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125-463: 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 fuse . A Farnsworth-Hirsch fusor consists of two wire cages, one inside

250-507: A Maxwellian cloud. However, the Lawson criterion does not apply for Polywells if Bussard's conjecture that the plasma is nonthermal is correct. Lawson stated in his founding report: "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

375-531: A Maxwellian cloud. This became the Lawson criterion . Fusors typically suffer from conduction losses due to the wire cage being in the path of the recirculating plasma. In the original fusor design, several small particle accelerators , essentially TV tubes with the ends removed, inject ions at a relatively low voltage into a vacuum chamber. In the Hirsch version of the fusor, the ions are produced by ionizing

500-410: A high-frequency magnetic field . The charge would then accumulate in the center of the tube, leading to high amplification. Unfortunately it also led to high erosion on the electrodes when the electrons eventually hit them, and today the multipactor effect is generally considered a problem to be avoided. What particularly interested Farnsworth about the device was its ability to focus electrons at

625-478: A conversion efficiency of 48%. In the late 1960s several investigations studied polyhedral magnetic fields as a possibility to confine a fusion plasma. 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. The idea was picked up by Robert Bussard in 1983. His 1989 patent application cited Lavrentiev, although in 2006 he appears to claim to have (re)discovered

750-420: 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. 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

875-401: A dilute gas in the chamber. In either version there are two concentric spherical electrodes , the inner one being charged negatively with respect to the outer one (to about 80 kV). Once the ions enter the region between the electrodes, they are accelerated towards the center. In the fusor, the ions are accelerated to several keV by the electrodes, so heating as such is not necessary (as long as

1000-493: 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. In experiments, direct conversion has demonstrated

1125-407: A few minutes before undergoing a fusion reaction, so that the monoenergetic picture of the fusor, at least for power production, is not appropriate. One consequence of the thermalization is that some of the ions will gain enough energy to leave the potential well, taking their energy with them, without having undergone a fusion reaction. There are a number of unsolved challenges with the electrodes in

1250-628: 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 against 80–90% theoretical efficiency. The energy generated by fusion inside a hot plasma cloud can be found with the following equation: where: Energy varies with temperature, density, collision speed and fuel. To reach net power production, reactions must occur rapidly enough to make up for energy losses. Plasma clouds lose energy through conduction and radiation . Conduction

1375-521: A fusion reaction occurring is controlled by the cross section of the fuel, which is in turn a function of its temperature. The easiest nuclei to fuse are deuterium and tritium . Their fusion occurs when the ions reach 4 keV ( kiloelectronvolts ), or about 45 million kelvins . The Polywell would achieve this by accelerating an ion with a charge of 1 down a 4,000 volt electric field. The high cost, short half-life and radioactivity of tritium make it difficult to work with. The second easiest reaction

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1500-449: A fusor power system. To begin with, the electrodes cannot influence the potential within themselves, so it would seem at first glance that the fusion plasma would be in more or less direct contact with the inner electrode, resulting in contamination of the plasma and destruction of the electrode. However, the majority of the fusion tends to occur in microchannels formed in areas of minimum electric potential, seen as visible "rays" penetrating

1625-448: A fusor-like device has been 3 × 10 neutrons per second with the deuterium-deuterium fusion reaction. Commercial startups have used the neutron fluxes generated by fusors to generate Mo-99 , a precursor to Technetium-99m , an isotope used for medical care. Diamagnetism Diamagnetism is the property of materials that are repelled by a magnetic field ; an applied magnetic field creates an induced magnetic field in them in

1750-434: A fusor. First, there is the high-voltage involved. Second, there are the x-ray and neutron emissions that are possible. Also there are the publicity / misinformation considerations with local and regulatory authorities. The fusor has been demonstrated as a viable neutron source . Typical fusors cannot reach fluxes as high as nuclear reactor or particle accelerator sources, but are sufficient for many uses. Importantly,

1875-404: A hot plasma cloud can be found with the following equation. where 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 . Conduction

2000-600: A letter to the 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. Bussard founded Energy/Matter Conversion Corporation, Inc. (aka EMC2) in 1985 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

