team. The second easiest reaction is to fuse deuterium with itself. Because of its low cost, deuterium is commonly used by Fusor amateurs, and Bussard's polywell experiments were performed using this fuel. Any fusion reaction using deuterium or tritium will produce a fast neutron and is therefore radioactive. Bussard's goal was to fuse boron-11 with protons; this is a fusion reaction which is aneutronic (does not produce neutrons). An advantage of p-11B as a fusion fuel is that the primary reactor output would be energetic alpha particles, which can be directly converted to electricity at high efficiency (>90%) using suitably engineered collectors.

### Lawson criterion

At such conditions, the atoms are ionized and make a plasma. The energy generated by fusion, inside a hot plasma cloud can be found with the following equation.[32]

$P_\text{fusion} = n_A n_B \langle \sigma v_{A,B} \rangle E_\text{fusion}$

where:

• $P_\text{fusion}$ is the fusion power density (energy per time per volume),
• n is the number density of species A or B (particles per volume),
• $\langle \sigma v_{A,B} \rangle$ is the product of the collision cross-section σ (which depends on the relative velocity) and the relative velocity of the two species v, averaged over all the particle velocities in the system.

This equation shows that energy varies with the temperature, density, speed of collision, and fuel used. To reach net power, fusion reactions have to occur fast enough to make up for energy losses. Any power plant using fusion will hold in this hot cloud. Plasma clouds lose energy through conduction and radiation.[32] Conduction is when ions, electrons or neutrals touch a surface and leak out. Energy is lost with the particle. Radiation is when energy leaves the cloud as light. Radiation increases as the temperature rises. To get net power from fusion, you must overcome these losses. This leads to an equation for power output (where: η is machine efficiency).

$P_\text{out} = \eta_\text{capture}\left(P_\text{fusion} - P_\text{conduction} - P_\text{radiation}\right)$

John Lawson used this equation to estimate some conditions for net power [32] based on a Maxwellian cloud.[32] This is the Lawson criterion.

However, the Lawson criterion could not be used for a Polywell if Bussard's conjecture about the plasma being nonthermal is proven to be right. John D. Lawson himself stated in his founding report (p. 4, part 5):[32] "It is of course easy to postulate systems in which the velocity distribution of the particle is not Maxwellian. These systems are outside the scope of this report." But he also rules-out the possibility of a nonthermal plasma to ignite: "Nothing may be gained by using a system in which electrons are at a lower temperature [than ions]. The energy loss in such a system by transfer to the electrons will always be greater than the energy which would be radiated by the electrons if they were are the [same] temperature."

### Criticism

In his thesis[33] and his 1995 publication,[30] MIT doctoral student Todd Rider had calculated that X-ray radiation losses with this fuel will exceed fusion power production by at least 20%. Rider modeled the system using the following assumptions:

• The plasma was quasineutral. Therefore positives and negatives were equally mixed together.[30]
• The fuel was evenly mixed throughout the volume.[30]
• The plasma was isotropic, meaning that its behavior was the same in any given direction.[30]
• The plasma had a uniform energy and temperature throughout the cloud.[30]
• The plasma was an unstructured Gaussian sphere, with a strongly converged dense central core. The core represented a small (~1%) part of the total volume.[30] In a later 1995 paper, William Nevins at LANL argued against this assumption. He argued that the particles would build up angular momentum, causing the dense core to degrade.[34] The loss of density inside the core would reduce fusion rates.
• The potential well was broad and flat.[30]

Based on these assumptions, Rider used general equations[35] to estimate the rates of different physical effects. These included, but were not limited to, the loss of ions to up-scattering, the ion thermalization rate, the energy loss due to X-ray radiation and the fusion rate.[30] His conclusions were that the device suffered from "fundamental flaws".[30]

By contrast, Bussard has argued[18] that the plasma inside the polywell has different structure, temperature distribution and well profile. These characteristics have not been fully measured and are central to the device's feasibility. Based on this his calculations indicate that the bremsstrahlung losses would be much smaller.[36][37] According to Bussard the high speed and therefore low cross section for Coulomb collisions of the ions in the core makes thermalizing collisions very unlikely, while the low speed at the rim means that thermalization there has almost no impact on ion velocity in the core.[38][39] Bussard calculated that a polywell reactor with a radius of 1.5 meters would produce net power fusing deuterium.[40]

