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{{Short description|Fusion reactor design}}

The '''polywell''' is a proposed design for a [[fusion reactor]] using an electric and magnetic field to heat ions to fusion conditions.

The design is related to the [[fusor]], the [[high beta fusion reactor]], the [[magnetic mirror]], and the [[biconic cusp]]. 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 [[nuclear fusion|fuse]].

{{toclimit|3}}

== Mechanism ==
=== Fusor heating ===
{{main|Fusor}}
[[File:Homemade fusion reactor.JPG|thumbnail|A homemade fusor]]
[[File:Fusor running.jpg|thumbnail|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. A fuel, typically, [[deuterium]] gas, is injected into this chamber. It is heated past its [[Ionization energy|ionization temperature]], making positive [[ion]]s. 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, a [[Coulomb's law|Coulomb force]] impels 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 [[Thermal conduction|conduct]] mass and energy away from the plasma, as well as spall off metal ions into the gas, which cools it.

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

[[File:Fusor Mechanism.png|thumb|center|400px|'''Figure 1''': Illustration of the basic mechanism of fusion in fusors. (1) The fusor contains two concentric wire cages. The cathode (blue) is inside the anode (red). (2) Positive ions are attracted to the inner cathode. 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.<ref name="Tim Thorson 1996">{{Cite thesis |last=Thorson |first=Timothy A. |title=Ion flow and fusion reactivity characterization of a spherically convergent ion focus |date=1996 |institution=University of Wisconsin-Madison |oclc=615996599}}</ref><ref name="Tim Thorston 1997">{{Cite journal | doi = 10.1088/0029-5515/38/4/302| title = Fusion reactivity characterization of a spherically convergent ion focus| journal = Nuclear Fusion| volume = 38| issue = 4| pages = 495| year = 1998| last1 = Thorson | first1 = T. A. | last2 = Durst | first2 = R. D. | last3 = Fonck | first3 = R. J. | last4 = Sontag | first4 = A. C. |bibcode = 1998NucFu..38..495T | citeseerx = 10.1.1.519.2429| s2cid = 250841151}}</ref>]]

=== Diamagnetic plasma trapping ===
The Polywell is attempting to hold a [[diamagnetic]] plasma - a material which rejects the outside magnetic fields created by the electromagnets.
* Most plasma in most fusion reactors (such as [[Magnetic mirror]]s, [[tokamak]]s and [[Stellarator]]s) are considered  [[Plasma (physics)#Magnetization|magnetized]].  A Magnetized plasma occurs when the external field is so strong that it completely penetrates and controls the plasma, such that the material behavior is dominated by the external field.
* Some fusion plasmas are self-magnetized (such as [[field-reversed configuration]]s, or [[Dynomak]]s) all of which can create their own weak magnetic fields through the formation of loops of plasma currents and other structures.

Both the Polywell and the [[high beta fusion reactor]] pre-suppose that the plasma self-generated field is so strong that it will reject the outside field. 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. In June 2014 EMC2 published a preprint<ref name="Park 2014" /> providing (1) x-ray and (2) flux loop measurements that the diamagnetic effect will impact the external field.

{{wide image|Proposed Mechainism for Wiffle Ball Confinement.png|700px|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 principle|superposition]] of six rings in a box. In the center is a null point - a zone of no magnetic field.<ref name="Carr thesis 2013"/> The plasma is [[Magnetization|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.<ref name="Park 2014">{{cite journal |last1=Park |first1=Jaeyoung |last2=Krall |first2=Nicholas A. |last3=Sieck |first3=Paul E. |last4=Offermann |first4=Dustin T. |last5=Skillicorn |first5=Michael |last6=Sanchez |first6=Andrew |last7=Davis  |first7=Kevin |last8=Alderson |first8=Eric |last9=Lapenta |first9=Giovanni |arxiv=1406.0133v1 |title=High Energy Electron Confinement in a Magnetic Cusp Configuration |journal=Physical Review X |volume=5 |issue=2 |pages=021024 |date=1 June 2014 |bibcode=2015PhRvX...5b1024P |doi=10.1103/PhysRevX.5.021024 |s2cid=118478508 }}</ref>  A current is predicted<ref name="Grad 1955"/><ref name = "Berkowitz"/> 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.<ref name="Carr thesis 2013"/>}}

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).<ref name="EMC2-0191-02">{{cite tech report |last1=Bussard |first1=Robert W. |last2=Krall |first2=Nicholas A. |title=Electron Leakage Through Magnetic Cusps in the Polywell Confinement Geometry |number=EMC2-0191-02 |institution=EMC2-DARPA |date=February 1991 |url=http://www.askmar.com/Fusion_files/EMC2%20Reports%20Reformatted/EMC2-0191-02%20Electron%20Leakage.pdf |format=PDF |access-date=2014-07-01 |archive-url=https://web.archive.org/web/20161003083828/http://www.askmar.com/Fusion_files/EMC2%20Reports%20Reformatted/EMC2-0191-02%20Electron%20Leakage.pdf |archive-date=2016-10-03 |url-status=dead }}</ref><ref name="IAC2006" />

In February 2013, [[Lockheed Martin]] [[Skunk Works]] announced a new compact fusion machine, the [[high beta fusion reactor]],<ref>{{cite web | url=http://www.fusenet.eu/node/400 | title=Lockheed Martin announces compact Fusion Reactor plans |website=FuseNet | date=17 April 2013 | author=M. Scheffer}}</ref><ref>{{cite web | url=http://nextbigfuture.com/2015/08/lockheed-martin-compact-fusion-reactor.html |title=A new fusion machine design |date=June 2014}}</ref> that may be related to the biconic cusp and the polywell, and working at ''β''&nbsp;=&nbsp;1.

== Other trapping mechanisms ==
=== 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.<ref name="Mirror Systems 1969">"Mirror Systems: Fuel Cycles, loss reduction and energy recovery" by Richard F. Post, BNES Nuclear fusion reactor conferences at Culham laboratory, September 1969.</ref> 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 ===

[[File:Cusps inside the Polywell.png|thumbnail|'''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.<ref>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).</ref> This is an improvement over the simpler magnetic mirror.<ref name="Spalding 1971">{{cite book |last=Spalding |first=Ian |chapter=Cusp Containment |title=Advances in Plasma Physics |editor1-last=Simon |editor1-first=Albert |editor2-last=Thompson |editor2-first=William B. |publisher=Wiley Interscience Publishers: John Wiley & Sons |location=New York |date=29 October 1971 |volume=4 |pages=79–123 |isbn=9780471792048}}</ref> 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.<ref name="patent1989">{{cite patent | country=US | number=4826646 | status=patent | title=Method and apparatus for controlling charged particles | gdate=1989-05-02 | fdate=1985-10-29 | pridate=1985-10-29 | inventor=Bussard, Robert W. | assign1=Energy/Matter Conversion Corporation, Inc.}}</ref> In 1955, [[Harold Grad]] theorized that a [[Beta (plasma physics)|high-beta]] plasma pressure combined with a cusped magnetic field would improve plasma confinement.<ref name="Grad 1955">{{Cite conference
 |last=Grad
 |first=Harold
 |title=Proceedings from Conference on Thermonuclear Reactions
 |date=February 1955
 |location=University of California Radiation Laboratory, Livermore
 |page=115
}}</ref> A [[Diamagnetism|diamagnetic]] plasma rejects the external fields and plugs the cusps. This system would be a much better trap.

Cusped confinement was explored theoretically<ref name = "Berkowitz">magnetohydrodynamic stability, j Berkowitz, h grad, p/376</ref> and experimentally.<ref>review paper, m g Haines, nuclear fusion, 17 4(1977)</ref> However, most cusped experiments failed and disappeared from national programs by 1980.

=== Beta in magnetic traps ===
[[File:Polywell Magnetic Field.jpg|thumbnail|'''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. It can be defined separately for electrons and ions. The polywell concerns itself only for the electron beta, whereas the ion beta is of greater interest within Tokamak and other neutral-plasma machines. The two vary by a very large ratio, because of the enormous difference in mass between an electron and any ion. Typically, in other devices the electron beta is neglected, as the ion beta determines more important plasma parameters. This is a significant point of confusion for scientists more familiar with more 'conventional' fusion plasma physics.

Note that for the electron beta, only the electron [[number density]] and temperature are used, as both of these, but especially the latter, can vary significantly from the ion parameters at the same location.<ref>{{cite book |last=Wesson |first=J. |title=Tokamaks |edition=3rd |page=115 |publisher=Oxford University Press |year=2004}}</ref>

<math display="block">\beta_e = \frac{p}{p_{mag}} = \frac{n_e k_B T_e}{(B^2/2\mu_0)}</math>

Most experiments on polywells involve [[Beta (plasma physics)|low-beta plasma]] regimes (where ''β'' < 1),<ref name="Low beta confinement in a Polywell modeled with conventional point cusp theories" /> where the plasma [[pressure]] is weak compared to the [[magnetic pressure]]. Several models describe magnetic trapping in polywells.{{Citation needed|date=July 2014}} 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.<ref>{{Cite journal|title = High-Energy Electron Confinement in a Magnetic Cusp Configuration|journal = Physical Review X|date = 2015-01-01|volume = 5|issue = 2|pages = 021024|doi = 10.1103/PhysRevX.5.021024|first = Jaeyoung|last = Park|arxiv = 1406.0133 |bibcode = 2015PhRvX...5b1024P |s2cid = 118478508}}</ref>

