# 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 that traps electrons. This creates a negative voltage, which attracts positive ions. As the ions accelerate towards the negative center, their kinetic energy rises. Ions that collide at high enough energies can fuse.

The polywell is one of many devices that 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 physicist Robert Bussard, as an improvement over the fusor. His company, EMC2, Inc., developed prototypical 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, often referred to as grids, that are placed inside a vacuum chamber. The outer cage has a positive voltage versus the inner cage. Typically, deuterium gas is injected into this chamber. It is heated past its ionization temperature, making positive ions. The ions are positive and move towards the negative inner cage. Those that miss the wires of the inner cage fly through the center of the device at high speeds and can fly out the other side of the inner cage. As the ions move outward, they feel a Coulomb force that directs them back towards the center. Over time, a core of ionized gas can form inside the inner cage. Ions pass back and forth through the core until they strike either the grid or another nucleus. Most nucleus strikes do not result in fusion. Grid strikes can raise the temperature of the grid as well as eroding it. These strikes conduct mass and energy away from the plasma.

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

Figure 1: 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

Figure 1: Sketch of a MaGrid in a polywell

The main problem with the fusor is that the inner 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. These are put inside a vacuum chamber [5]

• A set of positively charged electromagnet coils arranged in a polyhedron. The most common arrangement is a six sided 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. These shoot electrons into the center of the ring structure. Once inside, the electrons are confined by the magnetic fields. This has been measured in polywells using Langmuir probes.[6][7][8] Electrons that have enough energy to escape through the magnetic cusps can be re-attracted to the positive rings. They can slow down and return to the inside of the rings along the cusps. This reduces conduction losses, and improves the overall performance of the machine.[9] The electrons act as a negative voltage drop attracting positive ions. This is a virtual cathode.
• Gas puffers at corner. Gas is puffed inside the rings where it ionizes at the electron cloud. As ions fall down the potential well, the electric field works on them, heating it to fusion conditions. The ions build up speed. They can slam together in the center and fuse. Ions are electrostatically confined raising the density and increasing the fusion rate.

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][10][11]

## Magnetic trapping models

Figure 2: A plot of the magnetic field generated by the MaGrid inside a polywell. The null point is marked in red in the center.

Magnetic fields exert a pressure on the plasma. Beta is the ratio of plasma pressure to the magnetic field strength.

${\displaystyle \beta ={\frac {p}{p_{mag}}}={\frac {nk_{B}T}{(B^{2}/2\mu _{0})}}}$ [12]

Most experiments on polywells involve low-beta plasma regimes (where β < 1),[13] where the plasma pressure is weak compared to the magnetic pressure. Several models describe magnetic trapping in polywells.[citation needed] Tests indicated that plasma confinement is enhanced in a magnetic cusp configuration when β (plasma pressure/magnetic field pressure) is of order unity. This enhancement is required for a fusion power reactor based on cusp confinement to be feasible.[14]

### Magnetic mirror

Magnetic mirror dominates in low beta designs. Both ions and electrons are reflected from high to low density fields. This is known as the magnetic mirror effect.[15] The polywell's rings are arranged so the densest fields are on the outside, trapping electrons in the center. This can trap particles at low beta values.

### Cusp confinement

Figure 3: Polywell cusps. The line cusp runs along the seam between two electromagnets. The funny cusp is the cusp between three magnets, running along the corners. The point cusp lies in the middle of one electromagnet.

In high beta conditions, the machine may operate with cusp confinement.[16] This is an improvement over the simpler magnetic mirror.[17] The MaGrid has six point cusps, each located in the middle of a ring; 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 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.[18]

### Free-boundary plasma

In 1955, Harold Grad theorized that a high-beta plasma pressure combined with a cusped magnetic field would improve plasma confinement.[19] A diamagnetic plasma rejects the external fields and plugs the cusps. This system would be a much better trap.

Cusped confinement was explored theoretically [20] and experimentally.[21] 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.