Other studies also disproved some of assumptions made by Rider and Nevins, arguing the real fusion rate and the associated recirculating power (needed to overcome the thermalizing effect and sustain the non-Maxwellian ion profile) could be estimated only with a self-consistent collisional treatment of the ion distribution function, lacking in Rider's work.[41]

### Energy capture

It has been proposed that energy may be extracted in polywells using heat capture or, in the case of aneutronic fusion like D-3He or p-11B, direct energy conversion, though that scheme will have general challenges. The energetic alpha particles (up to a few MeV) generated by the aneutronic fusion reaction would exit the MaGrid through the six axial cusps as cones (spread ion beams). Direct conversion collectors inside the vacuum chamber would convert the kinetic energy of the positively charged alpha particles to a high-voltage direct current. If the alpha particles can slow down enough before they contact the collector plates, a very high conversion efficiency (over 90%) is expected.[42]

## History

In the late 1960s there were several investigations of polyhedral magnetic fields as a possibility to confine a fusion plasma.[43][44] The first proposal to combine this magnetic configuration with an electrostatic potential well in order to improve electron confinement was made by Oleg Lavrentiev in 1975.[4] The idea was picked up by Robert Bussard in 1983, a link acknowledged in the references cited by his 1989 patent application,[12] though in 2006 he appears to claim to have re-discovered the idea independently.[45]

### HEPS

Research was funded first by the Defense Threat Reduction Agency beginning in 1987 and later by DARPA.[24]:32:30 This funding resulted in a first machine known as the high energy power source (HEPS) experiment. This was built by Directed Technologies Inc in San Diego.[46] This machine was a large (190 cm across) machine, where the rings were placed outside of the vacuum chamber.[24]:32:33 This machine performed poorly because the magnetic fields sent electrons into the walls, driving up conduction losses. At the time, these losses were thought to be due to poor electron injection.[46] The United States Navy began providing low-level funding to the project in 1992.[47] Results from the HEPS program were published by Nicholas Krall in 1994.[46]

Bussard, who had been an advocate for Tokamak research, became the advocate for this concept, so that the idea is now indelibly associated with his name. In 1995 he sent a letter to the United States Congress stating that he had only supported Tokamaks in order to get fusion research sponsored by the government, but he now believed that there are better alternatives to Tokamaks.

### EMC2, Inc.

Robert Bussard founded Energy/Matter Conversion Corporation, Inc. (aka EMC2) in 1985[12][24] and after the HEPS program ended, the company took on the research. Successive machines were made, starting from WB-1 to WB-8. The company won an SBIR I grant in 1992–93 and an SBIR II grant in 1994–95, both from the US Navy.[45] In 1993, it received a grant from the Electric Power Research Institute to examine the use of this machine in power production.[45] In 1994, The company received small grants from NASA and LANL.[45] Starting in 1999, the company was primarily funded by the US Navy.[45]

One early design was WB-1, which had six conventional magnets in a cube. This device was 10 cm across.[45] This was followed by WB-2, which used coils of wires to generate the magnetic field. Each electromagnet had a square cross section, which created problems. The magnetic fields drove electrons into the metal rings raising conduction losses and affects electron trapping. This design also suffered from "funny cusp" losses at the joints between magnets. The WB-6 machine attempted to address these problems, by using circular rings and spacing them some distance apart.[24] The next device, PXL-1, was built in 1996 and 1997. This machine was 26 cm across and used flatter rings to generate the field.[45] From 1998 to 2005 the company built a succession of six machines: WB-3, MPG-1,2, WB-4, PZLx-1, MPG-4 and WB-5. All of these reactors were six magnet designs built as a cube or truncated cube. They ranged from 3 to 40 cm in radius.[45]