== Design ==
[[File:Polywell With Externally Mounted Rings.png|thumbnail|'''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]],<ref name="Lavrentiev">{{Cite conference
 | last=Lavrent'ev
 | first=O. A
 | title=Electrostatic and Electromagnetic High-Temperature Plasma Traps
 | conference=Conference on Electrostatic and Electromagnetic Confinement of Plasmas and the Phenomenology of Relativistic Electron Beams
 | location=New York City
 | date=4–7 March 1974
 | publication-date=8 May 1975
 | journal=Annals of the New York Academy of Sciences
 | publisher=New York Academy of Sciences
 | volume=251
 | pages=152–178
 | url=http://inis.iaea.org/search/search.aspx?orig_q=RN:7226297}} As cited by Todd H. Rider in [http://dspace.mit.edu/bitstream/handle/1721.1/29869/31763419.pdf "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".</ref> 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<ref name="patent1992">{{Cite patent | country=US | number=5160695 | status=patent | title=Method and apparatus for creating and controlling nuclear fusion reactions | gdate=1992-11-03 | fdate=1990-02-08 | pridate=1990-02-08 | invent1=Bussard, Robert W. | assign1=Qed, Inc.}}</ref>
* A set of positively charged [[electromagnet]] coils arranged in a [[polyhedron]]. The most common arrangement is a six sided [[cube]]. The six [[Magnet|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 gun]]s 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 probe]]s.<ref name="quasi" /><ref name="google"/><ref name="Carr thesis 2013" /> 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 [[Thermal conduction|conduction]] losses, and improves the overall performance of the machine.<ref>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.</ref> The electrons act as a negative [[electric potential|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 [[Work (physics)|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]].<ref name="quasi">{{cite journal
 |display-authors= 4
 |last1= Krall |first1= Nicholas A.
 |last2= Coleman |first2= Michael
 |last3= Maffei |first3= Kenneth C.
 |last4= Lovberg |first4= John A.
 |last5= Jacobsen |first5=R. A.
 |last6= Bussard |first6= Robert W.
 |title= Forming and Maintaining a Potential Well in a Quasispherical Magnetic Trap
 |journal= Physics of Plasmas
 |volume= 2
 |issue= 1
 |date= 18 April 1994
 |publication-date= January 1995
 |pages= 146–158
 |url=http://www.askmar.com/Fusion_files/Forming%20and%20Maintaining.pdf
 |doi= 10.1063/1.871103|bibcode = 1995PhPl....2..146K }}</ref><ref name="tech">{{cite journal
 |last= Bussard | first = Robert W.
 |title= Some Physics Considerations of Magnetic Inertial Electrostatic Confinement: A New Concept for Spherical Converging Flow Fusion
 |journal= Fusion Science and Technology
 |volume= 19
 |issue= 2
 |date= March 1991
 |pages= 273–293
 |url=http://www.askmar.com/Fusion_files/Some%20Physics%20Considerations.pdf
 | doi = 10.13182/FST91-A29364
 | bibcode = 1991FuTec..19..273B
 }}</ref><ref name="tech2">{{cite journal
 |last= Krall | first = Nicholas A.
 |title= The Polywell: A Spherically Convergent Ion Focus Concept
 |journal= Fusion Science and Technology
 |volume= 22
 |issue= 1
 |date= August 1992
 |pages= 42–49
 |url=http://www.askmar.com/Fusion_files/Polywell%20Ion%20Focus%20Concept.pdf
 | doi = 10.13182/FST92-A30052
 }}</ref>

== Other behavior ==

=== Single-electron motion ===
[[File:Single Electron Motion Illustration.jpg|thumbnail|'''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 [[Bremsstrahlung|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.<ref name="Low beta confinement in a Polywell modeled with conventional point cusp theories">{{cite journal | doi = 10.1063/1.3655446 | title=Low beta confinement in a Polywell modelled with conventional point cusp theories | journal=Physics of Plasmas | date=2011 | volume=18 | issue=11 | pages=112501 | first=Matthew | last=Carr|bibcode = 2011PhPl...18k2501C | url=https://zenodo.org/record/1244053 | type=Submitted manuscript }}</ref><ref name="GummersallCarr2013">{{cite journal|last1=Gummersall|first1=David V.|last2=Carr|first2=Matthew|last3=Cornish|first3=Scott|last4=Kachan|first4=Joe|title=Scaling law of electron confinement in a zero beta polywell device|journal=Physics of Plasmas|volume=20|issue=10|year=2013|pages=102701|issn=1070-664X|doi=10.1063/1.4824005|bibcode = 2013PhPl...20j2701G }}</ref> 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.<ref name="F. Chen 1984 pp. 30">{{cite book|first=F. |last=Chen |title=Introduction to Plasma Physics and Controlled Fusion |publisher=Plenum |location=New York |date=1984 |volume=1 |pages=30–34 |isbn=978-0-306-41332-2}}</ref><ref name="ReferenceA">{{cite tech report |first=Roger |last=Van Norton |title=The motion of a charged particle near a zero field point |number=MF23 NYO-9495 |institution=Magneto-Fluid Dynamics Division, Institute of Mathematical Sciences, New York University |location=New York |date=15 July 1961 |url=https://archive.org/details/motionofchargedp00vann |format=PDF}}</ref><ref name="P Chernnin 1978">{{cite journal | doi = 10.1088/0029-5515/18/1/008 | title=Ion losses from end-stoppered mirror trap | journal=Nuclear Fusion | date=1978 | volume=18 | issue=1 | pages=47–62 | first=D.P. | last=Chernin| bibcode=1978NucFu..18...47C | s2cid=120037549 }}</ref> Electron trapping has been measured in polywells with [[Langmuir probe]]s.<ref name="quasi" /><ref name="google"/><ref name="Carr thesis 2013" />

The polywell attempts to confine the [[ion]]s and [[electron]]s through two different means, borrowed from [[fusor]]s and [[magnetic mirror]]s. The electrons are easier to confine magnetically because they have so much less mass than the ions.<ref name="2013AussyWork" /> 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.<ref name = "Rider95Paper"/><ref name="Rider95Thesis"/> Electrons or ions move through the device without striking a surface, reducing [[Thermal conduction|conduction]] losses. Bussard stressed this; specifically emphasizing that electrons need to move through all cusps of the machine.<ref name="EMC2-0491-03">{{cite tech report |last1=Bussard |first1=Robert W. |last2=King |first2=Katherine E. |title=Electron Recirculation in Electrostatic Multicusp Systems: 1–Confinement and Losses in Simple Power Law Wells |number=EMC2-0491-03 |institution=EMC2-DARPA |date=April 1991 |url=http://www.askmar.com/Fusion_files/EMC2%20Reports/EMC2-0491-03%20Electron%20Recirculation.pdf |format=PDF}}</ref><ref name="EMC2-0791-04">{{cite tech report |last1=Bussard |first1=Robert W. |last2=King |first2=Katherine E. |title=Electron Recirculation in Electrostatic Multicusp Systems: 2–System Performance Scaling Of One-Dimensional "Rollover" Wells |institution=EMC2-DARPA |date=July 1991 |url=http://www.askmar.com/Fusion_files/EMC2%20Reports/EMC2-0791-04%201991%20Electron%20Recirculation.pdf |format=PDF}}</ref>

[[File:Rider model of ion energies in the polywell.png|thumbnail|'''Figure 5''': Thermalized plasma ion energy distribution inside a polywell.<ref name = "Rider95Paper"/> 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 ===

[[File:Model of electron energy in Polywell (Carr, 2013).png|thumbnail|'''Figure 6''': Non-thermalized plasma energy distribution inside a polywell.<ref>"A biased probe analysis of potential well formation in an electron only, low beta Polywell magnetic field" Physics of Plasma</ref> 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 [[Distribution function (physics)|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 [[Current–voltage characteristic|I-V Curve]].<ref>E. V. Shun'ko. "Langmuir Probe in Theory and Practice". Universal Publishers, Boca Raton, Fl. 2008. p. 243. {{ISBN|978-1-59942-935-9}}.</ref> From this signal, the energy distribution can be calculated. The energy distribution both drives and is driven by several physical rates,<ref name = "Rider95Paper"/> 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|date=October 2014}}
* 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 [[Maxwell–Boltzmann distribution|bell curve]] distribution;<ref name = "Rider95Paper"/> that the plasma is [[Plasma (physics)#Thermal vs. non-thermal plasmas|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<ref name = "Rider95Paper"/> the ion distribution is shown in Figure 5.

Supporters modeled a [[nonthermal plasma]].<ref name="EMC2-0491-03"/> The justification is the high amount of scattering in the device center.<ref name = "Carr13">M. Carr, D. Gummersall, S. Cornish, and J. Khachan, Phys. Plasmas 18, 112501 (2011)</ref> 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.<ref name = "Carr13"/> Bussard argued that constant electron injection would have the same effect.<ref name="patent1992"/> Such a distribution would help maintain a negative voltage in the center, improving performance.<ref name="patent1992"/>

== Considerations for net power ==

=== Fuel type ===

[[File:Fusion rxnrate.svg|thumbnail|'''Figure 7''': Plot of the cross section of different fusion reactions.]]