2125-422: A magnetic field, with no power consumption. Earnshaw's theorem seems to preclude the possibility of static magnetic levitation. However, Earnshaw's theorem applies only to objects with positive susceptibilities, such as ferromagnets (which have a permanent positive moment) and paramagnets (which induce a positive moment). These are attracted to field maxima, which do not exist in free space. Diamagnets (which induce

2250-404: A material, the diamagnetic contribution is usually negligible. Substances where the diamagnetic behaviour is the strongest effect are termed diamagnetic materials, or diamagnets. Diamagnetic materials are those that some people generally think of as non-magnetic , and include water , wood , most organic compounds such as petroleum and some plastics, and many metals including copper , particularly

2375-670: A monoenergetic distribution, like the one shown in Figure 6. This argument is supported by 2 dimensional particle-in-cell simulations. Bussard argued that constant electron injection would have the same effect. Such a distribution would help maintain a negative voltage in the center, improving performance. Nuclear fusion refers to nuclear reactions that combine lighter nuclei to become heavier nuclei. All chemical elements can be fused; for elements with fewer protons than iron, this process changes mass into energy that can potentially be captured to provide fusion power . The probability of

2500-412: A much better trap. Cusped confinement was explored theoretically and experimentally. However, most cusped experiments failed and disappeared from national programs by 1980. 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

2625-627: 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 electromagnets burned through, destroying the device. With no more funding during 2006, the project was stalled. This ended the US Navy's 11-year embargo on publication and publicizing between 1994 and 2005. The company's military-owned equipment

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2750-463: A negative moment) are attracted to field minima, and there can be a field minimum in free space. A thin slice of pyrolytic graphite , which is an unusually strongly diamagnetic material, can be stably floated in a magnetic field, such as that from rare earth permanent magnets. This can be done with all components at room temperature, making a visually effective and relatively convenient demonstration of diamagnetism. The Radboud University Nijmegen ,

2875-418: A new compact fusion machine, the high beta fusion reactor , that may be related to the biconic cusp and the polywell, and working at β  = 1. 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. The polywell's rings are arranged so the densest fields are on the outside, trapping electrons in

3000-438: A new trajectory, exit the grid at some new point, and accelerate back into the center again, providing the circulation that is required for a fusion event to eventually take place. It is important to consider the actual startup sequence of a fusor to understand the resulting operation. Normally the system is pumped down to a vacuum and then a small amount of gas is placed inside the vacuum chamber. This gas will spread out to fill

3125-449: A newly ionized atom of lower energy and thus cools the plasma. Scatterings may also increase the energy of an ion which allows it to move past the anode and escape, in this example anything above 15 keV. Additionally, the scatterings of both the ions, and especially impurities left in the chamber, lead to significant Bremsstrahlung , creating X-rays that carries energy out of the fuel. This effect grows with particle energy, meaning

3250-409: A particular point. One of the biggest problems in fusion research is to keep the hot fuel from hitting the walls of the container. If this is allowed to happen, the fuel cannot be kept hot enough for the fusion reaction to occur. Farnsworth reasoned that he could build an electrostatic plasma confinement system in which the "wall" fields of the reactor were electrons or ions being held in place by

3375-454: A plasma consists of free-moving charges, it can be controlled using magnetic and electrical fields. Fusion devices use this capability to retain the fuel at millions of degrees. The fusor is part of a broader class of devices that attempts to give the fuel fusion-relevant energies by directly accelerating the ions toward each other. In the case of the fusor, this is accomplished with electrostatic forces. For every volt that an ion of ±1 charge

3500-526: A power plant seems destined to also destroy its inner electrode. As one fundamental limitation, any method which produces a neutron flux that is captured to heat a working fluid will also bombard its electrodes with that flux, heating them as well. Attempts to resolve these problems include Bussard 's Polywell system, D. C. Barnes' modified Penning trap approach, and the University of Illinois's fusor which retains grids but attempts to more tightly focus

