# Polywell

Polywell WB-6 model assembled

A polywell is a type of fusion reactor that uses an electric field to do work on ions, to heat them to fusion conditions. It traps electrons using magnetic confinement. The negatively charged electrons then attract positively charged ions. This accelerates the ions. If the ions collide at high speeds in the center, they can fuse. This is a form of inertial electrostatic fusion and is closely related to the fusor, magnetic mirrors and the biconic cusp.

The polywell was developed by Robert Bussard as an improvement over the fusor. It uses a negative plasma instead of a negative wire cage to attract ions. Dr. Bussard theorized that a polywell could potentially produce net energy. His company developed the initial devices for the U.S. Navy. The name polywell is a portmanteau of "polyhedron" and "potential well."

## Description

A polywell consists of several parts. A set of positively charged electromagnet coils that are arranged in a polyhedron. This is called the MaGrid. This structure generates magnetic fields which are designed to trap electrons. The MaGrid is placed inside a wire cage within a vacuum chamber. Electrons are introduced into the cage and are accelerated towards the MaGrid using an electric field. Once inside the MaGrid, the electrons are confined by the magnetic fields. Those that escape are retained by the electric field. This configuration traps the electrons in the middle of the device. The electrons act as a virtual cathode (negative electric potential).

Gas is puffed into the cage. The gas ionizes when it reaches the electron cloud. The electron cloud generates a potential well. Ions fall down this well building up speed, slamming together and fusing in the center. Ions are also electrostatically confined so densely that they fuse, releasing energy. The energy required to confine the electrons is far smaller than that required to directly confine ions, as is done in other fusion projects such as ITER.

## Development

### Fusor

Farnsworth–Hirsch fusor during operation in so called "star mode" characterized by "rays" of glowing plasma which appear to emanate from the gaps in the inner grid.
Taylor Wilson presenting fusor work to Barack Obama, 2/7/2012

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

A benefit of a fusor is that it loses very little energy as light; it has low radiation losses. The device has no magnetic fields, which means there are no synchrotron losses. If the grid is kept cool, there is only a small amount of thermionic emission. Finally, if the grid is kept cool there is also a small amount of x-ray radiation.[1]

The fundamental problem with a fusor is with the grid itself. Far too often, nuclei strike the grid. This is a conduction loss: the energy leaves with the mass leaving the machine. This reduces the fusor's ability to generate power, by wasting the energy that went into ionizing and accelerating the particle. It also cools the plasma down and damages the grid. Even if the cooling problem was not critical, in a fusor scaled to power to a power plant, the fine mesh grid would overheat to the point of being vaporized.

### Elmore-Tuck-Watson

An Elmore-Tuck-Watson (ETW) fusor inverts the charge on the grids. It consists of a vacuum chamber containing a negatively charged outer grid (which may be the chamber) and a positively charged inner grid. Electrons (instead of ions) are injected into the system and accelerated toward the inner grid. As with normal fusors, the particles move back and forth through the inner grid and core. As they pass repeatedly through the core, they generate a negatively charged zone, a potential well, which is called a virtual cathode. Fusible atomic nuclei are then introduced inside the inner (positive) grid where they are ionized. The virtual cathode (electron cloud) accelerates the ions toward the center where they oscillate within the potential well. Since the ions never (in theory) reach the grid, they never lose their energy to impacts and continue to oscillate through the core. Given enough oscillations, the ions strike other high-energy ions and fuse.

This configuration avoids the conduction losses related to ions striking the inner negative grid. However, the fundamental problem with this system is still the grid itself. Far too often the electrons strike the grid, causing energy loss.