[[Nuclear fusion]] refers to [[nuclear reaction]]s that combine lighter [[atomic nucleus|nuclei]] to become heavier nuclei. All [[chemical element]]s can be fused; for elements with fewer protons than iron, this process changes [[Mass–energy equivalence|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 (physics)|cross section]] of the fuel,<ref>"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</ref> 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 ([[kiloelectronvolt]]s), or about 45 million [[kelvin]]s. The Polywell would achieve this by accelerating an ion with a charge of [[Elementary charge|1]] down a 4,000 volt electric field. The high cost, short [[half-life]] and [[radioactive|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 therefore produces radioactive waste. Bussard's choice was to fuse [[boron-11]] with protons; this reaction is [[Aneutronic fusion|aneutronic]] (does not produce neutrons). An advantage of p-<sup>11</sup>B 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<ref>"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.</ref> against 80–90% theoretical efficiency.<ref name="Mirror Systems 1969" />

=== Lawson criterion ===
{{Main|Lawson criterion}}

The energy generated by fusion inside a hot plasma cloud can be found with the following equation:<ref name="Lawson">{{Cite tech report
 |last        = Lawson
 |first       = J. D.
 |title       = Some Criteria for a Power producing thermonuclear reactor
 |date        = December 1955
 |issue       = A.E.R.E. GP/R 1807
 |institution = Atomic Energy Research Establishment, Harwell, Berkshire, U. K.
 |url         = http://www.efda.org/wpcms/wp-content/uploads/2012/10/dec05-aere-gpr1807.pdf
 |format      = PDF
}}{{Dead link|date=September 2018 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>

<math display="block">P_\text{fusion} = n_A n_B \langle \sigma v_{A,B} \rangle E_\text{fusion}</math>

where:
* <math>P_\text{fusion}</math> is the fusion power density (energy per time per volume),
* ''n'' is the number density of species A or B (particles per volume),
* <math>\langle \sigma v_{A,B} \rangle</math> 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 [[Thermal conduction|conduction]] and [[radiation]].<ref name = "Lawson"/> Conduction is when [[ion]]s, [[electron]]s or [[neutral particle|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:

{{block indent|1=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<ref name="Lawson" /> based on a [[Maxwell–Boltzmann distribution|Maxwellian]] cloud.<ref name="Lawson" />

However, the Lawson criterion does not apply for Polywells if Bussard's conjecture that the plasma is nonthermal is correct. [[John D. Lawson (scientist)|Lawson]] stated in his founding report:<ref name="Lawson" /> "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 ==
There are several general criticisms of the Polywell:
* The heating mechanism breaks the quasi-neutral assumption.  It is not easy or possible to concentrate negative charge robustly or for any long period.
* The plasma does not behave diamagnetically as presupposed. This challenges the basic trapping effect.
* Without a solid heating method, the plasma loses huge amounts of energy to radiation, becoming too cold to fuse (see Rider work below).
* With ions flying in from all directions, there is a buildup in angular momentum, leading to lots of ions being scattered out of the trap (see Nevins' work below).

=== Rider critique ===
Todd Rider (a biological engineer and former student of plasma physics)<ref>{{Cite web |url=https://www.ll.mit.edu/60thAnniversary/rider.html |title=60th Anniversary Celebration |access-date=2017-02-06 |archive-url=https://web.archive.org/web/20170314223354/http://www.ll.mit.edu/60thAnniversary/rider.html |archive-date=2017-03-14 |url-status=dead }}</ref> calculated that [[bremsstrahlung|X-ray radiation]] losses with this fuel would exceed fusion power production by at least 20%. Rider's model used the following assumptions:<ref name="Rider95Paper">{{Cite journal | doi = 10.1063/1.871273| title = A general critique of inertial-electrostatic confinement fusion systems| journal = Physics of Plasmas| volume = 2| issue = 6| pages = 1853–1872| year = 1995| last1 = Rider | first1 = T. H. | url = http://fsl.ne.uiuc.edu/IEC/Rider,%20Phys.ofPlasmas1995.pdf|bibcode = 1995PhPl....2.1853R | hdl = 1721.1/29869| s2cid = 12336904| hdl-access = free}}</ref><ref name="Rider95Thesis">{{Cite thesis |last=Rider |first=Todd Harrison |title=Fundamental limitations on fusion systems not in equilibrium |url=http://dspace.mit.edu/bitstream/1721.1/11412/1/33227017.pdf |date=June 1995 |publisher=Massachusetts Institute of Technology |oclc=37885069 |url-status=dead |archive-url=https://web.archive.org/web/20070629215546/http://dspace.mit.edu/bitstream/1721.1/11412/1/33227017.pdf |archive-date=2007-06-29 }}</ref>
* The plasma was [[Plasma (physics)|quasineutral]]. Therefore, positives and negatives equally mixed together.<ref name = "Rider95Paper"/>
* The fuel was evenly mixed throughout the volume.<ref name="Rider95Paper"/>
* The plasma was isotropic, meaning that its behavior was the same in any given direction.<ref name="Rider95Paper"/>
* The plasma had a uniform energy and temperature throughout the cloud.<ref name="Rider95Paper"/>
* The plasma was an unstructured Gaussian sphere, with a strongly converged core that represented a small (~1%) part of the total volume.<ref name = "Rider95Paper"/> Nevins challenged this assumption, stating that the particles would build up [[angular momentum]], causing the dense core to degrade.<ref name="Nevins95">{{Cite journal | doi = 10.1063/1.871080| title = Can inertial electrostatic confinement work beyond the ion–ion collisional time scale?| journal = Physics of Plasmas| volume = 2| issue = 10| pages = 3804–3819| year = 1995| last1 = Nevins | first1 = W. M.| url = http://fsl.ne.uiuc.edu/iec/nevins,%20phys.of%20plasmas(1995).pdf|bibcode = 1995PhPl....2.3804N | osti = 41400}}</ref> The loss of density inside the core would reduce fusion rates.
* The potential well was broad and flat.<ref name="Rider95Paper"/>

Based on these assumptions, Rider used general equations<ref>Lyman J Spitzer, "The Physics of Fully Ionized Gases" 1963</ref> 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 [[Bremsstrahlung|X-ray radiation]] and the fusion rate.<ref name="Rider95Paper"/> His conclusions were that the device suffered from "fundamental flaws".<ref name="Rider95Paper"/>

By contrast, Bussard argued<ref name="IAC2006"/> 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.<ref name="EMC2-0891-04">{{cite tech report |last1=Bussard |first1=Robert W. |last2=King |first2=Katherine E. |title=Bremmstrahlung Radiation Losses in Polywell Systems |number=EMC2-0891-04 |institution=EMC2-DARPA |date=August 1991 |url=http://www.askmar.com/Fusion_files/EMC2%20Reports/EMC2-0891-04%201991%20Bremmstrahlung%20Radiation%20Losses.pdf |format=PDF |quote=Table 2, p. 6. |access-date=2007-09-06 |archive-url=https://web.archive.org/web/20110914021318/http://www.askmar.com/Fusion_files/EMC2%20Reports/EMC2-0891-04%201991%20Bremmstrahlung%20Radiation%20Losses.pdf |archive-date=2011-09-14 |url-status=dead }}</ref><ref name="EMC2-1291-02">{{cite tech report |last1=Bussard |first1=Robert W. |last2=King |first2=Katherine E. |title=Bremsstrahlung and Synchrotron Radiation Losses in Polywell Systems |number=EMC2-1291-02 |institution=EMC2-DARPA |date=5 December 1991 |url=http://www.askmar.com/Fusion_files/EMC2%20Reports/EMC2-1291-02%201991%20Radiation%20Losses.pdf |format=PDF}}</ref> According to Bussard the high speed and therefore low cross section for [[Coulomb collision]]s of the ions in the core makes [[thermalisation|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.<ref name="EMC2-0890-03">{{cite tech report |last1=Bussard |first1=Robert W. |title=Collisional Equilibration |number=EMC2-0890-03 |institution=EMC2-DARPA |date=19 February 1991 |url=http://www.askmar.com/Fusion_files/EMC2%20Reports%20Reformatted/EMC2-0890-03%20Collisional%20Equilibration.pdf |format=PDF}}</ref><ref name="EMC2-1090-03">{{cite tech report |last1=Bussard |first1=Robert W. |title=Core Collisional Ion Upscattering and Loss Time |number=EMC2-1090-03 |institution=EMC2-DARPA |date=19 February 1991 |url=http://www.askmar.com/Fusion_files/EMC2%20Reports%20Reformatted/EMC2-1090-03%20Core%20Collisional%20Ion.pdf |format=PDF}}</ref> Bussard calculated that a polywell reactor with a radius of 1.5 meters would produce net power fusing [[deuterium]].<ref>{{Cite web |url=https://n3172061.readyexchange.net/lampoil/Fusor/Shared%20Documents/SGCPolywell.pdf |title=''Safe, Green, Clean – the p-B Polywell: A Different Kind of Nuclear'', p. 66 |access-date=2012-10-10 |archive-url=https://web.archive.org/web/20131012055737/https://n3172061.readyexchange.net/lampoil/Fusor/Shared%20Documents/SGCPolywell.pdf |archive-date=2013-10-12 |url-status=dead }}</ref>

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.<ref name="Chacon 2000">{{Cite journal | doi = 10.1063/1.1310199| title = Energy gain calculations in Penning fusion systems using a bounce-averaged Fokker–Planck model| journal = Physics of Plasmas| volume = 7| issue = 11| pages = 4547| year = 2000| last1 = Chacón | first1 = L.| last2 = Miley | first2 = G. H.| last3 = Barnes | first3 = D. C.| last4 = Knoll | first4 = D. A.| url = http://fsl.ne.uiuc.edu/IEC/Miley_Phys.ofPlasmas%28Dec%202000%29.pdf|bibcode = 2000PhPl....7.4547C }}</ref>

=== Energy capture ===

It has been proposed that energy may be extracted from polywells using [[Rankine cycle|heat capture]] or, in the case of aneutronic fusion like D-<sup>3</sup>He or ''p''-<sup>11</sup>B, [[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 particles' 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.<ref>{{Cite journal | doi = 10.1088/0741-3335/36/8/003| title = Generic issues for direct conversion of fusion energy from alternative fuels| journal = Plasma Physics and Controlled Fusion| volume = 36| issue = 8| pages = 1255| year = 1994| last1 = Rosenbluth | first1 = M. N. | last2 = Hinton | first2 = F. L. |bibcode = 1994PPCF...36.1255R | s2cid = 250805049}}</ref> In experiments, direct conversion has demonstrated a conversion efficiency of 48%.<ref>Barr, William, and Ralph Moir. "Test Results on Plasma Direct Converters". ''Nuclear Technology/Fusion'' 3 (1983): 98–111. Print.</ref>