This figure shows the development of the proposed “wiffle ball” confinement concept. Three rows of figures are shown: the magnetic field, the electron motion and the plasma density inside the polywell. (A) The field is the superposition of six rings in a box. In the center is a null point - a zone of no magnetic field.[8] The plasma is magnetized, meaning that the plasma and magnetic field intermix. (B) As plasma is injected, the density rises. (C) As the plasma density rises, the plasma becomes more diamagnetic, causing it to reject the outside magnetic field. As the plasma presses outwards, the density of the surrounding magnetic field rises. This tightens the corkscrewing motion of the particles outsides the center. A sharp boundary is formed.[22] A current is predicted [19][20] to form on this boundary. (D) If the pressures find equilibrium at a beta of one, this determines the shape of the plasma cloud. (E) In the center, there is no magnetic field from the rings. This means that its motion inside the field free radius should be relatively straight or ballistic.[8]

For many decades, cusped confinement never behaved experimentally as was predicted. Sharply bent fields were used by Lawrence Livermore National Laboratory in a series of magnetic mirror machines from the late 1960s to the mid-1980s. After hundreds of millions were spent, the machines still leaked plasma at the field ends. Many scientists shifted focus onto looping the fields, into a tokamak. Eventually it was thought that cusped confinement effect did not exist.

In June 2014 EMC2 published a preprint[22] providing evidence that the effect is real, based on x-ray measurements and magnetic flux measurements during its experiment.

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 (low beta) that he called cusp confinement; and several thousand passes in Wiffle-Ball confinement (high beta).[23][24]

In February 2013, Lockheed Martin Skunk Works announced a new compact fusion machine, the high beta fusion reactor,[25][26] that may be related to the biconic cusp and the polywell, and working at β = 1.

## Other behavior

### Single-electron motion

Figure 4: 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.

As an electron enters a magnetic field, it feels a Lorentz force and corkscrews. The radius of this motion is the gyroradius. As it moves it loses some energy as x-rays, every time it changes speed. The electron spins faster and tighter in denser fields, as it enters the MaGrid. Inside the MaGrid, single electrons travel straight through the null point, due to their infinite gyroradius in regions of no magnetic field. Next, they head towards the edges of the MaGrid field and corkscrew tighter along the denser magnetic field lines.[13][27] This is typical electron cyclotron resonance motion. Their gyroradius shrinks and when they hit a dense magnetic field they can be reflected using the magnetic mirror effect.[28][29][30] Electron trapping has been measured in polywells with Langmuir probes.[6][7][8]

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.[31] 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 electron cloud in the center. In the fusor, they are attracted to a negative wire cage in the center.

### Plasma recirculation

Plasma recirculation would significantly improve the function of these machines. It has been argued that efficient recirculation is the only way they can be viable.[32][33] Electrons or ions move through the device without striking a surface, reducing conduction losses. Bussard stressed this; specifically emphasizing that electrons need to move through all cusps of the machine.[34][35]

Figure 5: Thermalized plasma ion energy distribution inside a polywell.[32] This model assumes a maxwellian ion population, broken into different groups. (1) The ions which do not have enough energy to fuse, (2) the ions at the injection energy (3) the ions that have so much kinetic energy that they escape.

### Models of energy distribution

Figure 6: Non-thermalized plasma energy distribution inside a polywell.[36] It is argued that the region of unmagnetized space leads to electron scattering, this leads to a monoenergetic distribution with a cold electron tail. This is supported by 2 dimensional particle-in-cell simulations.

As of 2015 it had not been determined conclusively what the ion or electron energy distribution is. The energy distribution of the plasma can be measured using a Langmuir probe. This probe absorbs charge from the plasma as its voltage changes, making an I-V Curve.[37] From this signal, the energy distribution can be calculated. The energy distribution both drives and is driven by several physical rates,[32] the electron and ion loss rate, the rate of energy loss by radiation, the fusion rate and the rate of non-fusion collisions. The collision rate may vary greatly across the system[citation needed]:

• At the edge: where ions are slow and the electrons are fast.
• At the center: where ions are fast and electrons are slow.

Critics claimed that both the electrons and ion populations have bell curve distribution;[32] that the plasma is thermalized. The justification given is that the longer the electrons and ions move inside the polywell, the more interactions they undergo leading to thermalization. This model for [32] the ion distribution is shown in Figure 5.

Supporters modeled a nonthermal plasma.[34] The justification is the high amount of scattering in the device center.[38] Without a magnetic field, electrons scatter in this region. They claimed that this scattering leads to a monoenergetic distribution, like the one shown in Figure 6. This argument is supported by 2 dimensional particle-in-cell simulations.[38] Bussard argued that constant electron injection would have the same effect.[5] Such a distribution would help maintain a negative voltage in the center, improving performance.[5]

## Considerations for net power

### Fuel type

Figure 7: Plot of the cross section of different fusion reactions.

Nuclear fusion refers to nuclear reactions that combine lighter nuclei to become heavier nuclei. All chemical elements can be fused, but only for elements with fewer protons than iron, this process changes mass into energy that can potentially be captured to provide fusion power.