### Polywell

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

The polywell generates the negative voltage needed to accelerate the ions using a cloud of net electrons. The extra electrons in the center form a virtual cathode, which ideally behaves like the fusor's negative inner cage. This generates the electric field needed to accelerate ions to fusion conditions. The electrons forming this virtual cathode are confined using the magnetic mirror effect. Electrons are reflected from the dense magnetic fields at the corners of the rings. This design (in theory) avoids both types of losses; preventing both electrons and ions from hitting the grid. Ions are added, but an excess of electrons are kept to maintain the negative potential well.[2] The polywell differs from traditional magnetic confinement because the fields confines light electrons, which is much easier than containing the much heavier ions.[3][4][5]

Most experiments use six rings in a cube. This is referred to as the MaGrid. Each ring is a discrete, circular coil of wire inside a smooth shell. All the magnetic flux that enters the volume through the coils leaves it again through the spaces between the coils. These are electromagnets, each with a north and south pole. All poles are pointing toward (or all away from) the center. The magnetic field vanishes at the center by symmetry, creating a null point. Single electrons travel straight through the null point, due to their infinite gyroradius in regions of no magnetic field. As they head to the corners they experience a Lorentz force which causes them to corkscrew tighter and tighter along the denser magnetic field lines.[6] Their gyroradius shrinks and when they hit a dense magnetic field they can be reflected using the magnetic mirror effect.[7] This is typical of all Electron cyclotron resonance motion. This particle behavior is very similar to studies in the biconic cusp from the early 1960s.[8] This configuration and motion can confine electrons and ions inside the center of the rings. Ideally, the plasma would be electron rich to create the negative voltage drop. Bussard claimed that the MaGrid arrangement of the magnetic field has only point cusps but acknowledged that the circular coils produce line-like cusps at the closest approaches of the coils.[9]

#### Results

Despite initial difficulties in spherical electron confinement, at the time of the 2005 research project's termination, Bussard reported a fusion rate of 109 per second running D-D fusion reactions at only 12.5 kV (based on detecting a total of nine neutrons in five tests,[10][11] 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.[12][13] By comparison, researchers at the University of Wisconsin–Madison reported a neutron rate of up to 5×109 per second at voltages of 120 kV with an electrostatic fusor without magnetic fields.[14]

Bussard asserted, by using superconductor coils, the only significant energy loss channel is through electron losses proportional to the surface area. He also stated that the density would scale with the square of the field (constant beta conditions), and the maximum attainable magnetic field would scale with the radius (technological constraints). Under those conditions, the fusion power produced would scale with the seventh power of the radius, and the energy gain would scale with the fifth power. While Bussard did not publicly document the physical reasoning underlying this estimate,[15] if true, it would enable a model only ten times larger to be useful as a fusion power plant.[10]

## Behavior

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

### Single electron motion

Particle-in-cell simulations of the polywell have shown electron motion.[6] Free electrons are released outside the rings. They are subject to the surrounding electric field pulling them into the center.[16] As they accelerate, their kinetic energy rises. They begin to be affected by the magnetic field. Ideally, the magnetic overtakes the electric lorentz force and the electron start corkscrewing. This is known as electron cyclotron resonance motion. Electrons corkscrew around the magnetic field lines, spinning in a tighter orbit in denser fields. The radius of this motion is known as the gyroradius.[7] They enter the ring structure in a tight corkscrew, which widens as they move into the center. In the center there is a null point, a region of no magnetic field.[6] Single electrons travel straight through this null point, due to their infinite gyroradius in regions of no magnetic field.[17] This straight motion can scatter the electrons.[6] Next, the electrons head towards the cusps at the corners or sides of the rings.[6][18] They enter regions with denser and denser magnetic fields, causing their gyroradius to shrink. Ideally, they are reflected back into the center using the magnetic mirror effect.[7][19] This particle behavior is very similar to studies of the biconic cusp from the early 1960s.[8] As the particle changes speed, it radiates energy as light. This radiation is a way that the machine can lose energy. Radiation increases as the plasma gets hotter. This can be calculated using the Larmor formula [20]

A visualization of particle motion in polywell has been made in 3D simulations by Indrek Mare [21] and by John Coady.

### Electron Trapping

Electron trapping has been measured in polywells.[16][22][23][24] This test is done by putting a Langmuir probe in the center of the device and measuring a negative voltage during operation. The machine traps the electrons inside the rings using magnetic fields, the same way the magnetic mirror machines and biconic cusp concept traps them.[19][25] These magnetic fields will also simultaneously affect the ions. When a charged particle enters a dense magnetic field it feels a repulsive force reflecting it back to a lower density field.[26] This is the magnetic mirror effect. This has been used in several confinement schemes to trap charged particles.