Despite initial difficulties in spherical electron confinement, at the time of the 2005 research project's termination, Bussard reported a fusion rate of 109 per second running D-D fusion reactions at only 12.5 kV (based on detecting a total of nine neutrons in five tests,[18][48] giving a wide confidence interval). He stated that the fusion rate achieved by WB-6 was roughly 100,000 times greater than what Farnsworth achieved at similar well depth and drive conditions.[49][50] By comparison, researchers at the University of Wisconsin–Madison reported a neutron rate of up to 5×109 per second at voltages of 120 kV with an electrostatic fusor without magnetic fields.[51]

Bussard asserted, by using superconductor coils, the only significant energy loss channel is through electron losses proportional to the surface area. He also stated that the density would scale with the square of the field (constant beta conditions), and the maximum attainable magnetic field would scale with the radius (technological constraints). Under those conditions, the fusion power produced would scale with the seventh power of the radius, and the energy gain would scale with the fifth power. While Bussard did not publicly document the physical reasoning underlying this estimate,[52] if true, it would enable a model only ten times larger to be useful as a fusion power plant.[18]

#### WB-6

##### WB-7

A more robust version of the WB-6 fusion device, was constructed at a machine shop in San Diego and shipped to Santa Fe to the EMC2 testing facility. The device was termed WB-7 and like prior ones, was designed by engineer Mike Skillicorn. This machine has a design similar to WB-6. WB-7, achieved "1st plasma" in early January, 2008.[60][61] In August 2008, the team finished the first phase of their experiment and submitted the results to a peer review board. Based on this review, federal funders agreed the team should proceed to the next phase. Nebel has said "we have had some success", referring to the team's effort to reproduce the promising results obtained by Bussard. "It's kind of a mix", Nebel reported. "We're generally happy with what we've been getting out of it, and we've learned a tremendous amount" he also said.[62]

##### FY 2009 work

In September 2008 the Naval Air Warfare Center, Weapons Division, China Lake, California publicly pre-solicited a contract for research on an Electrostatic "Wiffle Ball" Fusion Device.[63] In October 2008 the US Navy publicly pre-solicited two more contracts[64][65] also targeted toward EMC2 as preferred supplier. These two tasks were to develop better instrumentation and to develop an ion injection gun.[66][67] In December 2008, following many months of review by the expert review panel of the submission of the final WB-7 results, Richard Nebel commented that "There's nothing in [the research] that suggests this will not work", but "That's a very different statement from saying that it will work."[68]

In January 2009 the Naval Air Warfare Center pre-solicited another contract for "modification and testing of plasma wiffleball 7"[69] which appears to be funding to install the instrumentation developed in a prior contract, install a new design for the connector (joint) between coils, and operate the WB-7 with the modifications. The modified unit is now called WB-7.1. This pre-solicitation started as a $200k contract but the final award was for$300k.

##### FY 2014 work

In June 2014, EMC2 demonstrated for the first time that the electron cloud becomes diamagnetic in the center of a magnetic cusp configuration when beta is high, resolving an earlier conjecture.[13][16] Whether the electrons are thermalized and the plasma is thermal or not remains to be demonstrated experimentally.

### University of Wisconsin

Carl Sovinec and his graduate student have performed Vlasov–Poisson, particle-in-cell simulation work on the polywell. This was funded through the National Defense Science and Engineering Graduate Fellowship and was presented at the 2013 American Physical Society conference.[92]

### Convergent Scientific, Inc.

Convergent Scientific, Inc. (CSI) is an American company founded in December 2010 and based in Huntington Beach, California.[93] Their first polywell design, the Model 1, has been tested on steady-state operations from January to late summer 2012. The MaGrid was made of a unique diamond shaped hollow wire, into which an electric current and a liquid coolant are flowing.[94][95][96] They now has an effort to build a small-scale polywell fusing deuterium.[97][98] The company filed several patents[99][100][101] and in the Fall of 2013, did a series of web-based investor pitches.[102] The presentations mention encountering plasma instabilities including the Diocotron, two stream and Weibel instabilities. The company wants to make and sell Nitrogen-13 for PET scans.[103]

### Radiant Matter Research

Radiant Matter[104] is an organization in the Netherlands which has built a number of fusors and has plans to build a polywell.