3625-508: A purely classical system. However, the classical theory of Langevin for diamagnetism gives the same prediction as the quantum theory. The classical theory is given below. Paul Langevin 's theory of diamagnetism (1905) applies to materials containing atoms with closed shells (see dielectrics ). A field with intensity B , applied to an electron with charge e and mass m , gives rise to Larmor precession with frequency ω = eB / 2 m . The number of revolutions per unit time

3750-427: A reactor similar in design to the fusor, now called the polywell , that he stated would be capable of useful power generation. Most recently, the fusor has gained popularity among amateurs, who choose them as home projects due to their relatively low space, money, and power requirements. An online community of "fusioneers", The Open Source Fusor Research Consortium, or Fusor.net, is dedicated to reporting developments in

3875-501: A real net power clean fusion system" 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,

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4000-466: 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. Initial difficulties in spherical electron confinement led to the 2005 research project's termination. However, Bussard reported a fusion rate of 10 per second running D-D fusion reactions at only 12.5 kV (based on detecting nine neutrons in five tests, giving

4125-405: A susceptibility of χ v = −4.00 × 10 in one plane. Nevertheless, these values are orders of magnitude smaller than the magnetism exhibited by paramagnets and ferromagnets. Because χ v is derived from the ratio of the internal magnetic field to the applied field, it is a dimensionless value. In rare cases, the diamagnetic contribution can be stronger than paramagnetic contribution. This

4250-578: 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." There are several general criticisms of the Polywell: Todd Rider (a biological engineer and former student of plasma physics) calculated that X-ray radiation losses with this fuel would exceed fusion power production by at least 20%. Rider's model used

4375-461: A thin surface layer) due to the Meissner effect . If a powerful magnet (such as a supermagnet ) is covered with a layer of water (that is thin compared to the diameter of the magnet) then the field of the magnet significantly repels the water. This causes a slight dimple in the water's surface that may be seen by a reflection in its surface. Diamagnets may be levitated in stable equilibrium in

4500-465: A viable concept for large-scale energy production by scientists. Fusion takes place when nuclei approach to a distance where the nuclear force can pull them together into a single larger nucleus. Opposing this close approach are the positive charges in the nuclei, which force them apart due to the electrostatic force . In order to produce fusion events, the nuclei must have initial energy great enough to allow them to overcome this Coulomb barrier . As

4625-432: 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. By comparison, researchers at University of Wisconsin–Madison reported a neutron rate of up to 5×10 per second at voltages of 120 kV from an electrostatic fusor without magnetic fields. Bussard asserted, by using superconductor coils, that

4750-649: Is where E F {\displaystyle E_{\rm {F}}} is the Fermi energy . This is equivalent to − μ 0 μ B 2 g ( E F ) / 3 {\displaystyle -\mu _{0}\mu _{\rm {B}}^{2}g(E_{\rm {F}})/3} , exactly − 1 / 3 {\textstyle -1/3} times Pauli paramagnetic susceptibility, where μ B = e ℏ / 2 m {\displaystyle \mu _{\rm {B}}=e\hbar /2m}

4875-625: Is ω / 2 π , so the current for an atom with Z electrons is (in SI units ) The magnetic moment of a current loop is equal to the current times the area of the loop. Suppose the field is aligned with the z axis. The average loop area can be given as π ⟨ ρ 2 ⟩ {\displaystyle \scriptstyle \pi \left\langle \rho ^{2}\right\rangle } , where ⟨ ρ 2 ⟩ {\displaystyle \scriptstyle \left\langle \rho ^{2}\right\rangle }

5000-434: Is a device that uses an electric field to heat ions to a temperature at which they undergo nuclear fusion . The machine induces a potential difference between two metal cages, inside a vacuum. Positive ions fall down this voltage drop, building up speed. If they collide in the center, they can fuse. This is one kind of an inertial electrostatic confinement device – a branch of fusion research. A Farnsworth–Hirsch fusor

5125-418: Is accelerated across it gains 1 electronvolt in energy. To reach the required ~10 keV, a voltage of 10 kV is required, applied to both particles. For comparison, the electron gun in a typical television cathode-ray tube is on the order of 3 to 6 kV, so the complexity of such a device is fairly limited. For a variety of reasons, energies on the order of 15 keV are used. This corresponds to