The probability of a fusion reaction occurring is controlled by the cross section of the fuel,[39] which is in turn a function of its temperature. The easiest nuclei to fuse are deuterium and tritium. Their fusion occurs when the ions reach 4 keV (kiloelectronvolts) or about 45 million Kelvins. 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 make it difficult to work with.

The second easiest reaction is to fuse deuterium with itself. Because of its low cost, deuterium is commonly used by Fusor amateurs. Bussard's polywell experiments were performed using this fuel. Fusion of deuterium or tritium produces a fast neutron and is therefore radioactive. Bussard's choice was to fuse boron-11 with protons; this reaction 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 using direct energy conversion. Direct conversion has achieved a 48% power efficiency[40] against 80–90% theoretical efficiency.[15]

### Lawson criterion

Main article: Lawson criterion

The energy generated by fusion inside a hot plasma cloud can be found with the following equation:[41]

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

where:

• ${\displaystyle P_{\text{fusion}}}$ is the fusion power density (energy per time per volume),
• n is the number density of species A or B (particles per volume),
• ${\displaystyle \langle \sigma v_{A,B}\rangle }$ 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.

Energy varies with temperature, density, collision speed and fuel. To reach net power production, reactions must occur rapidly enough to make up for energy losses. Plasma clouds lose energy through conduction and radiation.[41] Conduction is when ions, electrons or neutrals touch a surface and escape. Energy is lost with the particle. Radiation is when energy escapes as light. Radiation increases with temperature. To get net power from fusion, these losses must be overcome. This leads to an equation for power output.

Net Power = Efficiency *(Fusion - Radiation Loss - Conduction Loss)

• Net Power — power output
• Efficiency — fraction of energy needed to drive the device and convert it to electricity.
• Fusion — energy generated by the fusion reactions.
• Radiation — energy lost as light, leaving the plasma.
• Conduction — energy lost, as mass leaves the plasma.

Lawson used this equation to estimate conditions for net power [41] based on a Maxwellian cloud.[41]

However, the Lawson criterion does not apply for Polywells if Bussard's conjecture that the plasma is nonthermal is correct. Lawson stated in his founding report:[41] "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." He also ruled 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 the [same] temperature."

### Criticism

Todd Rider [42] calculated that X-ray radiation losses with this fuel would exceed fusion power production by at least 20%. Rider's model used the following assumptions:[32][33]

• The plasma was quasineutral. Therefore, positives and negatives equally mixed together.[32]
• The fuel was evenly mixed throughout the volume.[32]
• The plasma was isotropic, meaning that its behavior was the same in any given direction.[32]
• The plasma had a uniform energy and temperature throughout the cloud.[32]
• The plasma was an unstructured Gaussian sphere, with a strongly converged core that represented a small (~1%) part of the total volume.[32] Nevins challenged this assumption, stating that the particles would build up angular momentum, causing the dense core to degrade.[43] The loss of density inside the core would reduce fusion rates.
• The potential well was broad and flat.[32]

Based on these assumptions, Rider used general equations[44] to estimate the rates of different physical effects. These included the loss of ions to up-scattering, the ion thermalization rate, the energy loss due to X-ray radiation and the fusion rate.[32] His conclusions were that the device suffered from "fundamental flaws".[32]

By contrast, Bussard argued[24] that the plasma had a different structure, temperature distribution and well profile. These characteristics have not been fully measured and are central to the device's feasibility. Bussard's calculations indicated that the bremsstrahlung losses would be much smaller.[45][46] 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.[47][48] Bussard calculated that a polywell reactor with a radius of 1.5 meters would produce net power fusing deuterium.[49]

Other studies disproved some of the 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.[50]

### Energy capture

It has been proposed that energy may be extracted from polywells using heat capture or, in the case of aneutronic fusion like D-3He or p-11B, direct energy conversion, though that scheme faces 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 alpha particle's kinetic energy to a high-voltage direct current. The alpha particles must slow down before they contact the collector plates to realize high conversion efficiency.[51] In experiments, direct conversion has demonstrated a conversion efficiency of 48%.[52]

## History

In the late 1960s several investigations studied polyhedral magnetic fields as a possibility to confine a fusion plasma.[53][54] The first proposal to combine this 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. His 1989 patent application cited Lavrentiev,[18] although in 2006 he appears to claim to have (re)discovered the idea independently.[55]