## References in literature

The polywell has been referenced in two novels: "A Green Sun" by Charles Gray[105] and a "To Fly From Folly" by William Flint.

## References

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37. ^ Bussard, Robert W.; King, Katherine E. (5 December 1991). Bremsstrahlung and Synchrotron Radiation Losses in Polywell™ Systems (PDF) (Technical report). EMC2-DARPA. EMC2-1291-02.
38. ^ Bussard, Robert W. (19 February 1991). Collisional Equilibration (PDF) (Technical report). EMC2-DARPA. EMC2-0890-03.
39. ^ Bussard, Robert W. (19 February 1991). Core Collisional Ion Upscattering and Loss Time (PDF) (Technical report). EMC2-DARPA. EMC2-1090-03.
40. ^ Safe, Green, Clean – the p-B Polywell: A Different Kind of Nuclear, p. 66
41. ^ Chacón, L.; Miley, G. H.; Barnes, D. C.; Knoll, D. A. (2000). "Energy gain calculations in Penning fusion systems using a bounce-averaged Fokker–Planck model" (PDF). Physics of Plasmas 7 (11): 4547. doi:10.1063/1.1310199. edit
42. ^ Rosenbluth, M. N.; Hinton, F. L. (1994). "Generic issues for direct conversion of fusion energy from alternative fuels". Plasma Physics and Controlled Fusion 36 (8): 1255. doi:10.1088/0741-3335/36/8/003. edit
43. ^ Keller, R.; Jones, I. R. (June 1966). "Confinement d'un Plasma par un Système Polyédrique à Courant Alternatif" [Plasma confinement by a polyhedral system with alternating current]. Zeitschrift für Naturforschung A (in French) 21: 1085–1089. Bibcode:1966ZNatA..21.1085K. "as cited by R.W. Bussard in U.S. Patent 4,826,646, "Method and apparatus for controlling charged particles", issued May 2, 1989, p.12."
44. ^ Sadowski, M. (1969). "Spherical Multipole Magnets for Plasma Research". Review of Scientific Instruments 40 (12): 1545. doi:10.1063/1.1683858. edit
45. Robert W. Bussard (December 2006). "A quick history of the EMC2 Polywell IEF concept" (PDF). Energy/Matter Conversion Corporation. Retrieved 16 June 2014.
46. ^ a b c "Forming and maintaining a potential well in a quasispherical magnetic trap" Nicholas Krall, M Coleman, K Maffei, J Lovberg Physics of Plasma 2 (1), 1995
47. ^ Posted to the web by Robert W. Bussard. "Inertial electrostatic fusion (IEF): A clean energy future" (Microsoft Word document). Energy/Matter Conversion Corporation. Retrieved 2006-12-03.
48. ^ a b Final Successful Tests of WB-6, EMC2 Report, currently (July 2008) not publicly available
49. ^ a b Robert W. Bussard (2006-03-29). "Inertial Electrostatic Fusion systems can now be built". fusor.net forums. Retrieved 2006-12-03.
50. ^ a b c SirPhilip (posting an e-mail from "RW Bussard") (2006-06-23). "Fusion, eh?". James Randi Educational Foundation forums. Retrieved 2006-12-03.
51. ^ "Inertial Electrostatic Confinement Project – University of Wisconsin – Madison". Iec.neep.wisc.edu. Retrieved 2013-06-17.
52. ^ Possibly he assumed that the ion energy distribution is fixed, that the magnetic field scales with the linear size, and that the ion pressure (proportional to density) scales with the magnetic pressure (proportional to B²). The R7 scaling results from multiplying the fusion power density (proportional to density squared, or B4) with the volume (proportional toR³). On the other hand, if it is important to maintain the ratio of the Debye length or the gyroradius to the machine size, then the magnetic field strength would have to scale inversely with the radius, so that the total power output would actually be lower in a larger machine.
53. ^ Robert L. Hirsch, "Inertial-Electrostatic Confinement of Ionized Fusion Gases", Journal of Applied Physics, v. 38, no. 7, October 1967
54. ^ There is this clause in the "Solicitation, Offer and Award" for the "plasma wiffleball development project", awarded on March 3, 2009, to Matter Conversion Corporation:

5252.204-9504 DISCLOSURE OF CONTRACT INFORMATION (NAVAIR) (JAN 2007) (a) The Contractor shall not release to anyone outside the Contractor's organization any unclassified information (e.g., announcement of contract award), regardless of medium (e.g., film, tape, document), pertaining to any part of this contract or any program related to this contract, unless the Contracting Officer has given prior written approval. (b) Requests for approval shall identify the specific information to be released, the medium to be used, and the purpose for the release. The Contractor shall submit its request to the Contracting Officer at least ten (10) days before the proposed date for release. (c) The Contractor agrees to include a similar requirement in each subcontract under this contract. Subcontractors shall submit requests for authorization to release through the prime contractor to the Contracting Officer.

55. ^ Askmar summary of IEC fusion
56. ^ M. Simon (2007-10-08). "Dr. Robert W. Bussard Has Passed". Classical Values. Retrieved 2007-10-09.
57. ^ "Fusion we can believe in?" (Science subsite of MSNBC.com). MSNBC.com. December 2008. Retrieved 2008-12-18.
58. ^ "Funding Continues for Bussard's Fusion Reactor". New Energy and Fuel. 2007-08-27. Note that this source is a blog and not necessarily reliable.
59. ^ William Matthews (2007-11-06). "Fusion Researcher Bussard Dies at 79" (webpage). Online article. Defencenews.com. Retrieved 2007-11-06.
60. ^ "Strange Science Takes Time". MSNBC. 2008-01-09.
61. ^ "Fusion Quest Goes Forward". MSNBC. 2008-06-12.
62. ^ Posted to the web by Alan Boyle (September 2008). "Fusion effort in Flux". MSNBC. Retrieved 2008-09-08.
63. ^ "A—Fusion Device Research, Solicitation Number: N6893608T0283". Federal Business Opportunities. September 2008. Retrieved 2008-10-02.
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65. ^ "A—Spatially Resolved Plasma Densities/Particle Energies, Solicitation Number: N6893609T0019". Federal Business Opportunities. October 2008. Retrieved 2008-11-07.
66. ^ "Found this during google search on Polywell Fusion". Talk-polywell.org. Retrieved 2013-06-17.
67. ^ "Found this during google search on Polywell Fusion" (Discussion forum). Talk-Polywell.org. October 2008. Retrieved 2008-11-07.
68. ^ "WB-6 Results Confirmed – Continuous Operation The Next Step". iecfusiontech. October 2012. Retrieved 2012-09-10.
69. ^ "A—Plasma Wiffleball, Solicitation Number: N6893609R0024". Federal Business Opportunities. January 2009. Retrieved 2009-01-26.
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71. ^ a b c "Statement of work for advanced gaseous electrostatic energy (AGEE) concept exploration" (PDF). United States Navy. June 2009. Retrieved 2009-06-18.
72. ^ "U.S. Department of Defense – Office of the Assistant Secretary of Defense (Public Affairs) – Contracts". United States Department of Defense. September 2009. Retrieved 2009-09-13.
73. "Project Summary – ENERGY/MATTER CONVERSION CORPORATION". Recovery.gov. Retrieved 2013-06-17.
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75. ^ "Project Summary 2011 Q3". Recovery.gov. Retrieved 2013-06-17.
76. ^ "Project Summary 2011 Q4". Recovery.gov. Retrieved 2012-03-31.
77. ^ "Recovery.Gov Project Tracker at Talk-Polywell.org". Talk-Polywell.org. 2011-04-29. Retrieved 2012-03-31.
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81. ^ Park, Jaeyoung (12 June 2014). SPECIAL PLASMA SEMINAR: Measurement of Enhanced Cusp Confinement at High Beta (Speech). Plasma Physics Seminar. Department of Physics & Astronomy, University of California, Irvine: Energy Matter Conversion Corp (EMC2).