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5250-538: Is attempting to hold a diamagnetic plasma - a material which rejects the outside magnetic fields created by the electromagnets. This kind of behavior is not normal for fusing plasmas. 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

5375-554: Is characterized by a broad symmetric glow, with one or two electron beams exiting the structure. There is little fusion. The halo mode occurs in higher pressure tanks, and as the vacuum improves, the device transitions to star mode. Star mode appears as bright beams of light emanating from the device center. Because the electric field made by the cages is negative, it cannot simultaneously trap both positively charged ions and negative electrons. Hence, there must be some regions of charge accumulation , which will result in an upper limit on

5500-431: Is defined as χ v = μ v − 1 . This means that diamagnetic materials are repelled by magnetic fields. However, since diamagnetism is such a weak property, its effects are not observable in everyday life. For example, the magnetic susceptibility of diamagnets such as water is χ v = −9.05 × 10 . The most strongly diamagnetic material is bismuth , χ v = −1.66 × 10 , although pyrolytic carbon may have

5625-504: Is done in other fusion projects such as ITER . As an electron enters a magnetic field, it feels a Lorentz force and corkscrews. The radius of this motion is the gyroradius . As it moves it loses some energy as x-rays , every time it changes speed. The electron spins faster and tighter in denser fields, as it enters the MaGrid. Inside the MaGrid, single electrons travel straight through the null point, due to their infinite gyroradius in regions of no magnetic field. Next, they head towards

5750-400: Is not applicable to IEC fusion, as a quasineutral plasma cannot be contained by an electric field, which is a fundamental part of IEC fusion. However, in an earlier paper, "A general critique of inertial-electrostatic confinement fusion systems" , Rider addresses the common IEC devices directly, including the fusor. In the case of the fusor the electrons are generally separated from the mass of

5875-545: Is simple to demonstrate that the scattering chance is many orders of magnitude higher than the fusion rate, meaning that the vast majority of the energy supplied to the ions will go to waste and those fusion reactions that do occur cannot make up for these losses. To be energy positive, a fusion device must recycle these ions back into the fuel mass so that they have thousands or millions of such chances to fuse, and their energy must be retained as much as possible during this period. The fusor attempts to meet this requirement through

6000-410: 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." Bussard died on October 6, 2007, from multiple myeloma at age 79. Fusor A fusor

6125-418: Is that the inner cage conducts away too much energy and mass. The solution, suggested by Robert Bussard and Oleg Lavrentiev , 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 The magnetic energy density required to confine electrons is far smaller than that required to directly confine ions, as

6250-456: Is the Bohr magneton and g ( E ) {\displaystyle g(E)} is the density of states (number of states per energy per volume). This formula takes into account the spin degeneracy of the carriers (spin-1/2 electrons). In doped semiconductors the ratio between Landau and Pauli susceptibilities may change due to the effective mass of the charge carriers differing from

6375-432: Is the case for gold , which has a magnetic susceptibility less than 0 (and is thus by definition a diamagnetic material), but when measured carefully with X-ray magnetic circular dichroism , has an extremely weak paramagnetic contribution that is overcome by a stronger diamagnetic contribution. Superconductors may be considered perfect diamagnets ( χ v = −1 ), because they expel all magnetic fields (except in

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6500-863: Is the mean square distance of the electrons perpendicular to the z axis. The magnetic moment is therefore If the distribution of charge is spherically symmetric, we can suppose that the distribution of x,y,z coordinates are independent and identically distributed . Then ⟨ x 2 ⟩ = ⟨ y 2 ⟩ = ⟨ z 2 ⟩ = 1 3 ⟨ r 2 ⟩ {\displaystyle \scriptstyle \left\langle x^{2}\right\rangle \;=\;\left\langle y^{2}\right\rangle \;=\;\left\langle z^{2}\right\rangle \;=\;{\frac {1}{3}}\left\langle r^{2}\right\rangle } , where ⟨ r 2 ⟩ {\displaystyle \scriptstyle \left\langle r^{2}\right\rangle }