### HEPS

Research was funded first by the Defense Threat Reduction Agency beginning in 1987 and later by DARPA.[7]:32:30 This funding resulted in a machine known as the high energy power source (HEPS) experiment. It was built by Directed Technologies Inc.[56] This machine was a large (1.9 m across) machine, with the rings outside the vacuum chamber.[7]:32:33 This machine performed poorly because the magnetic fields sent electrons into the walls, driving up conduction losses. These losses were attributed to poor electron injection.[56] The US Navy began providing low-level funding to the project in 1992.[57] Krall published results in 1994.[56]

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

### EMC2, Inc.

Bussard founded Energy/Matter Conversion Corporation, Inc. (aka EMC2) in 1985[7][18] and after the HEPS program ended, the company continued its research. Successive machines were made, evolving 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.[55] In 1993, it received a grant from the Electric Power Research Institute.[55] In 1994, The company received small grants from NASA and LANL.[55] Starting in 1999, the company was primarily funded by the US Navy.[55]

WB-1 had six conventional magnets in a cube. This device was 10 cm across.[55] WB-2 used coils of wires to generate the magnetic field. Each electromagnet had a square cross section that created problems. The magnetic fields drove electrons into the metal rings, raising conduction losses and electron trapping. This design also suffered from "funny cusp" losses at the joints between magnets. WB-6 attempted to address these problems, by using circular rings and spacing further apart.[7] 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.[55] 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.[55]

Initial difficulties in spherical electron confinement led to the 2005 research project's termination. However, Bussard reported a fusion rate of 109 per second running D-D fusion reactions at only 12.5 kV (based on detecting nine neutrons in five tests,[24][58] 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.[59][60] By comparison, researchers at University of Wisconsin–Madison reported a neutron rate of up to 5×109 per second at voltages of 120 kV from an electrostatic fusor without magnetic fields.[61]

Bussard asserted, by using superconductor coils, that 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. 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 reasoning underlying this estimate,[62] if true, it would enable a model only ten times larger to be useful as a fusion power plant.[24]

#### WB-6

##### WB-7

WB-7 was constructed in San Diego and shipped to the EMC2 testing facility. The device was termed WB-7 and like prior editions, was designed by engineer Mike Skillicorn. This machine has a design similar to WB-6. WB-7 achieved "1st plasma" in early January, 2008.[70][71] 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 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.[72]

##### 2008

In September 2008 the Naval Air Warfare Center publicly pre-solicited a contract for research on an Electrostatic "Wiffle Ball" Fusion Device.[73] In October 2008 the US Navy publicly pre-solicited two more contracts[74][75] with EMC2 the preferred supplier. These two tasks were to develop better instrumentation and to develop an ion injection gun.[76][77] In December 2008, following many months of review by the expert review panel of the submission of the final WB-7 results, 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."[78]

### Going public

#### 2014

In June 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.[19][22] Whether the plasma is thermalized remains to be demonstrated experimentally. Park presented these findings at various universities,[91][92][93][94][95] the Annual 2014 Fusion Power Associates meeting [96] and the 2014 IEC conference.

### University of Wisconsin

Researchers 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.[111]

### Convergent Scientific, Inc.

Convergent Scientific, Inc. (CSI) is an American company founded in December 2010 and based in Huntington Beach, California.[112] They tested their first polywell design, the Model 1, 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 flowed.[113][114][115] They are making an effort to build a small-scale polywell fusing deuterium.[116][117] The company filed several patents[118][119][120] and in the Fall of 2013, did a series of web-based investor pitches.[121] 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.[122]

Radiant Matter[123] is a Netherlands organization that has built fusors and has plans to build a polywell.

### ProtonBoron

ProtonBoron[124] is an organization that plans to build a proton-boron polywell.

## References in literature

The polywell was referenced in two novels: A Green Sun by Charles Gray[125] and a To Fly From Folly by William Flint.