The polywell uses the mirror effect every time a charged particle moves from a low density to a high density magnetic field. The charged particle is reflected back to the low density field. Ideally, the machine is set up so that the lowest density field (the null point) is in the center.[27] This means that electrons are reflected and trapped internally by the mirror effect. This is a very similar design to the biconic cusp. In several configurations, this magnetic containment is boosted by adding an outside electric field.[16] If the electron escapes the rings, it is attracted back to the positive rings. This machine attempts to confine a non-thermal distribution of electrone (a nonthermal plasma). In some mirror configurations, the field in the center is a minimum in every direction, as it is in the central region of a polywell.[16]

### Ion confinement

Ideally, the polywell confines the ions and electrons through two different means, borrowed from fusors and magnetic mirrors. The electrons are easier to confine magnetically because they have so much less mass than the ions.[28]

The machine confines ions using an electric field in the same way a fusor confines the ions. In the polywell, the ions are attracted to the negative cloud in the center. In the fusor, they are attracted to a negative wire cage in the center. This is the same method used for all inertial electrostatic confinement devices. Both concepts intend to operate with a highly Nonthermal plasma, ideally mono-energetic, distribution of ion energies.[4] If the ion energies can be held near the optimum value, the fusion rate for a given plasma pressure can be a few times higher than the maximum rate possible for ions with a thermal distribution. On the other hand, collisions and collective instabilities have a tendency to restore a thermal distribution, so that it generally costs power to maintain a mono-energetic distribution.

## Considerations for net power

### Fuel type

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

Nuclear fusion refers to reactions in which lighter nuclei are combined to become heavier nuclei. This process changes mass into energy which may be captured to provide fusion power. Many types of atoms can be fused. The probability of a fusion reaction occurring is controlled by the cross section of the fuel,[29] which is in turn a function of its temperature. The easiest nuclei to fuse are deuterium and tritium, and their fusion occurs when the ions have a temperature of at least 4 keV (kiloelectronvolts) or about 45 million Kelvin. The polywell would achieve this by accelerating an ion with a charge of 1 down a 4,000 volt electric field. The high cost, short half-life and radioactivity of tritium made it difficult to be used by Bussard's team. The second easiest reaction is to fuse deuterium with itself. Because of its low cost, deuterium is commonly used by Fusor amateurs, and Bussard's polywell experiments were performed using this fuel. Any fusion reaction using deuterium or tritium will produce a fast neutron and is therefore radioactive. Dr. Bussard's goal was to fuse boron-11 with protons; this is a fusion reaction which is aneutronic (does not produce neutrons).

### Lawson criterion

At such conditions, the atoms are ionized and make a plasma. The energy generated by fusion, inside a hot plasma cloud can be found with the following equation.[30]

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

where:

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

This equation shows that energy varies with the temperature, density, speed of collision, and fuel used. To reach net power, fusion reactions have to occur fast enough to make up for energy losses. Any power plant using fusion will hold in this hot cloud. Plasma clouds lose energy through conduction and radiation.[30] Conduction is when ions, electrons or neutrals touch a surface and leak out. Energy is lost with the particle. Radiation is when energy leaves the cloud as light. Radiation increases as the temperature rises. To get net power from fusion, you must overcome these losses. This leads to an equation for power output (where: η is machine efficiency).

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

John Lawson used this equation to estimate some conditions for net power [30] based on a Maxwellian cloud.[30] This is the Lawson criterion.