6625-570: Is the mean square distance of the electrons from the nucleus. Therefore, ⟨ ρ 2 ⟩ = ⟨ x 2 ⟩ + ⟨ y 2 ⟩ = 2 3 ⟨ r 2 ⟩ {\displaystyle \scriptstyle \left\langle \rho ^{2}\right\rangle \;=\;\left\langle x^{2}\right\rangle \;+\;\left\langle y^{2}\right\rangle \;=\;{\frac {2}{3}}\left\langle r^{2}\right\rangle } . If n {\displaystyle n}

6750-488: Is the most common type of fusor. This design came from work by Philo T. Farnsworth in 1964 and Robert L. Hirsch in 1967. A variant type of fusor had been proposed previously by William Elmore, James L. Tuck , and Ken Watson at the Los Alamos National Laboratory though they never built the machine. Fusors have been built by various institutions. These include academic institutions such as

6875-510: Is the number of atoms per unit volume, the volume diamagnetic susceptibility in SI units is In atoms, Langevin susceptibility is of the same order of magnitude as Van Vleck paramagnetic susceptibility . The Langevin theory is not the full picture for metals because there are also non-localized electrons. The theory that describes diamagnetism in a free electron gas is called Landau diamagnetism , named after Lev Landau , and instead considers

7000-403: 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 (does not produce neutrons). An advantage of p-B as

7125-571: Is used in chemistry to determine whether a particle (atom, ion, or molecule) is paramagnetic or diamagnetic: If all electrons in the particle are paired, then the substance made of this particle is diamagnetic; If it has unpaired electrons, then the substance is paramagnetic. Diamagnetism is a property of all materials, and always makes a weak contribution to the material's response to a magnetic field. However, other forms of magnetism (such as ferromagnetism or paramagnetism ) are so much stronger such that, when different forms of magnetism are present in

7250-436: Is when ions , electrons or neutrals touch a surface and escape. Energy is lost with the particle. Radiation is when energy escapes as light. Radiation increases with temperature. To get net power from fusion, these losses must be overcome. This leads to an equation for power output. Net Power = Efficiency × (Fusion − Radiation Loss − Conduction Loss) Lawson used this equation to estimate conditions for net power based on

7375-411: 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 it's necessary to overcome these losses. This leads to an equation for power output. where: John Lawson used this equation to estimate some conditions for net power based on

7500-583: The Netherlands , has conducted experiments where water and other substances were successfully levitated. Most spectacularly, a live frog (see figure) was levitated. In September 2009, NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California announced it had successfully levitated mice using a superconducting magnet , an important step forward since mice are closer biologically to humans than frogs. JPL said it hopes to perform experiments regarding

7625-854: The University of Wisconsin–Madison , the Massachusetts Institute of Technology and government entities, such as the Atomic Energy Organization of Iran and the Turkish Atomic Energy Authority . Fusors have also been developed commercially, as sources for neutrons by DaimlerChrysler Aerospace and as a method for generating medical isotopes. Fusors have also become very popular for hobbyists and amateurs. A growing number of amateurs have performed nuclear fusion using simple fusor machines. However, fusors are not considered

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7750-411: The magnetic fields sent electrons into the walls, driving up conduction losses. These losses were attributed to poor electron injection. The US Navy began providing low-level funding to the project in 1992. Krall published results in 1994. 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

7875-436: The multipactor . Fuel could then be injected through the wall, and once inside it would be unable to escape. He called this concept a virtual electrode, and the system as a whole the fusor . Farnsworth's original fusor designs were based on cylindrical arrangements of electrodes, like the original multipactors. Fuel was ionized and then fired from small accelerators through holes in the outer (physical) electrodes. Once through

8000-495: The neutron generator easily sits on a benchtop, and can be turned off at the flick of a switch. A commercial fusor was developed as a non-core business within DaimlerChrysler Aerospace – Space Infrastructure, Bremen between 1996 and early 2001. After the project was effectively ended, the former project manager established a company which is called NSD-Fusion. To date, the highest neutron flux achieved by