== History ==

In the late 1960s several investigations studied polyhedral magnetic fields as a possibility to confine a fusion plasma.<ref>{{Cite journal
 |last1=Keller
 |first1=R.
 |last2=Jones
 |first2=I. R.
 |title=Confinement d'un Plasma par un Système Polyédrique à Courant Alternatif
 |language=fr
 |trans-title=Plasma confinement by a polyhedral system with alternating current
 |date=June 1966
 |journal=Zeitschrift für Naturforschung A
 |volume=21
 |issue=7
 |pages=1085–1089
 |quote=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.|bibcode = 1966ZNatA..21.1085K |doi = 10.1515/zna-1966-0732 |s2cid=93253557
 |doi-access=free
 }}</ref><ref>{{Cite journal | doi = 10.1063/1.1683858| title = Spherical Multipole Magnets for Plasma Research| journal = Review of Scientific Instruments| volume = 40| issue = 12| pages = 1545–1549| year = 1969| last1 = Sadowski | first1 = M.|bibcode = 1969RScI...40.1545S }}</ref> 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.<ref name="Lavrentiev" /> The idea was picked up by [[Robert Bussard]] in 1983. His 1989 patent application cited Lavrentiev,<ref name="patent1989" /> although in 2006 he appears to claim to have (re)discovered the idea independently.<ref name="quick">{{cite web
 |url= http://www.emc2fusion.org/QuikHstryOfPolyPgm0407.pdf
 |title= A quick history of the EMC2 Polywell IEF concept
 |author= Robert W. Bussard
 |access-date= 16 June 2014
 |date=December 2006
 |publisher= Energy/Matter Conversion Corporation
}}</ref>

=== HEPS ===

Research was funded first by the [[Defense Threat Reduction Agency]] beginning in 1987 and later by [[DARPA]].<ref name=google/>{{rp|32:30}} This funding resulted in a machine known as the high energy power source (HEPS) experiment. It was built by Directed Technologies Inc.<ref name="autogenerated1995">"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</ref> This machine was a large (1.9&nbsp;m across) machine, with the rings outside the vacuum chamber.<ref name=google/>{{rp|32:33}} This machine performed poorly because the [[magnetic field]]s sent [[electron]]s into the walls, driving up conduction losses. These losses were attributed to poor electron injection.<ref name="autogenerated1995"/> The [[United States Navy|US Navy]] began providing low-level funding to the project in 1992.<ref name="clean">{{cite web
 |url          = http://www.fusor.net/board/getfile.php?bn=fusor_announce&att_id=2493
 |title        = Inertial electrostatic fusion (IEF): A clean energy future
 |author       = Posted to the web by Robert W. Bussard
 |access-date   = 2006-12-03
 |format       = [[Microsoft Word]] document
 |publisher    = Energy/Matter Conversion Corporation
 |archive-url  = https://web.archive.org/web/20070928151554/http://www.fusor.net/board/getfile.php?bn=fusor_announce&att_id=2493
 |archive-date = 2007-09-28
 |url-status     = dead
}}</ref> [[Nicholas Krall|Krall]] published results in 1994.<ref name="autogenerated1995"/>

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 [[United States Congress|US Congress]] 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<ref name="google"/><ref name="patent1989" /> 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.<ref name="quick" /> In 1993, it received a grant from the [[Electric Power Research Institute]].<ref name="quick" /> In 1994, The company received small grants from [[NASA]] and [[LANL]].<ref name="quick"/> Starting in 1999, the company was primarily funded by the US Navy.<ref name="quick"/>

WB-1 had six conventional [[magnet]]s in a cube. This device was 10&nbsp;cm across.<ref name="quick"/> 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.<ref name="google"/> The next device, PXL-1, was built in 1996 and 1997. This machine was 26&nbsp;cm across and used flatter rings to generate the field.<ref name="quick"/> 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&nbsp;cm in radius.<ref name="quick"/>

Initial difficulties in spherical electron confinement led to the 2005 research project's termination. However, Bussard reported a fusion rate of 10<sup>9</sup> per second running D-D fusion reactions at only 12.5 kV (based on [[neutron detection|detecting]] nine neutrons in five tests,<ref name="IAC2006">[http://www.askmar.com/ConferenceNotes/2006-9%20IAC%20Paper.pdf "The Advent of Clean Nuclear Fusion: Super-performance Space Power and Propulsion"] {{Webarchive|url=https://web.archive.org/web/20110929075949/http://www.askmar.com/ConferenceNotes/2006-9%20IAC%20Paper.pdf |date=2011-09-29 }}, Robert W. Bussard, Ph.D., 57th International Astronautical Congress, October 2–6, 2006</ref><ref name="lab_notes">''Final Successful Tests of WB-6'', EMC2 Report, currently (July 2008) not publicly available<!-- {{
cite web
 |title      = Final Successful Tests of WB-6
 |author     = EMC2 Report
 |url        = http://ecow.engr.wisc.edu/cgi-bin/getbig/ne/527/anderson/notes/bussard_wb6rpt080604fnl0107.pdf
 |accessdate = 2007-11-08
}}{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }} --></ref> 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.<ref name="fusor.net">{{cite web
 |title       = Inertial Electrostatic Fusion systems can now be built
 |author      = Robert W. Bussard
 |date        = 2006-03-29
 |work        = fusor.net forums
 |url         = http://www.fusor.net/board/view.php?site=fusor&bn=fusor_announce&key=1143684406
 |access-date  = 2006-12-03
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20070224220614/http://www.fusor.net/board/view.php?site=fusor&bn=fusor_announce&key=1143684406
 |archive-date = 2007-02-24
}}</ref><ref name="randi">{{cite web
 |title= Fusion, eh?
 |author= SirPhilip (posting an e-mail from "RW Bussard")
 |date= 2006-06-23
 |work= [[James Randi Educational Foundation]] forums
 |url= http://forums.randi.org/showthread.php?t=58665#27
 |access-date= 2006-12-03
 }}{{Dead link|date=May 2025 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> By comparison, researchers at [[University of Wisconsin–Madison]] reported a neutron rate of up to 5 billion per second at voltages of 120 kV from an electrostatic fusor without magnetic fields.<ref>{{cite web|url=http://iec.neep.wisc.edu/results.php |title=Inertial Electrostatic Confinement Project – University of Wisconsin – Madison |publisher=Iec.neep.wisc.edu |access-date=2013-06-17}}</ref>

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 (plasma physics)|beta]] conditions), and the maximum attainable magnetic field would scale with the radius. Under those conditions, the fusion power produced would scale with [[Power law|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,<ref>
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 ''B''<sup>2</sup>). The ''R''<sup>7</sup> scaling results from multiplying the fusion power density (proportional to density squared, or ''B''<sup>4</sup>) with the volume (proportional to''R''<sup>3</sup>). 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.</ref> if true, it would enable a model only ten times larger to be useful as a fusion power plant.<ref name="IAC2006"/>

==== WB-6 ====

Funding became tighter and tighter. According to [[Bussard]], "The funds were clearly needed for the more important [[2003 Invasion of Iraq|War in Iraq]]."<ref name="randi"/> An extra $900k of [[Office of Naval Research]] funding allowed the program to continue long enough to reach WB-6 testing in November 2005. WB-6 had rings with circular cross sections that space apart at the joints. This reduced the metal surface area unprotected by magnetic fields. These changes dramatically improved system performance, leading to more electron recirculation and better electron confinement, in a progressively tighter core. This machine produced a fusion rate of 10<sup>9</sup> per second. This is based on a total of nine neutrons in five tests, giving a wide confidence interval.<ref name="IAC2006"/><ref name="lab_notes"/> Drive voltage on the WB-6 tests was about 12.5 kV, with a resulting potential well depth of about 10 kV.<ref name="IAC2006"/> Thus deuterium ions could have a maximum of 10 keV of kinetic energy in the center. By comparison, a [[Fusor]] running deuterium fusion at 10 kV would produce a fusion rate almost too small to detect. [[Robert L. Hirsch|Hirsch]] reported a fusion rate this high only by driving his machine with a 150 kV drop between the inside and outside cages.<ref>Robert L. Hirsch, "Inertial-Electrostatic Confinement of Ionized Fusion Gases", Journal of Applied Physics, v. 38, no. 7, October 1967</ref> Hirsch also used [[deuterium]] and [[tritium]], a much easier fuel to fuse, because it has a higher [[nuclear cross section]].

While the WB-6 pulses were sub-millisecond, Bussard felt the physics should represent steady state. A last-minute test of WB-6 ended prematurely when the insulation on one of the hand-wound [[electromagnet]]s burned through, destroying the device.

==== Efforts to restart funding ====

With no more funding during 2006, the project was stalled. This ended the US Navy's [[Robert Bussard#Appeal for funding|11-year embargo on publication and publicizing]] between 1994 and 2005.<ref>There is this clause in the [https://www.neco.navy.mil/upload/N68936/N6893609R0024RFP.pdf "Solicitation, Offer and Award"] {{webarchive|url=https://web.archive.org/web/20110722210109/https://www.neco.navy.mil/upload/N68936/N6893609R0024RFP.pdf |date=2011-07-22 }} for the "plasma wiffleball development project", [https://www.fbo.gov/index?s=opportunity&mode=form&id=754cf58a3fd1b02abfe8521ff4f488a7&tab=core&_cview=1&cck=1&au=&ck= awarded] on March 3, 2009, to Matter Conversion Corporation:
<blockquote>
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.
</blockquote></ref> The company's military-owned equipment was transferred to [[SpaceDev]], which hired three of the team's researchers.<ref name="randi"/> After the transfer, Bussard tried to attract new investors, giving talks trying to raise interest in his design. He gave a talk at [[Google]] entitled, "Should Google Go Nuclear?"<ref name="google">{{cite web |url= https://www.youtube.com/watch?v=FhL5VO2NStU |title= Should Google Go Nuclear? Clean, cheap, nuclear power (no, really) |author=Robert Bussard (lecturer) |access-date= 2006-12-03 |date= 2006-11-09 |format= [[Adobe Flash|Flash]] video|work= Google Tech Talks }}</ref> He also presented and published an overview at the 57th [[International Astronautical Congress]] in October 2006.<ref name="IAC2006"/> He presented at an internal [[Yahoo!]] Tech Talk on April 10, 2007.<ref>{{cite web|url=http://www.askmar.com/Fusion.html|title=askmar - Inertial Electrostatic Confinement Fusion|author=Mark Duncan|access-date=2007-08-21|archive-url=https://web.archive.org/web/20080723182449/http://www.askmar.com/Fusion.html|archive-date=2008-07-23|url-status=dead}}</ref> and spoke on the internet talk radio show ''The Space Show'' on May 8, 2007. Bussard had plans for WB-8 that was a higher-order polyhedron, with 12 electromagnets. However, this design was not used in the actual WB-8 machine.