## References

1. ^ Miley, George H.; Murali, S. Krupakar (8 January 2014). Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications. New York, Heidelberg, Dordrecht, London: Springer Science+Business Media. doi:10.1007/978-1-4614-9338-9. ISBN 978-1-4614-9337-2.
2. ^ Thorson, Timothy A. (1996). Ion flow and fusion reactivity characterization of a spherically convergent ion focus (Thesis). University of Wisconsin-Madison. OCLC 615996599.
3. ^ Thorson, T. A.; Durst, R. D.; Fonck, R. J.; Sontag, A. C. (1998). "Fusion reactivity characterization of a spherically convergent ion focus". Nuclear Fusion. 38 (4): 495. Bibcode:1998NucFu..38..495T. doi:10.1088/0029-5515/38/4/302.
4. ^ a b Lavrent'ev, O. A (4–7 March 1974). Electrostatic and Electromagnetic High-Temperature Plasma Traps. Conference on Electrostatic and Electromagnetic Confinement of Plasmas and the Phenomenology of Relativistic Electron Beams. Annals of the New York Academy of Sciences. 251. New York City: New York Academy of Sciences (published 8 May 1975). pp. 152–178. as cited by Todd H. Rider in "A general critique of inertial-electrostatic confinement fusion systems", Phys. Plasmas 2 (6), June 1995. Rider specifically stated that Bussard has revived an idea originally suggested by Lavrent'ev.
5. ^ a b c US patent 5160695, Bussard, Robert W., "Method and apparatus for creating and controlling nuclear fusion reactions", issued 1992-11-03, assigned to Qed, Inc.
6. ^ a b c Krall, Nicholas A.; Coleman, Michael; Maffei, Kenneth C.; Lovberg, John A.; et al. (18 April 1994). "Forming and Maintaining a Potential Well in a Quasispherical Magnetic Trap" (PDF). Physics of Plasmas. American Institute of Physics (published January 1995). 2 (1): 146–158. Bibcode:1995PhPl....2..146K. doi:10.1063/1.871103.
7. Robert Bussard (lecturer) (2006-11-09). "Should Google Go Nuclear? Clean, cheap, nuclear power (no, really)" (Flash video). Google Tech Talks. Google. Retrieved 2006-12-03.
8. Carr, Matthew (2013). Electrostatic potential measurements and point cusp theories applied to a low beta polywell fusion device (Thesis). The University of Sydney. OCLC 865167070.
9. ^ Lawson, J. D. (December 1955). Some Criteria for a Power producing thermonuclear reactor (PDF) (Technical report). Atomic Energy Research Establishment, Harwell, Berkshire, U. K. A.E.R.E. GP/R 1807.
10. ^ Bussard, Robert W. (March 1991). "Some Physics Considerations of Magnetic Inertial Electrostatic Confinement: A New Concept for Spherical Converging Flow Fusion" (PDF). Fusion Science and Technology. American Nuclear Society. 19 (2): 273–293.
11. ^ Krall, Nicholas A. (August 1992). "The Polywell: A Spherically Convergent Ion Focus Concept" (PDF). Fusion Science and Technology. American Nuclear Society. 22 (1): 42–49.
12. ^ Wesson, J: "Tokamaks", 3rd edition page 115, Oxford University Press, 2004
13. ^ a b c Carr, Matthew (2011). "Low beta confinement in a Polywell modelled with conventional point cusp theories". Physics of Plasmas. 18 (11): 112501. Bibcode:2011PhPl...18k2501C. doi:10.1063/1.3655446.
14. ^ Park, Jaeyoung (2015-01-01). "High-Energy Electron Confinement in a Magnetic Cusp Configuration". Physical Review X. 5 (2): 021024. arXiv:. Bibcode:2015PhRvX...5b1024P. doi:10.1103/PhysRevX.5.021024.
15. ^ a b "Mirror Systems: Fuel Cycles, loss reduction and energy recovery" by Richard F. Post, BNES Nuclear fusion reactor conferences at Culham laboratory, September 1969.