8125-417: The "electron gun" which forms the basis for old-style television display tubes), as well as magnetron type devices, (which are the power sources for microwave ovens), which can enhance ion formation using high-voltage electromagnetic fields. Any method which increases ion density (within limits which preserve ion mean-free path), or ion energy, can be expected to enhance the fusion yield, typically measured in

8250-505: The AEC decided to concentrate funding on large tokamak projects, and reduce backing for alternative concepts. George H. Miley at the University of Illinois reexamined the fusor and re-introduced it into the field. A low but steady interest in the fusor has persisted since. An important development was the successful commercial introduction of a fusor-based neutron generator . From 2006 until his death in 2007, Robert W. Bussard gave talks on

8375-564: The US Navy. In 1993, it received a grant from the Electric Power Research Institute . In 1994, The company received small grants from NASA and LANL . Starting in 1999, the company was primarily funded by the US Navy. WB-1 had six conventional magnets in a cube. This device was 10 cm across. 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

8500-457: The WB-6 tests was about 12.5 kV, with a resulting potential well depth of about 10 kV. 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. Hirsch reported a fusion rate this high only by driving his machine with a 150 kV drop between the inside and outside cages. Hirsch also used deuterium and tritium ,

8625-514: The achievable density. This could place an upper limit on the machine's power density, which may keep it too low for power production. When they first fall into the center of the fusor, the ions will all have the same energy, but the velocity distribution will rapidly approach a Maxwell–Boltzmann distribution . This would occur through simple Coulomb collisions in a matter of milliseconds, but beam-beam instabilities will occur orders of magnitude faster still. In comparison, any given ion will require

8750-403: The average kinetic energy at a temperature of approximately 174 million Kelvin, a typical magnetic confinement fusion plasma temperature. The problem with this colliding beam fusion approach, in general, is that the ions will most likely never hit each other no matter how precisely aimed. Even the most minor misalignment will cause the particles to scatter and thus fail to fuse. It

8875-400: 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 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

9000-409: The center. This can trap particles at low beta values. In high beta conditions, the machine may operate with cusp confinement. This is an improvement over the simpler magnetic mirror. 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

9125-483: The change, in a similar way to superconductors, which are essentially perfect diamagnets. However, since the electrons are rigidly held in orbitals by the charge of the protons and are further constrained by the Pauli exclusion principle , many materials exhibit diamagnetism, but typically respond very little to the applied field. The Bohr–Van Leeuwen theorem proves that there cannot be any diamagnetism or paramagnetism in

9250-440: The cloud lose energy as light. The radiation from a fusor can (at least) be in the visible , ultraviolet and X-ray spectrum, depending on the type of fusor used. These changes in speed can be due to electrostatic interactions between particles (ion to ion, ion to electron, electron to electron). This is referred to bremsstrahlung radiation, and is common in fusors. Changes in speed can also be due to interactions between

9375-426: The core. These form because the forces within the region correspond to roughly stable "orbits". Approximately 40% of the high energy ions in a typical grid operating in star mode may be within these microchannels. Nonetheless, grid collisions remain the primary energy loss mechanism for Farnsworth–Hirsch fusors. Complicating issues is the challenge in cooling the central electrode; any fusor producing enough power to run

9500-469: The device without striking a surface, reducing conduction losses. Bussard stressed this; specifically emphasizing that electrons need to move through all cusps of the machine. As of 2015 it had not been determined conclusively what the ion or electron energy distribution is. The energy distribution of the plasma can be measured using a Langmuir probe . This probe absorbs charge from the plasma as its voltage changes, making an I-V Curve . From this signal,

9625-574: The diamagnetic effect will impact the external field. 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). In February 2013, Lockheed Martin Skunk Works announced

9750-570: The edges of the MaGrid field and corkscrew tighter along the denser magnetic field lines. 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. Electron trapping has been measured in polywells with Langmuir probes . The polywell attempts to confine the ions and electrons through two different means, borrowed from fusors and magnetic mirrors . The electrons are easier to confine magnetically because they have so much less mass than