Bussard believed that the WB-6 machine had demonstrated progress and that no intermediate-scale models would be needed. He noted, "We are probably the only people on the planet who know how to make a real net power clean fusion system"<ref name="fusor.net"/> He proposed to rebuild WB-6 more robustly to verify its performance. After publishing the results, he planned to convene a conference of experts in the field in an attempt to get them behind his design. The first step in that plan was to design and build two more small scale designs (WB-7 and WB-8) to determine which full scale machine would be best. He wrote "The only small scale machine work remaining, which can yet give further improvements in performance, is test of one or two WB-6-scale devices but with "square" or polygonal coils aligned approximately (but slightly offset on the main faces) along the edges of the vertices of the polyhedron. If this is built around a [[truncated dodecahedron]], near-optimum performance is expected; about 3–5 times better than WB-6."<ref name="IAC2006"/> Bussard died on October 6, 2007, from [[multiple myeloma]] at age 79.<ref>{{cite web|title=''Dr. Robert W. Bussard Has Passed''|url=http://www.classicalvalues.com/archives/2007/10/dr_robert_w_bus.html|date=2007-10-08|access-date=2007-10-09|work=Classical Values|author=M. Simon}}</ref>

In 2007, [[Steven Chu]], [[Nobel Prize in Physics|Nobel laureate]] and former [[United States Secretary of Energy]], answered a question about polywell at a tech talk at [[Google]]. He said: "So far, there's not enough information so [that] I can give an evaluation of the probability that it might work or not...But I'm trying to get more information."<ref>{{cite web
 |url= http://cosmiclog.nbcnews.com/_news/2008/12/16/4351315-fusion-we-can-believe-in |title= Fusion we can believe in? |access-date=2016-02-16|date=December 2008
 |format= Science subsite of MSNBC.com |publisher= MSNBC.com}}</ref>

==== Bridge funding 2007–2009 ====

=====Reassembling team=====

In August 2007, EMC2 received a $1.8M U.S. Navy contract.<ref name="New Energy and Fuel">{{cite web |url= http://newenergyandfuel.com/http://newenergyandfuel/com/2007/08/23/funding-continues-for-bussards-fusion-reactor/ |title= Funding Continues for Bussard's Fusion Reactor |date= 2007-08-27 |publisher= New Energy and Fuel |access-date= 2008-06-11 |archive-url= https://web.archive.org/web/20111031121724/http://newenergyandfuel.com/http://newenergyandfuel/com/2007/08/23/funding-continues-for-bussards-fusion-reactor/ |archive-date= 2011-10-31 |url-status= dead }} Note that this source is a blog and not necessarily reliable.</ref> Before Bussard's death in October, 2007,<ref name="defencenews">{{cite web |url= http://www.defensenews.com/story.php?F=3139619&C=america |archive-url= https://archive.today/20130102085811/http://www.defensenews.com/story.php?F=3139619&C=america |url-status= dead |archive-date= 2013-01-02 |title= Fusion Researcher Bussard Dies at 79 |author= William Matthews |access-date= 2007-11-06 |date= 2007-11-06 |format= webpage |work= Online article |publisher= Defencenews.com }}</ref> Dolly Gray, who co-founded EMC2 with Bussard and served as its president and CEO, helped assemble scientists in [[Santa Fe, New Mexico|Santa Fe]] to carry on. The group was led by Richard Nebel and included Princeton trained physicist Jaeyoung Park. Both physicists were on leave from [[LANL]]. The group also included Mike Wray, the physicist who ran the key 2005 tests; and Kevin Wray, the computer specialist for the operation.

=====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.<ref name="MSNBC - CosmicLog">{{cite web |url= http://cosmiclog.nbcnews.com/_news/2008/01/09/4351271-strange-science-takes-time |title=Strange Science Takes Time|date= 2008-01-09| publisher = MSNBC}}</ref><ref name="MSNBC - CosmicLog2">{{cite web |url= http://cosmiclog.nbcnews.com/_news/2008/06/12/4350196-fusion-quest-goes-forward |title=Fusion Quest Goes Forward|date= 2008-06-12 |publisher= MSNBC}}</ref> 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.<ref>{{cite web |url= http://cosmiclog.nbcnews.com/_news/2008/08/28/4350263-fusion-effort-in-flux |title=Fusion effort in Flux |author=to the web by Alan Boyle |access-date=2016-02-16|date=September 2008 |publisher= MSNBC}}</ref>

===== 2008 =====

In September 2008 the [[Naval Air Warfare Center]] publicly pre-solicited a contract for research on an Electrostatic "[[Wiffle Ball]]" Fusion Device.<ref>{{cite web |url= https://www.fbo.gov/?tab=core&s=opportunity&mode=form&id=3ea62e93d6aa0220c884d316af43c00b |title= A—Fusion Device Research, Solicitation Number: N6893608T0283 |access-date=2008-10-02 |date=September 2008 |publisher= Federal Business Opportunities }}</ref> In October 2008 the US Navy publicly pre-solicited two more contracts<ref>{{cite web |url= https://www.fbo.gov/?tab=core&s=opportunity&mode=form&id=80e8b7c1181e3e54d92a8d23e3eec700 |title= A—Polywell Fusion Device Research, Solicitation Number: N6893609T0011 |access-date=2008-11-07 |date=October 2008 |publisher= Federal Business Opportunities}}</ref><ref>{{cite web |url= https://www.fbo.gov/?tab=core&s=opportunity&mode=form&id=8e59e11465cc26d4079ac9201008f960 |title= A—Spatially Resolved Plasma Densities/Particle Energies, Solicitation Number: N6893609T0019
 |access-date=2008-11-07 |date=October 2008 |publisher= Federal Business Opportunities}}</ref> with EMC2 the preferred supplier. These two tasks were to develop better instrumentation and to develop an ion injection gun.<ref>{{cite web|url=http://www.talk-polywell.org/bb/viewtopic.php?p=11400&highlight=#11400 |title=Found this during google search on Polywell Fusion |publisher=Talk-polywell.org |access-date=2013-06-17}}</ref><ref>{{cite web
 |url= http://www.talk-polywell.org/bb/viewtopic.php?p=11400&highlight=#11400
 |title= Found this during google search on Polywell Fusion |access-date=2008-11-07 |date=October 2008 |format= Discussion forum
 |publisher= Talk-Polywell.org}}</ref> 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."<ref>{{cite web |url=http://iecfusiontech.blogspot.com.br/2008/12/wb-6-results-confirmed-continuous.html |title= WB-6 Results Confirmed – Continuous Operation The Next Step |access-date=2012-09-10 |date=October 2012|publisher= iecfusiontech}}</ref>

=== 2009 to 2014 ===

====2009====
In January 2009 the [[Naval Air Warfare Center]] pre-solicited another contract for "modification and testing of plasma wiffleball 7"<ref>
{{cite web
 | url = https://www.fbo.gov/index?s=opportunity&mode=form&tab=core&id=9cdc1fbbe6a740519220459e47f26249&_cview=0
 | title = A—Plasma Wiffleball, Solicitation Number: N6893609R0024
 | access-date = 2009-01-26
 | date = January 2009
 | publisher = Federal Business Opportunities
}}
</ref> that appeared 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 modified device. The modified unit was called WB-7.1. This pre-solicitation started as a $200k contract but the final award was for $300k. In April 2009, DoD published a plan to provide EMC2 a further $2 million as part of the [[American Recovery and Reinvestment Act of 2009]]. The citation in the legislation was labelled as ''Plasma Fusion (Polywell) – Demonstrate fusion plasma confinement system for shore and shipboard applications; Joint [[Office of the Secretary of Defense|OSD]]/USN project.''<ref>
{{cite web
 | url = http://www.defenselink.mil/recovery/plans_reports/2009/march/Final_ARRA_Report_to_Congress-24_Mar_09ver2.pdf
 | title = American Recovery and Reinvestment Act of 2009 – Department of Defense Expenditure Plans
 | access-date = 2009-05-05
 | date = May 2009
 | format = PDF Report to US Congress|publisher=Defencelink.mil
}}
</ref> The Recovery Act funded the Navy for $7.86M to construct and test a WB-8.<ref name="SOA-WB8">
{{cite web
 |url         = https://www.neco.navy.mil/upload/N68936/N6893609R0044RFP_09-R-0044.pdf
 |title       = Statement of work for advanced gaseous electrostatic energy (AGEE) concept exploration
 |access-date  = 2009-06-18
 |date        = June 2009
 |publisher   = United States Navy
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20100210075902/https://www.neco.navy.mil/upload/N68936/N6893609R0044RFP_09-R-0044.pdf
 |archive-date = 2010-02-10
}}
</ref> The Navy contract had an option for an additional $4.46M.<ref name="SOA-WB8" /> The new device increased the magnetic field strength eightfold over WB-6.<ref>
{{cite web
 | url = http://www.globalsecurity.org/military/library/news/2009/09/dod-contracts_4116.htm
 | title = U.S. Department of Defense – Office of the Assistant Secretary of Defense (Public Affairs) – Contracts
 | access-date = 2009-09-13
 | date = September 2009
 | publisher = United States Department of Defense
}}
</ref>

====2010====
The team built WB-8 and the computational tools to analyze and understand the data from it.<ref name="Recovery">{{cite web|url = http://www.recovery.gov/Transparency/RecipientReportedData/pages/RecipientProjectSummary508.aspx?AwardIdSur=46419&AwardType=Contracts|title = Project Summary – ENERGY/MATTER CONVERSION CORPORATION|publisher = Recovery.gov|access-date = 2013-06-17|url-status = dead|archive-url = https://web.archive.org/web/20130731084305/http://www.recovery.gov/Transparency/RecipientReportedData/pages/RecipientProjectSummary508.aspx?AwardIdSur=46419&AwardType=Contracts|archive-date = 2013-07-31}}
</ref> The team relocated to San Diego.<ref>
{{cite web
 | url = http://www.talk-polywell.org/bb/viewtopic.php?p=51065#51065
 | title = Recovery.Gov Project Tracker Discussion at Talk-Polywell.org
 | publisher = Talk-Polywell.org
 | date = 2011-11-09
 | access-date=2012-03-31
}}
</ref>