82. ^ Boyle, Alan (13 June 2014). "Low-Cost Fusion Project Steps Out of the Shadows and Looks for Money". NBC News.
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84. ^ "An End to Four Years of". Prometheus Fusion Perfection. 2013-07-07. Retrieved 2014-06-14.
85. ^ Carr, M.; Khachan, J. (2010). "The dependence of the virtual cathode in a Polywell™ on the coil current and background gas pressure". Physics of Plasmas 17 (5): 052510. Bibcode:2010PhPl...17e2510C. doi:10.1063/1.3428744. edit
86. ^ Khachan, Joe; Carr, Matthew; Gummersall, David; Cornish, Scott; Israel, Adam; Bandara, Rehan; Ren, Johnson (14–17 October 2012). "Overview of IEC at the University of Sydney" (PDF). 14th US-Japan Workshop on Inertial Electrostatic Confinement Fusion. University of Maryland, College Park, MD.
87. ^ Gummersall, David; Khachan, Joe (14–17 October 2012). "Analytical orbital theory analysis of electron confinement in a PolywellTM device" (PDF). 14th US-Japan Workshop on Inertial Electrostatic Confinement Fusion. University of Maryland, College Park, MD.
88. ^ "Agenda of 12th US-Japan Workshop on Inertial Electrostatic Confinement Fusion". 2010-10-20. Retrieved 2013-06-17.
89. ^ Santarius, John. "Summary & Thoughts". 13th Workshop on Inertial-Electrostatic Confinement Fusion. University of Wisconsin. Retrieved 31 March 2012.
90. ^ "Iran to build nuclear fusion producing plant". Trend News Agency. 13 November 2012. Retrieved 2013-02-08.
91. ^ Kazemyzade, F.; Mahdipoor, H.; Bagheri, A.; Khademzade, S.; Hajiebrahimi, E.; Gheisari, Z.; Sadighzadeh, A.; Damideh, V. (2011). "Dependence of Potential Well Depth on the Magnetic Field Intensity in a Polywell Reactor". Journal of Fusion Energy 31 (4): 341. doi:10.1007/s10894-011-9474-4. edit
92. ^ "Vlasov-Poisson calculations of electron confinement times in Polywell(TM) devices using a steady-state particle-in-cell method". The DPP13 Meeting of The American Physical Society. Retrieved 2013-10-01.
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95. ^ "We have to Try". The Polywell Blog. 31 January 2014.
96. ^ Talk. "Commercial Applications of IEC Devices" Web presentation, performed by Devlin Baker, 22 October 2013.
97. ^ Rogers, Joel G.; Baker, Devlin (14–16 October 2012). "Designing a Small-Scale D+D Reactor". 14th US-Japan Workshop on IEC Fusion. College Park, Maryland.
98. ^ "Convergent Scientific Incorporated website". Convsci.com. Retrieved 2013-06-17.
99. ^ US application 2010284501, Rogers, Joel Guild, "Modular Apparatus for Confining a Plasma", published 2010-11-11, assigned to Rogers, Joel Guild
100. ^ US patent 8279030, Baker, Devlin & Bateman, Daniel, "Method and apparatus for electrical, mechanical and thermal isolation of superconductive magnets", issued 2012-10-02, assigned to Magnetic-Electrostatic Confinement (MEC) Corporation
101. ^ US application 2013012393, Bateman, Daniel & Pourrahimi, Shahin, "Apparatus to confine a plurality of charged particles", published 2013-01-10, assigned to Bateman, Daniel and Pourrahimi, Shahin
102. ^ Talk. "Numerical Simulations of IEC Plasmas." Web presentation, Performed by Devlin Baker, November 5, 2013
103. ^ Talk. "Commercial Applications of IEC Devices" Web presentation, performed by Devlin Baker, December 3, 2013.
104. ^ http://www.radiantmatter.com/content/farnsworth-fusor, Accessed: 12/25/2013
105. ^ "A Green Sun (The Fusion Age)" by Charles Gray, August 7, 2011, Amazon Digital Services