9875-658: The effects of microgravity on bone and muscle mass. Recent experiments studying the growth of protein crystals have led to a technique using powerful magnets to allow growth in ways that counteract Earth's gravity. A simple homemade device for demonstration can be constructed out of bismuth plates and a few permanent magnets that levitate a permanent magnet. The electrons in a material generally settle in orbitals, with effectively zero resistance and act like current loops. Thus it might be imagined that diamagnetism effects in general would be common, since any applied magnetic field would generate currents in these loops that would oppose

10000-601: The electrodes needs to be at least 25 kV for fusion to occur. All of this work had taken place at the Farnsworth Television labs , which had been purchased in 1949 by ITT Corporation , as part of its plan to become the next RCA . However, a fusion research project was not regarded as immediately profitable. In 1965, the board of directors started asking Harold Geneen to sell off the Farnsworth division, but he had his 1966 budget approved with funding until

10125-618: 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. β e = p p m a g = n e k B T e ( B 2 / 2 μ 0 ) {\displaystyle \beta _{e}={\frac {p}{p_{mag}}}={\frac {n_{e}k_{B}T_{e}}{(B^{2}/2\mu _{0})}}} Most experiments on polywells involve low-beta plasma regimes (where β < 1), where

10250-400: The energy distribution can be calculated. The energy distribution both drives and is driven by several physical rates, 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: Critics claimed that both the electrons and ion populations have bell curve distribution; that

10375-408: The energy needed in a fusor system is higher than one where the fuel is heated by some other method, as some will be "lost" during startup. Real electrodes are not infinitely thin, and the potential for scattering off the wires or even capture of the ions within the electrodes is a significant issue that causes high conduction losses. These losses can be at least five orders of magnitude higher than

10500-430: The energy released from the fusion reaction, even when the fusor is in star mode, which minimizes these reactions. There are numerous other loss mechanisms as well. These include charge exchange between high-energy ions and low-energy neutral particles, which causes the ion to capture the electron, become electrically neutral, and then leave the fusor as it is no longer accelerated back into the chamber. This leaves behind

10625-407: The far side of the central reaction area. The fuel atoms inside the inner area during the startup period are not ionized. The accelerated ions scatter with these and lose their energy, while ionizing the formerly cold atom. This process, and the scatterings off other ions, causes the ion energies to become randomly distributed and the fuel rapidly takes on a non-thermal distribution. For this reason,

10750-629: The fifth power. While Bussard did not publicly document the reasoning underlying this estimate, if true, it would enable a model only ten times larger to be useful as a fusion power plant. Funding became tighter and tighter. According to Bussard , "The funds were clearly needed for the more important War in Iraq ." 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

10875-401: The following assumptions: Based on these assumptions, Rider used general equations to estimate the rates of different physical effects. These included the loss of ions to up-scattering, the ion thermalization rate, the energy loss due to X-ray radiation and the fusion rate. His conclusions were that the device suffered from "fundamental flaws". By contrast, Bussard argued that the plasma had

11000-421: The fuel isolated near the electrodes, which limits the loss rate. However, Rider demonstrates that practical fusors operate in a range of modes that either lead to significant electron mixing and losses, or alternately lower power densities. This appears to be a sort of catch-22 that limits the output of any fusor-like system. There are several key safety considerations involved with the building and operation of

11125-611: The fuel to temperatures where the Maxwell-Boltzmann distribution of their resulting energies is high enough that some of the particles in the long tail have the required energy. High enough in this case is such that the rate of the fusion reactions produces enough energy to offset energy losses to the environment and thus heat the surrounding fuel to the same temperatures and produce a self-sustaining reaction known as ignition . Calculations show this takes place at about 50 million  kelvin (K), although higher numbers on

11250-454: The heavy ones with many core electrons , such as mercury , gold and bismuth . The magnetic susceptibility values of various molecular fragments are called Pascal's constants (named after Paul Pascal  [ fr ] ). Diamagnetic materials, like water, or water-based materials, have a relative magnetic permeability that is less than or equal to 1, and therefore a magnetic susceptibility less than or equal to 0, since susceptibility