====2011====
Jaeyoung Park became president.<ref>
{{cite web
 | url = http://www.talk-polywell.org/bb/viewtopic.php?t=1681&postdays=0&postorder=asc&start=345
 | title = Recovery.Gov Project Tracker at Talk-Polywell.org
 | publisher = Talk-Polywell.org
 | date = 2011-04-29
 | access-date = 2012-03-31
}}
</ref> In a May interview, Park commented that "This machine [WB8] should be able to generate 1,000 times more nuclear activity than WB-7, with about eight times more magnetic field"<ref>
{{Cite web
 | url = http://cosmiclog.nbcnews.com/_news/2011/05/10/6619613-fusion-goes-forward-from-the-fringe
 | archive-url = https://web.archive.org/web/20110513095500/http://cosmiclog.msnbc.msn.com/_news/2011/05/10/6619613-fusion-goes-forward-from-the-fringe
 | archive-date = 13 May 2011
 | url-status = dead
 | title = Fusion goes forward from the fringe
 | last1 = Boyle
 | first1 = Alan
 | date = 10 May 2011
 | website = MSNBC
 | publisher = NBCUniversal
 | access-date = 16 February 2016
}}
</ref> The first WB-8 plasma was generated on November 1, 2010.<ref name="Recovery" /> By the third quarter over 500 high power plasma shots had been conducted.<ref>
{{cite web
 |url         = http://www.recovery.gov/Transparency/RecipientReportedData/Pages/RecipientProjectSummary508.aspx?AwardIDSUR=46419&qtr=2011Q3
 |title       = Project Summary 2011 Q3
 |publisher   = Recovery.gov
 |access-date  = 2013-06-17
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20131005172205/http://www.recovery.gov/Transparency/RecipientReportedData/Pages/RecipientProjectSummary508.aspx?AwardIDSUR=46419&qtr=2011Q3
 |archive-date = 2013-10-05
}}
</ref><ref>{{cite web
 |url          = http://www.recovery.gov/Transparency/RecipientReportedData/pages/RecipientProjectSummary508.aspx?AwardIDSUR=46419&qtr=2011Q4
 |title        = Project Summary 2011 Q4
 |publisher    = Recovery.gov
 |access-date   = 2012-03-31
 |archive-url  = https://web.archive.org/web/20130824151834/http://www.recovery.gov/Transparency/RecipientReportedData/pages/RecipientProjectSummary508.aspx?AwardIDSUR=46419&qtr=2011Q4
 |archive-date = 2013-08-24
 |url-status     = dead
}}</ref>

====2012====
As of August 15, the Navy agreed to fund EMC2 with an additional $5.3 million over 2 years to work on pumping electrons into the wiffleball. They planned to integrate a pulsed power supply to support the electron guns (100+A, 10kV). WB-8 operated at 0.8 Tesla. Review of the work produced the recommendation to continue and expand the effort,<ref>{{Cite web|url=https://www.fpds.gov/ezsearch/search.do?indexName=awardfull&templateName=1.4.3&s=FPDSNG.COM&q=energy%2Fmatter&sortBy=SIGNED_DATE&desc=Y|title=US Federal Program Data Source}}</ref> stating: "The experimental results to date were consistent with the underlying theoretical framework of the polywell fusion concept and, in the opinion of the committee, merited continuation and expansion."<ref>[https://www.neco.navy.mil/synopsis_file/N6893609C0125%20_Redacted_JA.pdf Justification and Approval for Other than Full and Open Competition] p.2.</ref>

=== Going public ===

==== 2014 ====
In June EMC2 demonstrated for the first time that the electron cloud becomes [[diamagnetism|diamagnetic]] in the center of a magnetic cusp configuration when [[Beta (plasma physics)|beta]] is high, resolving an earlier conjecture.<ref name="Grad 1955" /><ref name="Park 2014" /> Whether the plasma is thermalized remains to be demonstrated experimentally. Park presented these findings at various universities,<ref>{{Cite speech |last=Park |first=Jaeyoung |title=SPECIAL PLASMA SEMINAR: Measurement of Enhanced Cusp Confinement at High Beta |date=12 June 2014 |event=Plasma Physics Seminar |place=Department of Physics & Astronomy, University of California, Irvine |publisher=Energy Matter Conversion Corp (EMC2) |url=http://www.physics.uci.edu/seminar/special-plasma-seminar-measurement-enhanced-cusp-confinement-high-beta}}</ref><ref>"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</ref><ref>{{Cite web|url=http://www.pa.ucla.edu/events/polywell-fusion-%E2%80%93-electric-fusion-magnetic-cusp%E2%80%9D-jaeyoung-park-emc2-fusion-development-corp|title="Polywell Fusion – Electric Fusion in a Magnetic Cusp," by Jaeyoung Park (EMC2 Fusion Development Corp.)}}</ref><ref>Talk at University of Wisconsin Madison, Monday, June 16, 2:30 PM room 106 ERB, Jaeyoung Park</ref><ref>University of Maryland, Colloquium & Seminars, "Measurement of Enhanced Confinement at High Pressure Magnetic Cusp System", Jaeyoung Park, September 9th 2014</ref> the Annual 2014 Fusion Power Associates meeting<ref>{{cite web |title=Polywell Fusion Electrostatic Fusion in a Magnetic Cusp (Presentation)|first=Jaeyoung |last=Park |url=http://fire.pppl.gov/FPA14_IECM_EMC2_Park.pdf |date=December 16, 2014 }}</ref> and the 2014 IEC conference.

==== 2015 ====

On January 22, EMC2 presented at [[Microsoft Research]].<ref>{{cite web|url=http://research.microsoft.com/apps/video/default.aspx?id=238715&r=1|title=Polywell Fusion: Electrostatic Fusion in a Magnetic Cusp - Microsoft Research|date=22 January 2015 |publisher=Microsoft}}</ref> EMC2 planned a three-year, $30 million commercial research program to prove that the Polywell can work.<ref name="CBS">{{Cite news |last=Boyle |first=Alan |title=Low-Cost Fusion Project Steps Out of the Shadows and Looks for Money |date=13 June 2014 |website=NBC News |url=http://www.nbcnews.com/science/science-news/low-cost-fusion-project-steps-out-shadows-looks-money-n130661 }}</ref> On March 11, the company filed a patent application that refined the ideas in Bussard's 1985 patent.<ref>{{patent|US|14/645306|application|Method and Apparatus for Confining High Energy Charged Particles In Magnetic Cusp Configuration}}</ref> The article "High-Energy Electron Confinement in a Magnetic Cusp Configuration" was published in Physical Review X.<ref>{{Cite journal|last1=Park|first1=Jaeyoung|last2=Krall|first2=Nicholas A.|last3=Sieck|first3=Paul E.|last4=Offermann|first4=Dustin T.|last5=Skillicorn|first5=Michael|last6=Sanchez|first6=Andrew|last7=Davis|first7=Kevin|last8=Alderson|first8=Eric|last9=Lapenta|first9=Giovanni|date=2015-06-11|title=High-Energy Electron Confinement in a Magnetic Cusp Configuration|journal=Physical Review X|volume=5|issue=2|pages=021024|doi=10.1103/PhysRevX.5.021024|arxiv=1406.0133|bibcode=2015PhRvX...5b1024P|s2cid=118478508}}</ref>

==== 2016 ====

On April 13, [http://nextbigfuture.com/2016/04/2013-independent-review-of-emc2-fusions.html Next Big Future] published an [https://drive.google.com/file/d/0Bx2cC35KJTwscUktUDkyWk5kRkRnZkxhWTJnd3N2OC1BeVFB/view article] on information of the Wiffle Ball reactor dated to 2013 through the [[Freedom of Information Act (United States)|Freedom of Information Act]].

On May 2, Jaeyoung Park delivered a lecture at [[Khon Kaen University]] in Thailand, claiming that the world has so underestimated the timetable and impact that practical and economic [[fusion power]] will have, that its ultimate arrival will be highly disruptive. Park stated that he expected to present "final scientific proof of principle for the polywell technology around 2019-2020", and expects "a first generation commercial fusion reactor being developed by 2030 and then mass production and commercialisation of the technology in the 2030s. This is approximately 30 years faster than expected by the [[ITER|International Thermonuclear Energy Reactor]] (ITER) project. It would also be tens of billions of dollars cheaper."<ref>{{cite web |url=http://www.prachatai.com/english/node/6114 |title=Fusion to Be Commercialised Thirty Years Faster than Expected - Civil Society's Role |date=4 May 2016 |access-date=16 May 2016}}</ref>

==== 2018 ====

In May 2018 Park and Nicholas Krall filed WIPO Patent WO/2018/208953.<ref>{{Cite web | url=https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2018208953&recNum=27276 | title=Generating Nuclear Fusion Reactions with the Use of Ion Beam Injection in High Pressure Magnetic Cusp Devices}}</ref> "Generating nuclear fusion reactions with the use of ion beam injection in high pressure magnetic cusp devices," which described the polywell device in detail.