16. ^ 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).
17. ^ Spalding, Ian (29 October 1971). "Cusp Containment". In Simon, Albert; Thompson, William B. Advances in Plasma Physics. 4. New York: Wiley Interscience Publishers: John Wiley & Sons. pp. 79–123. ISBN 9780471792048.
18. ^ a b c US patent 4826646, Bussard, Robert W., "Method and apparatus for controlling charged particles", issued 1989-05-02, assigned to Energy/Matter Conversion Corporation, Inc.
19. ^ a b c Grad, Harold (February 1955). Proceedings from Conference on Thermonuclear Reactions. University of California Radiation Laboratory, Livermore. p. 115.
20. ^ a b magnetohydrodynamic stability, j Berkowitz, h grad, p/376
21. ^ review paper, m g Haines, nuclear fusion, 17 4(1977)
22. ^ a b c Park, Jaeyoung; Krall, Nicholas A.; Sieck, Paul E.; Oﬀermann, Dustin T.; Skillicorn, Michael; Sanchez, Andrew; Davis, Kevin; Alderson, Eric; Lapenta, Giovanni (1 June 2014). "High Energy Electron Confinement in a Magnetic Cusp Configuration". arXiv: [physics.plasm-ph].
23. ^ Bussard, Robert W.; Krall, Nicholas A. (February 1991). Electron Leakage Through Magnetic Cusps in the Polywell Confinement Geometry (PDF) (Technical report). EMC2-DARPA. EMC2-0191-02.
24. "The Advent of Clean Nuclear Fusion: Super-performance Space Power and Propulsion", Robert W. Bussard, Ph.D., 57th International Astronautical Congress, October 2–6, 2006
25. ^ M. Scheffer (17 April 2013). "Lockheed Martin announces compact Fusion Reactor plans". FuseNet.
26. ^ "A new fusion machine design". June 2014.
27. ^ a b Gummersall, David V.; Carr, Matthew; Cornish, Scott; Kachan, Joe (2013). "Scaling law of electron confinement in a zero beta polywell device". Physics of Plasmas. 20 (10): 102701. Bibcode:2013PhPl...20j2701G. doi:10.1063/1.4824005. ISSN 1070-664X.
28. ^ a b Chen, F. (1984). Introduction to Plasma Physics and Controlled Fusion. 1. New York: Plenum. pp. 30–34. ISBN 978-0-306-41332-2.
29. ^ a b Van Norton, Roger (15 July 1961). The motion of a charged particle near a zero field point (PDF) (Technical report). New York: Magneto-Fluid Dynamics Division, Institute of Mathematical Sciences, New York University. MF23 NYO-9495.
30. ^ Chernin, D.P. (1978). "Ion losses from end-stoppered mirror trap". Nuclear Fusion. 18 (1): 47–62. doi:10.1088/0029-5515/18/1/008.
31. ^ a b c d Carr, M.; Khachan, J. (2013). "A biased probe analysis of potential well formation in an electron only, low beta Polywell magnetic field". Physics of Plasmas. 20 (5): 052504. Bibcode:2013PhPl...20e2504C. doi:10.1063/1.4804279.
32. Rider, T. H. (1995). "A general critique of inertial-electrostatic confinement fusion systems" (PDF). Physics of Plasmas. 2 (6): 1853. Bibcode:1995PhPl....2.1853R. doi:10.1063/1.871273.
33. ^ a b Rider, Todd Harrison (June 1995). Fundamental limitations on fusion systems not in equilibrium (PDF) (Thesis). Massachusetts Institute of Technology. OCLC 37885069.
34. ^ a b Bussard, Robert W.; King, Katherine E. (April 1991). Electron Recirculation in Electrostatic Multicusp Systems: 1–Confinement and Losses in Simple Power Law Wells (PDF) (Technical report). EMC2-DARPA. EMC2-0491-03.
35. ^ Bussard, Robert W.; King, Katherine E. (July 1991). Electron Recirculation in Electrostatic Multicusp Systems: 2–System Performance Scaling Of One-Dimensional "Rollover" Wells (PDF) (Technical report). EMC2-DARPA.