### Criticism

In his thesis[31] and his 1995 publication,[32] MIT doctoral student Todd Rider had calculated that x-ray radiation losses with this fuel will exceed fusion power production by at least 20%. Rider modeled the system using the following assumptions:

• The plasma was quasineutral. Therefore positives and negatives were equally mixed together.[31]
• The fuel was evenly mixed throughout the volume.[31]
• The plasma was isotropic, meaning that its behavior was the same in any given direction.[31]
• The plasma had a uniform energy and temperature throughout the cloud.[31]
• The plasma was an unstructured Gaussian sphere, with a strongly converged dense central core. The core represented a small (~1%) part of the total volume.[31] In a later 1995 paper, Dr. William Nevins at LANL argued against this assumption. He argued that the particles would build up angular momentum, causing the dense core to degrade.[33] The loss of density inside the core would reduce fusion rates.
• The potential well was broad and flat.[31]

Based on these assumptions, Rider used general equations[34] to estimate the rates of different physical effects. These included, but were not limited to, the loss of ions to up-scattering, the ion thermalization rate, the energy loss due to x-ray radiation and the fusion rate.[31] His conclusions were that the device suffered from "fundamental flaws".[31]

By contrast, Bussard has argued [10] that the plasma inside the polywell has different structure, temperature distribution and well profile. These characteristics have not been fully measured and are central to the device's feasibility. Based on this his calculations indicate that the bremsstrahlung losses would be much smaller.[35] According to Bussard the high speed and therefore low cross section for Coulomb collisions of the ions in the core makes thermalizing collisions very unlikely, while the low speed at the rim means that thermalization there has almost no impact on ion velocity in the core.[10] Bussard calculated that a polywell reactor with a radius of 1.5 meters would produce net power fusing deuterium.[36]

### Energy capture

It has been proposed that energy may be extracted in polywells using heat capture or direct conversion though that scheme will have general challenges.[37]

## History

WB-2
WB-3
WB-6 during assembly with coils showing

In the late 1960s there were several investigations of polyhedral magnetic fields as a possibility to confine a fusion plasma.[38][39] The first proposal to combine this magnetic configuration with an electrostatic potential well in order to improve electron confinement was made by Lavrentiev in 1975.[40] The idea was picked up by Robert Bussard in 1983, a link acknowledged in the references cited by his 1989 patent application,[9] though in 2006 he appears to claim to have re-discovered the idea independently.[41]

### HEPS

Research was funded first by the Defense Threat Reduction Agency beginning in 1987 and later by DARPA.[16]:32:30 This funding resulted in a first machine known as the high energy power source (HEPS) experiment. This was built by Directed Technologies Inc in San Diego.[17] This machine was a large (190 cm across) machine, where the rings were placed outside of the vacuum chamber.[16]:32:33 This machine performed poorly because the magnetic fields sent electrons into the walls, driving up conduction losses. At the time, these losses were thought to be due to poor electron injection.[17] The United States Navy began providing low-level funding to the project in 1992.[42] Results from the HEPS program were published by Dr. Nicholas Krall in 1994.[17]

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

### EMC inc

Robert Bussard founded EMCC incorporated in 1987 [16] and after the HEPS program ended, the company took on the research. Successive machines were made, starting from WB-1 to WB-8. The company won an SBIR I grant in 92-93 and an SBIR II grant in 94-95, both from the US Navy.[41] In 1993, it received a grant from the Electric Power Research Institute to examine the use of this machine in power production.[41] In 1994, The company received small grants from NASA and LANL.[41] Starting in 1999, the company was primarily funded by the US Navy.[41]

One early design was WB-1, which had six conventional magnets in a cube. This device was 10 cm across.[41] This was followed by WB-2, which used coils of wires to generate the magnetic field. Each electromagnet had a square cross section, which created problems. The magnetic fields drove electrons into the metal rings raising conduction losses and affects electron trapping. This design also suffered from "funny cusp" losses at the joints between magnets. The WB-6 machine attempted to address these problems, by using circular rings and spacing them some distance apart.[16] The next device, PXL-1, was built in 1996 and 1997. This machine was 26 cm across and used flatter rings to generate the field.[41] From 1998 to 2005 the company built a succession of six machines: WB-3, MPG-1,2, WB-4, PZLx-1, MPG-4 and WB-5. All of these reactors were six magnet designs built as a cube or truncated cube. They ranged from 3 to 40 cm in radius.[41]