== University of Sydney experiments ==
In June 2019, the results of long-running experiments at the [[University of Sydney]] (USyd) were published in PhD thesis form by Richard Bowden-Reid. Using an experimental machine built at the university, the team probed the formation of the virtual electrodes.<ref name=bowden>{{cite tech report |publisher=University of Sydney |first=Richard |last=Bowden-Reid |url=https://ses.library.usyd.edu.au/handle/2123/21070 |title=An Experimental Study of Gridded and Virtual Cathode Inertial Electrostatic Confinement Fusion Systems |date=7 June 2019}}</ref>

Their work demonstrated that little or no trace of virtual electrode formation could be found. This left a mystery; both their machine and previous experiments showed clear and consistent evidence of the formation of a [[potential well]] that was trapping ions, which was previously ascribed to the formation of the electrodes. Exploring this problem, Bowden-Reid developed new field equations for the device that explained the potential well without electrode formation, and demonstrated that this matched both their results and those of previous experiments.<ref name=bowden/>

Further, exploring the overall mechanism of the virtual electrode concept demonstrated that its interactions with the ions and itself would make it "leak" at a furious rate. Assuming plasma densities and energies required for net energy production, it was calculated that new electrons would have to be supplied at an unfeasible rate of 200,000&nbsp;[[Ampere|amps]].<ref name=bowden/>
{{quote|Initial results indicate negligible charge trapping with little to no potential well formation. Further, it is shown that the existence of potential wells reported in previous publications can be explained without the requirement of a virtual cathode produced by trapped electrons. Moreover, it is shown that potential wells, which produce electron confinement and heating from virtual cathodes, no longer exist with increasing plasma density.<ref name=bowden/>}}

==Related projects==

===Prometheus Fusion Perfection===
Mark Suppes built a polywell in Brooklyn. He was the first amateur to detect electron trapping using a [[Langmuir probe]] inside a polywell. He presented at the 2012 LIFT conference and the 2012 WIRED conference.<ref>{{YouTube|Jvkoklpubiw|WIRED video}}</ref> The project officially ended in July 2013 due to a lack of funding.<ref>{{cite news|url=http://prometheusfusionperfection.com/2013/07/07/an-end-to-four-years-of-prometheus-fusion-perfection/ |title=An End to Four Years of |newspaper=Prometheus Fusion Perfection |date=2013-07-07 |access-date=2014-06-14}}</ref>

===University of Sydney===
The [[University of Sydney]] in Australia conducted polywell experiments, leading to five papers in ''[[Physics of Plasmas]]''.<ref name="Low beta confinement in a Polywell modeled with conventional point cusp theories"/><ref name="GummersallCarr2013"/><ref name = "2013AussyWork">{{Cite journal | last1 = Carr | first1 = M. | last2 = Khachan | first2 = J. | doi = 10.1063/1.4804279 | title = A biased probe analysis of potential well formation in an electron only, low beta Polywell magnetic field | journal = Physics of Plasmas | volume = 20 | issue = 5 | pages = 052504 | year = 2013 |bibcode = 2013PhPl...20e2504C | url = https://zenodo.org/record/1244056 }}</ref><ref>{{Cite journal | last1 = Carr | first1 = M. | last2 = Khachan | first2 = J. | doi = 10.1063/1.3428744 | title = The dependence of the virtual cathode in a Polywell on the coil current and background gas pressure | journal = Physics of Plasmas | volume = 17 | issue = 5 | pages = 052510 | year = 2010 |bibcode = 2010PhPl...17e2510C | url = https://zenodo.org/record/1244060 | type = Submitted manuscript }}</ref><ref>"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)</ref> They also published two PhD theses<ref name="Carr thesis 2013">{{Cite thesis |last=Carr |first=Matthew |title=Electrostatic potential measurements and point cusp theories applied to a low beta polywell fusion device |date=2013 |publisher=The University of Sydney |oclc=865167070}}</ref><ref name="Cornish thesis 2016">{{Cite thesis |last=Cornish |first=Scott |title=A study of scaling physics in a Polywell device |date=2016 |publisher=The University of Sydney |url=https://ses.library.usyd.edu.au/handle/2123/14305}}</ref> and presented their work at IEC Fusion conferences.<ref>{{Cite conference |display-authors=4 |last1=Khachan |first1=Joe |last2=Carr |first2=Matthew |last3=Gummersall |first3=David |last4=Cornish |first4=Scott |last5=Israel |first5=Adam |last6=Bandara |first6=Rehan |last7=Ren |first7=Johnson |title=Overview of IEC at the University of Sydney |conference=14th US-Japan Workshop on Inertial Electrostatic Confinement Fusion|location=University of Maryland, College Park, MD |date=14–17 October 2012 |url=http://www.aero.umd.edu/html/sedwick/presentations/S1P3_Joe_Khachan_Presentation.pdf }}</ref><ref>{{Cite conference |last1=Gummersall  |first1=David |last2=Khachan |first2=Joe |title=Analytical orbital theory analysis of electron confinement in a Polywell device |conference=14th US-Japan Workshop on Inertial Electrostatic Confinement Fusion |location=University of Maryland, College Park, MD |date=14–17 October 2012 |url=http://www.aero.umd.edu/html/sedwick/presentations/S4P4_David_Gummersall_Presentation.pdf }}</ref>

A May 2010 paper discussed a small device's ability to capture electrons. The paper posited that the machine had an ideal magnetic field strength that maximized its ability to catch electrons. The paper analyzed polywell magnetic confinement using analytical solutions and simulations. The work linked the polywell magnetic confinement to [[magnetic mirror]] theory.<ref name="F. Chen 1984 pp. 30"/><ref>{{cite web |url=http://www.plasma.ee.kansai-u.ac.jp/iec2010/Agenda.html |title=Agenda of 12th US-Japan Workshop on Inertial Electrostatic Confinement Fusion |date=2010-10-20 |access-date=2013-06-17 |archive-url=https://web.archive.org/web/20130513125106/http://www.plasma.ee.kansai-u.ac.jp/iec2010/Agenda.html |archive-date=2013-05-13 |url-status=dead }}</ref><ref>{{cite web|last=Santarius|first=John|title=Summary & Thoughts|url=http://fti.neep.wisc.edu/presentations/jfs_summary_iec2011.pdf|work=13th Workshop on Inertial-Electrostatic Confinement Fusion|publisher=University of Wisconsin|access-date=31 March 2012}}</ref> The 2011 work used [[Particle-in-cell]] simulations to model particle motion in polywells with a small electron population. Electrons behaved in a similar manner to particles in the [[biconic cusp]].<ref name="ReferenceA"/>

A 2013 paper measured a negative [[voltage]] inside a 4-inch aluminum polywell.<ref name="2013AussyWork"/> Tests included measuring an internal [[Charged particle beam|beam]] of electrons, comparing the machine with and without a [[magnetic field]], measuring the [[voltage]] at different locations and comparing voltage changes to the [[magnetic]] and [[electric]] field strength.<ref name="2013AussyWork"/>

A 2015 paper entitled "Fusion in a magnetically-shielded-grid inertial electrostatic confinement device" presented a theory for a gridded [[inertial electrostatic confinement]] (IEC) fusion system that shows a net energy gain is possible if the grid is magnetically shielded from ion impact. The analysis indicated that better than break-even performance is possible even in a deuterium-deuterium system at bench-top scales. The proposed device had the unusual property that it can avoid both the cusp losses of traditional magnetic fusion systems and the grid losses of traditional IEC configurations.<ref>{{Cite journal|last1=Hedditch|first1=John|last2=Bowden-Reid|first2=Richard|last3=Khachan|first3=Joe|date=October 2015|title=Fusion in a magnetically-shielded-grid inertial electrostatic confinement device|journal=Physics of Plasmas|volume=22|issue=10|pages=102705|doi=10.1063/1.4933213|issn=1070-664X|arxiv=1510.01788|bibcode=2015PhPl...22j2705H }}</ref>

=== Iranian Nuclear Science and Technology Research Institute ===
In November 2012, ''[[Trend News Agency]]'' reported that the [[Atomic Energy Organization of Iran]] had allocated "$8 million"<ref>{{cite web|url=http://en.trend.az/regions/iran/2087514.html |title=Iran to build nuclear fusion producing plant |website=Trend News Agency |date=13 November 2012 |access-date=2013-02-08}}</ref> to inertial electrostatic confinement research and about half had been spent. The funded group published a paper in the ''Journal of Fusion Energy'', stating that particle-in-cell simulations of a polywell had been conducted. The study suggested that well depths and ion focus control can be achieved by variations of field strength, and referenced older research with traditional fusors. The group had run a fusor in continuous mode at −140 kV and 70 mA of current, with D-D fuel, producing 2×10<sup>7</sup> neutrons per second.<ref>{{Cite journal | doi = 10.1007/s10894-011-9474-4| title = Dependence of Potential Well Depth on the Magnetic Field Intensity in a Polywell Reactor| journal = Journal of Fusion Energy| volume = 31| issue = 4| pages = 341| year = 2011| last1 = Kazemyzade | first1 = F.| last2 = Mahdipoor | first2 = H.| last3 = Bagheri | first3 = A.| last4 = Khademzade | first4 = S.| last5 = Hajiebrahimi | first5 = E.| last6 = Gheisari | first6 = Z.| last7 = Sadighzadeh | first7 = A.| last8 = Damideh | first8 = V.|bibcode = 2012JFuE...31..341K | s2cid = 121745855}}</ref>

=== 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.<ref>{{cite journal |url=http://absimage.aps.org/image/DPP13/MWS_DPP13-2013-000611.pdf |title=Vlasov-Poisson calculations of electron confinement times in Polywell(TM) devices using a steady-state particle-in-cell method |journal=APS Division of Plasma Physics Meeting Abstracts |volume=2013 |pages=JP8.124 |publisher=The DPP13 Meeting of The American Physical Society|access-date=2013-10-01|bibcode=2013APS..DPPJP8124K |last1=Kollasch |first1=Jeffrey |last2=Sovinec |first2=Carl |last3=Santarius |first3=John |year=2013 }}</ref>