36. ^ "A biased probe analysis of potential well formation in an electron only, low beta Polywell magnetic field" Physics of Plasma
37. ^ E. V. Shun'ko. "Langmuir Probe in Theory and Practice". Universal Publishers, Boca Raton, Fl. 2008. p. 243. ISBN 978-1-59942-935-9.
38. ^ a b M. Carr, D. Gummersall, S. Cornish, and J. Khachan, Phys. Plasmas 18, 112501 (2011)
39. ^ "Development of the indirect drive approach to inertial confinement fusion and the target physics basis for ignition and gain" John Lindl, Physics of Plasma, 1995
40. ^ “Experimental Results from a beam direct converter at 100 kV” journal of fusion energy, Volume 2, Number 2, (1982) by R. W. MOIR, W. L. BARR.
41. Lawson, J. D. (December 1955). Some Criteria for a Power producing thermonuclear reactor (PDF) (Technical report). Atomic Energy Research Establishment, Harwell, Berkshire, U. K.
42. ^ https://www.ll.mit.edu/60thAnniversary/rider.html
43. ^ Nevins, W. M. (1995). "Can inertial electrostatic confinement work beyond the ion–ion collisional time scale?" (PDF). Physics of Plasmas. 2 (10): 3804. Bibcode:1995PhPl....2.3804N. doi:10.1063/1.871080.
44. ^ Lyman J Spitzer, "The Physics of Fully Ionized Gases" 1963
45. ^ Bussard, Robert W.; King, Katherine E. (August 1991). Bremmstrahlung Radiation Losses in Polywell™ Systems (PDF) (Technical report). EMC2-DARPA. EMC2-0891-04. Table 2, p. 6.
46. ^ 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.
47. ^ Bussard, Robert W. (19 February 1991). Collisional Equilibration (PDF) (Technical report). EMC2-DARPA. EMC2-0890-03.
48. ^ Bussard, Robert W. (19 February 1991). Core Collisional Ion Upscattering and Loss Time (PDF) (Technical report). EMC2-DARPA. EMC2-1090-03.
49. ^ Safe, Green, Clean – the p-B Polywell: A Different Kind of Nuclear, p. 66
50. ^ 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. Bibcode:2000PhPl....7.4547C. doi:10.1063/1.1310199.
51. ^ 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. Bibcode:1994PPCF...36.1255R. doi:10.1088/0741-3335/36/8/003.
52. ^ Barr, William, and Ralph Moir. "Test Results on Plasma Direct Converters." Nuclear Technology/Fusion 3 (1983): 98-111. Print.
53. ^ 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. doi:10.1515/zna-1966-0732 (inactive 2017-01-27). 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.
54. ^ Sadowski, M. (1969). "Spherical Multipole Magnets for Plasma Research". Review of Scientific Instruments. 40 (12): 1545. Bibcode:1969RScI...40.1545S. doi:10.1063/1.1683858.
55. Robert W. Bussard (December 2006). "A quick history of the EMC2 Polywell IEF concept" (PDF). Energy/Matter Conversion Corporation. Retrieved 16 June 2014.
56. ^ 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
57. ^ 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.
58. ^ a b Final Successful Tests of WB-6, EMC2 Report, currently (July 2008) not publicly available
59. ^ a b Robert W. Bussard (2006-03-29). "Inertial Electrostatic Fusion systems can now be built". fusor.net forums. Retrieved 2006-12-03.
60. ^ 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.
61. ^ "Inertial Electrostatic Confinement Project – University of Wisconsin – Madison". Iec.neep.wisc.edu. Retrieved 2013-06-17.
62. ^ 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.
63. ^ Robert L. Hirsch, "Inertial-Electrostatic Confinement of Ionized Fusion Gases", Journal of Applied Physics, v. 38, no. 7, October 1967
64. ^ 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.