### WB-7

A more robust version of the WB-6 fusion device, was constructed at a machine shop in San Diego and shipped to Santa Fe to the EMC2 testing facility. The device was termed WB-7 and like prior ones, was designed by engineer Mike Skillicorn. This machine has a design similar to WB-6. WB-7, achieved "1st plasma" in early January, 2008.[51][52] 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. Dr. Nebel has said "we have had some success", referring to the team's effort to reproduce the promising results obtained by Dr. Bussard. "It's kind of a mix", Dr. 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.[53]

### FY 2009 work

In September 2008 the Naval Air Warfare Center, Weapons Division, China Lake, California publicly pre-solicited a contract for research on an Electrostatic "Wiffle Ball" Fusion Device.[54] In October 2008 the US Navy publicly pre-solicited two more contracts[55][56] also targeted toward EMC2 as preferred supplier. These two tasks were to develop better instrumentation and to develop an ion injection gun.[57][58] In December 2008, following many months of review by the expert review panel of the submission of the final WB-7 results, Dr Richard Nebel commented that "There's nothing in there [the research] that suggests this will not work", but that "That's a very different statement from saying that it will work."[59]

In January 2009 the Naval Air Warfare Center pre-solicited another contract for "modification and testing of plasma wiffleball 7"[60] which appears to be funding to install the instrumentation developed in a prior contract, install a new design for the connector (joint) between coils, and operate the WB-7 with the modifications. The modified unit is now called WB-7.1. This pre-solicitation started as a $200k contract but the final award was for$300k.

## Other projects

### Prometheus Fusion Perfection

Mark Suppes, a web developer, built his own polywell in a warehouse in Brooklyn, New York. He was the first amateur in the world to detect electron trapping using a Langmuir probe inside a polywell.[23] He presented at the 2012 LIFT conference and the 2012 WIRED conference.[72] The project officially ended in July 2013, while the blog will remain online indefinitely.[73]

### University of Sydney

The University of Sydney in Australia have been conducting studies and experiments with polywell devices. To date, they have published four papers in Physics of Plasmas on this topic, one in 2010,[74] one in late 2011,[6] and two in 2013.[18][75] They also published one PhD thesis[76] on the subject.

The May 2010 paper discussed experimental work, testing a small device for its ability to capture electrons. The paper posited that the machine had an ideal magnetic field strength which maximized its ability to catch electrons. The paper analyzed magnetic confinement in the polywell using analytical solutions as well as simulations. The work linked the magnetic confinement in the polywell to magnetic mirror theory.[7] This research was presented at the 12th US-Japan Workshop on Inertial Electrostatic Confinement Fusion,[77] and summarized by John Santarius of the University of Wisconsin [78] The 2011 work uses 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.[8]

The first 2013 paper, measured a negative voltage inside a 4 inch aluminum polywell.[75] This was performed using pairs of biased Langmuir probes. Several tests were undertaken that included: measuring an internal 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.[75]

### Iranian Nuclear Science and Technology Research Institute

In November 2012, Trend News Agency reported that AEO Iran had allocated "\$8 million"[79] to inertial electrostatic confinement research and about half had been spent. The funded group published a report in the Journal of Plasma Physics. The report stated 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. The report referenced older research with traditional fusors. The group had run a fusor in continuous mode at -140KV with 70mA of current, with D-D fuel, producing 2x10^7 neutrons per second.[80]

### University of Wisconsin

Dr. Carl Sovinec and his graduate student have performed Vlasov–Poisson, particle-in-cell simulation work on the polywell. This was funded through the National Defense Science and Engineering Graduate Fellowship and was presented at the 2013 American Physical Society conference.[81]

### Convergent Scientific Inc.

Convergent Scientific Inc, is a company which has an effort to build a small scale polywell fusing deuterium.[82][83] The company has a US patent on appeal [84] and in the Fall of 2013, did a series of web-based investor pitches.[24][85] The presentations mention encountering plasma instabilities including the Diocotron, two stream and Weibel instabilities. The company wants to make and sell Nitrogen-13 for PET scans.[86]

Radiant Matter[87] is an organization in the Netherlands which has built a number of fusors and has plans to build a polywell.

## References in literature

The polywell has been referenced in two novels: "A Green Sun" by Charles Gray[88]

## References

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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.

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