=== Convergent Scientific, Inc. ===
Convergent Scientific, Inc. (CSI) is an American company founded in December 2010 and based in Huntington Beach, California.<ref>{{Cite web |title=Convergent Scientific, Inc. (Company Info) |author=<!--Staff writer(s); no by-line.--> |website=Gust.com |url=http://gust.com/companies/convsci}}</ref> 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.<ref>{{YouTube|id=yHGO2Fbskok|title="Polywell Model One, by Convergent Scientific"|link=no}}</ref><ref>{{Cite web |title=We have to Try |author=<!--Staff writer(s); no by-line.--> |date=31 January 2014 |website=The Polywell Blog |url=http://thepolywellblog.blogspot.fr/2014/01/we-have-to-try.html}}</ref><ref>Talk. [http://sproutvideo.com/videos/1c9bd8bd171be4c994 "Commercial Applications of IEC Devices"] {{Webarchive|url=https://web.archive.org/web/20140103002540/http://sproutvideo.com/videos/1c9bd8bd171be4c994 |date=2014-01-03 }} Web presentation, performed by Devlin Baker, 22 October 2013.</ref> They are making an effort to build a small-scale polywell fusing [[deuterium]].<ref>{{Cite conference |last1=Rogers |first1=Joel G. |last2=Baker |first2=Devlin |title=Designing a Small-Scale D+D Reactor |date=14–16 October 2012 |conference=14th US-Japan Workshop on IEC Fusion |location=College Park, Maryland |url=http://www.aero.umd.edu/html/sedwick/presentations/S4P3_Joel_Rogers_Presentation.pdf}}</ref><ref>{{cite web|url=http://convsci.com/login |title=Convergent Scientific Incorporated website |publisher=Convsci.com |access-date=2013-06-17}}</ref> The company filed several patents<ref>{{Cite patent | country=US | number=2010284501 | status=application | title=Modular Apparatus for Confining a Plasma | pubdate=2010-11-11 | fdate=2008-06-18 | pridate=2008-06-18  | invent1=Rogers, Joel Guild | assign1=Rogers, Joel Guild}}</ref><ref>{{Cite patent |country=US |number=8279030 |status=patent |title=Method and apparatus for electrical, mechanical and thermal isolation of superconductive magnets |gdate=2012-10-02 |fdate=2009-09-26 |pridate=2008-09-27 |invent1=Baker, Devlin |invent2=Bateman, Daniel |assign1=Magnetic-Electrostatic Confinement (MEC) Corporation}}</ref><ref>{{Cite patent |country=US |number=2013012393 |status=application |title=Apparatus to confine a plurality of charged particles |pubdate=2013-01-10 |fdate=2012-07-09 |pridate=2011-07-07 |invent1=Bateman, Daniel |invent2=Pourrahimi, Shahin |assign1=Bateman, Daniel |assign2=Pourrahimi, Shahin}}</ref> and in the Fall of 2013, did a series of web-based investor pitches.<ref>Talk. [http://sproutvideo.com/videos/e89bd8bd1314edca60 "Numerical Simulations of IEC Plasmas."]{{Dead link|date=May 2025 |bot=InternetArchiveBot |fix-attempted=yes }} Web presentation, Performed by Devlin Baker, November 5, 2013</ref> The presentations mention encountering plasma instabilities including the [[Diocotron instability|Diocotron]], [[Two-stream instability|two stream]] and [[Weibel instability|Weibel]] instabilities. The company wants to make and sell [[Nitrogen-13]] for [[Positron emission tomography|PET]] scans.<ref>Talk. [http://sproutvideo.com/videos/189bd8bd131be6c290 "Commercial Applications of IEC Devices"] {{Webarchive|url=https://web.archive.org/web/20140107060822/http://sproutvideo.com/videos/189bd8bd131be6c290 |date=2014-01-07 }} Web presentation, performed by Devlin Baker, December 3, 2013.</ref>

=== Radiant Matter Research ===
Radiant Matter<ref>[http://www.radiantmatter.com/content/farnsworth-fusor Radiant Matter fusor] {{Webarchive|url=https://web.archive.org/web/20131203015122/http://www.radiantmatter.com/content/farnsworth-fusor |date=2013-12-03 }} Accessed: 12/25/2013</ref> is a Dutch organization that has built [[fusor]]s and has plans to build a polywell.{{Citation needed|date=June 2021}}

=== ProtonBoron ===
ProtonBoron<ref>[https://web.archive.org/web/20201001201451/http://www.protonboron.com/] Radiant Matter fusor] {{dead link|date=June 2018}} Accessed: 05/03/2016</ref> is an organization that plans to build a proton-boron polywell.

=== Progressive Fusion Solutions ===
Progressive Fusion Solutions is an IEC fusion research startup who are researching Fusor and Polywell type devices.

=== Fusion One Corporation ===
Fusion One Corporation was a US organization founded by Dr. Paul Sieck (former Lead Physicist of EMC2), Dr. Scott Cornish of the University of Sydney, and Randall Volberg. It ran from 2015 to 2017. They developed a magneto-electrostatic reactor named "F1" that was based in-part on the polywell. It introduced a system of externally mounted electromagnet coils with internally mounted cathode repeller surfaces to provide a means of preserving energy and particle losses that would otherwise be lost through the magnetic cusps. In response to Todd Rider's 1995 power balance conclusions, a new analytical model was developed based on this recovery function as well as a more accurate quantum relativistic treatment of the bremsstrahlung losses that was not present in Rider's analysis. Version 1 of the analytical model was developed by Senior Theoretical Physicist Dr Vladimir Mirnov and demonstrated ample multiples of net gain with D-T and sufficient multiples with D-D to be used for generating electricity. These preliminary results were presented at the ARPA-E ALPHA 2017 Annual Review Meeting.<ref>{{Cite web|url=https://arpa-e.energy.gov/?q=site-page/alpha-2017-annual-review-meeting|title=ALPHA 2017 ANNUAL REVIEW MEETING}}</ref>  Phase 2 of the model removed key assumptions in the Rider analysis by incorporating a self-consistent treatment of the ion energy distribution (Rider assumed a purely Maxwellian distribution) and the power required to maintain the distribution and ion population. The results yielded an energy distribution that was non-thermal but more Maxwellian than monoenergetic. The input power required to maintain the distribution was calculated to be excessive and ion-ion thermalization was a dominant loss channel. With these additions, a pathway to commercial electricity generation was no longer feasible.{{Citation needed|date=December 2019}}

== See also ==
{{portal|Nuclear technology|Energy|Physics}}
{{div col|colwidth=25em}}
* [[China Fusion Engineering Test Reactor]]
* [[Dense plasma focus]]
* [[Fusion Industry Association]]
* {{format link|Fusion power#History}}
* [[General Fusion]]
* [[George H. Miley]]
* [[Inertial electrostatic confinement]]
* [[List of fusion experiments]]
* [[Magnetized target fusion]]
* [[Pinch (plasma physics)]]
* [[Spherical Tokamak for Energy Production]]
* [[Stellarator]]
* [[Timeline of nuclear fusion]]
* [[Tokamak]]
* [[TAE Technologies]]
* [[Z-pinch]] (zeta pinch)
{{div col end}}

== References ==
{{Reflist|30em}}

== External links ==
* [https://web.archive.org/web/20201001201451/http://www.protonboron.com/ ProtonBoron]
* [http://research.microsoft.com/apps/video/default.aspx?id=238715&r=1 Polywell Talk At Microsoft Research]
* [http://www.emc2fusion.org EMC2 website] {{Webarchive|url=https://web.archive.org/web/20090329070036/http://www.emc2fusion.org/ |date=2009-03-29 }}
* [https://web.archive.org/web/20130810075355/http://www.polywellnuclearfusion.com/ Polywell Nuclear Fusion]
* {{YouTube|FhL5VO2NStU|Should Google Go Nuclear?}} Video of Bussard's presentation to Google
* [https://web.archive.org/web/20110707175054/http://askmar.com/ConferenceNotes/Should%20Google%20Go%20Nuclear.pdf Should Google Go Nuclear?(transcript)] Illustrated transcript of Bussard's Google presentation
* [https://medium.com/@timventura/robert-bussard-on-iec-fusion-power-the-polywell-reactor-be4a59dc7318 Robert Bussard on IEC Fusion Power & The Polywell Reactor] Transcript of Bussard Polywell Interview from May 10, 2007
* [https://web.archive.org/web/20070928174245/http://isdc2.xisp.net/~kmiller/isdc_archive/fileDownload.php/?link=fileSelect&file_id=422 Presentation] at International Space Development Conference (ISDC). Dallas, May 2007
* [http://www.strout.net/info/science/polywell/index.html Links] Compendium of informative links related to polywell fusion
* [https://web.archive.org/web/20080723182449/http://www.askmar.com/Fusion.html List] of technical papers and references
* {{YouTube|jmp1cg3-WDY|IEC Fusion for Dummies}} Graphical explanation of a polywell
* [http://www.talk-polywell.org/bb/index.php Talk-Polywell.org] BBS for discussing polywell
* [https://iec.neep.wisc.edu/overview.php University of Wisconsin–Madison] Introduction to [[inertial electrostatic confinement|IEC]] including the polywell
* [http://cosmiclog.nbcnews.com/_news/2008/06/12/4350196-fusion-quest-goes-forward Latest Fusion developments (WB-7 – June 2008) based on the work of Dr. Robert Bussard]
* [https://prometheusfusionperfection.com/ Prometheus Fusion] – A blog describing amateur experiments aimed at creating a polywell
* [https://www.progressivefusionsolution.com/ Progressive Fusion Solutions] - developing fusion with a fresh outlook
* {{YouTube|u=happyjack27|Simulation videos of a polywell reactor}}
* [https://thepolywellblog.blogspot.com/ The Polywell Blog] – An amateur blog discussing the polywell
* {{YouTube|id=Jvkoklpubiw|title= Wired 2012 Presentation}} – Mark Suppes talk at Wired 2012 on the polywell
* {{YouTube|id=IFp0WFCK714 Polywell 101 - A 10-minute film explaining the polywell}}
* [https://web.archive.org/web/20150224134524/http://msrvideo.vo.msecnd.net/rmcvideos/238715/238715.mp4 2015 Jaeyoung Park video]
* {{YouTube|id=ao0Erhsnor4 |title=Polywell simulation 3D}}

{{Fusion power}}

[[Category:Fusion power]]
[[Category:Soviet inventions]]