65. ^ Mark Duncan. "askmar - Inertial Electrostatic Confinement Fusion".
66. ^ M. Simon (2007-10-08). "Dr. Robert W. Bussard Has Passed". Classical Values. Retrieved 2007-10-09.
67. ^ "Fusion we can believe in?" (Science subsite of MSNBC.com). MSNBC.com. December 2008. Retrieved 2016-02-16.
68. ^ "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.
69. ^ William Matthews (2007-11-06). "Fusion Researcher Bussard Dies at 79" (webpage). Online article. Defencenews.com. Retrieved 2007-11-06.
70. ^ "Strange Science Takes Time". MSNBC. 2008-01-09.
71. ^ "Fusion Quest Goes Forward". MSNBC. 2008-06-12.
72. ^ to the web by Alan Boyle (September 2008). "Fusion effort in Flux". MSNBC. Retrieved 2016-02-16.
73. ^ "A—Fusion Device Research, Solicitation Number: N6893608T0283". Federal Business Opportunities. September 2008. Retrieved 2008-10-02.
74. ^ "A—Polywell Fusion Device Research, Solicitation Number: N6893609T0011". Federal Business Opportunities. October 2008. Retrieved 2008-11-07.
75. ^ "A—Spatially Resolved Plasma Densities/Particle Energies, Solicitation Number: N6893609T0019". Federal Business Opportunities. October 2008. Retrieved 2008-11-07.
76. ^ "Found this during google search on Polywell Fusion". Talk-polywell.org. Retrieved 2013-06-17.
77. ^ "Found this during google search on Polywell Fusion" (Discussion forum). Talk-Polywell.org. October 2008. Retrieved 2008-11-07.
78. ^ "WB-6 Results Confirmed – Continuous Operation The Next Step". iecfusiontech. October 2012. Retrieved 2012-09-10.
79. ^ "A—Plasma Wiffleball, Solicitation Number: N6893609R0024". Federal Business Opportunities. January 2009. Retrieved 2009-01-26.
80. ^ "American Recovery and Reinvestment Act of 2009 – Department of Defense Expenditure Plans" (PDF Report to US Congress). Defencelink.mil. May 2009. Retrieved 2009-05-05.
81. ^ a b "Statement of work for advanced gaseous electrostatic energy (AGEE) concept exploration" (PDF). United States Navy. June 2009. Retrieved 2009-06-18.
82. ^ "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.
83. ^ a b "Project Summary – ENERGY/MATTER CONVERSION CORPORATION". Recovery.gov. Retrieved 2013-06-17.
84. ^ "Recovery.Gov Project Tracker Discussion at Talk-Polywell.org". Talk-Polywell.org. 2011-11-09. Retrieved 2012-03-31.
85. ^ "Recovery.Gov Project Tracker at Talk-Polywell.org". Talk-Polywell.org. 2011-04-29. Retrieved 2012-03-31.
86. ^ Boyle, Alan (10 May 2011). "Fusion goes forward from the fringe". MSNBC. NBCUniversal. Archived from the original on 13 May 2011. Retrieved 16 February 2016.
87. ^ "Project Summary 2011 Q3". Recovery.gov. Retrieved 2013-06-17.
88. ^ "Project Summary 2011 Q4". Recovery.gov. Retrieved 2012-03-31.
89. ^ US Federal Program Data Source
90. ^
91. ^ 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).
92. ^ "Polywell Fusion – Electric Fusion in a Magnetic Cusp" Jaeyoung Park, Friday, December 5, 2014 - 1:00pm to 2:00pm, Physics and Astronomy Building (PAB) Room 4-330, UCLA
93. ^
94. ^ Talk at University of Wisconsin Madison, Monday, June 16, 2:30 PM room 106 ERB, Jaeyoung Park
95. ^ University of Maryland, Colloquium & Seminars, "Measurement of Enhanced Confinement at High Pressure Magnetic Cusp System", Jaeyoung Park, September 9th 2014
96. ^ Park, Jaeyoung (December 16, 2014). "Polywell Fusion Electrostatic Fusion in a Magnetic Cusp (Presentation)" (PDF).
97. ^
98. ^ Boyle, Alan (13 June 2014). "Low-Cost Fusion Project Steps Out of the Shadows and Looks for Money". NBC News.
99. ^ US application 14/645306  Method and Apparatus for Confining High Energy Charged Particles In Magnetic Cusp Configuration
100. ^ "Fusion to Be Commercialised Thirty Years Faster than Expected - Civil Society's Role". Retrieved 16 May 2016.
101. ^
102. ^ "An End to Four Years of". Prometheus Fusion Perfection. 2013-07-07. Retrieved 2014-06-14.
103. ^ 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.
104. ^ "The dependence of potential well formation on the magnetic field strength and electron injection current in a polywell device" S. Cornish, D. Gummersall, M. Carr and J. Khachan Phys. Plasmas 21, 092502 (2014)
105. ^ Khachan, Joe; Carr, Matthew; Gummersall, David; Cornish, Scott; et al. (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.
106. ^ 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.
107. ^ "Agenda of 12th US-Japan Workshop on Inertial Electrostatic Confinement Fusion". 2010-10-20. Retrieved 2013-06-17.
108. ^ Santarius, John. "Summary & Thoughts" (PDF). 13th Workshop on Inertial-Electrostatic Confinement Fusion. University of Wisconsin. Retrieved 31 March 2012.
109. ^ "Iran to build nuclear fusion producing plant". Trend News Agency. 13 November 2012. Retrieved 2013-02-08.
110. ^ 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. Bibcode:2012JFuE...31..341K. doi:10.1007/s10894-011-9474-4.
111. ^ "Vlasov-Poisson calculations of electron confinement times in Polywell(TM) devices using a steady-state particle-in-cell method" (PDF). The DPP13 Meeting of The American Physical Society. Retrieved 2013-10-01.
112. ^ "Convergent Scientific, Inc. (Company Info)". Gust.com.
113. ^
114. ^ "We have to Try". The Polywell Blog. 31 January 2014.
115. ^ Talk. "Commercial Applications of IEC Devices" Web presentation, performed by Devlin Baker, 22 October 2013.
116. ^ Rogers, Joel G.; Baker, Devlin (14–16 October 2012). Designing a Small-Scale D+D Reactor (PDF). 14th US-Japan Workshop on IEC Fusion. College Park, Maryland.
117. ^ "Convergent Scientific Incorporated website". Convsci.com. Retrieved 2013-06-17.
118. ^ US application 2010284501, Rogers, Joel Guild, "Modular Apparatus for Confining a Plasma", published 2010-11-11, assigned to Rogers, Joel Guild
119. ^ 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
120. ^ 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
121. ^ Talk. "Numerical Simulations of IEC Plasmas." Web presentation, Performed by Devlin Baker, November 5, 2013
122. ^ Talk. "Commercial Applications of IEC Devices" Web presentation, performed by Devlin Baker, December 3, 2013.
123. ^ Radiant Matter fusor Accessed: 12/25/2013
124. ^ Radiant Matter fusor Accessed: 05/03/2016
125. ^ "A Green Sun (The Fusion Age)" by Charles Gray, August 7, 2011, Amazon Digital Services