11375-401: The hole they were accelerated towards the inner reaction area at high velocity. Electrostatic pressure from the positively charged electrodes would keep the fuel as a whole off the walls of the chamber, and impacts from new ions would keep the hottest plasma in the center. He referred to this as inertial electrostatic confinement , a term that continues to be used to this day. The voltage between

11500-488: The idea independently. Research was funded first by the Defense Threat Reduction Agency beginning in 1987 and later by DARPA . This funding resulted in a machine known as the high energy power source (HEPS) experiment. It was built by Directed Technologies Inc. This machine was a large (1.9 m across) machine, with the rings outside the vacuum chamber. This machine performed poorly because

11625-410: 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

11750-507: 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

11875-617: The ions fuse before losing their energy by any process). Whereas 45 megakelvins is a very high temperature by any standard, the corresponding voltage is only 4 kV, a level commonly found in such devices as neon signs and CRT televisions. To the extent that the ions remain at their initial energy, the energy can be tuned to take advantage of the peak of the reaction cross section or to avoid disadvantageous (for example neutron-producing) reactions that might occur at higher energies. Various attempts have been made at increasing deuterium ionization rate, including heaters within "ion-guns", (similar to

12000-543: The ions into microchannels to attempt to avoid losses. While all three are Inertial electrostatic confinement (IEC) devices, only the last is actually a "fusor". Charged particles will radiate energy as light when they change velocity. This loss rate can be estimated for nonrelativistic particles using the Larmor formula . Inside a fusor there is a cloud of ions and electrons . These particles will accelerate or decelerate as they move about. These changes in speed make

12125-426: The ions must be at a temperature of at least 4 keV ( kiloelectronvolts ), or about 45 million kelvins . The second easiest reaction is fusing deuterium with itself. Because this gas is cheaper, it is the fuel commonly used by amateurs. The ease of doing a fusion reaction is measured by its cross section . At such conditions, the atoms are ionized and make a plasma . The energy generated by fusion, inside

12250-460: The ions. 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 would significantly improve the function of these machines. It has been argued that efficient recirculation is the only way they can be viable. Electrons or ions move through

12375-403: 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 per second. This is based on a total of nine neutrons in five tests, giving a wide confidence interval. Drive voltage on

12500-421: The low speed at the rim means that thermalization there has almost no impact on ion velocity in the core. Bussard calculated that a polywell reactor with a radius of 1.5 meters would produce net power fusing deuterium . 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

12625-460: The material. The magnetic permeability of diamagnetic materials is less than the permeability of vacuum , μ 0 . In most materials, diamagnetism is a weak effect which can be detected only by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it entirely expels any magnetic field from its interior (the Meissner effect ). Diamagnetism was first discovered when Anton Brugmans observed in 1778 that bismuth

12750-409: 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. 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. From 1998 to 2005 the company built

12875-411: The middle of 1967. Further funding was refused, and that ended ITT's experiments with fusion. Things changed dramatically with the arrival of Robert Hirsch , and the introduction of the modified Hirsch–Meeks fusor patent. New fusors based on Hirsch's design were first constructed between 1964 and 1967. Hirsch published his design in a paper in 1967. His design included ion beams to shoot ions into

13000-458: 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. It has been proposed that energy may be extracted from polywells using heat capture or, in the case of aneutronic fusion like D-He or p -B, direct energy conversion , though that scheme faces challenges. The energetic alpha particles (up to

13125-433: The nuclear force is increased with the number of nucleons, protons and neutrons, and the electromagnetic force is increased with the number of protons only, the easiest atoms to fuse are isotopes of hydrogen, deuterium with one neutron, and tritium with two. With hydrogen fuels, about 3 to 10 keV is needed to allow the reaction to take place. Traditional approaches to fusion power have generally attempted to heat

13250-435: The number of neutrons produced per second. The ease with which the ion energy can be increased appears to be particularly useful when "high temperature" fusion reactions are considered, such as proton-boron fusion , which has plentiful fuel, requires no radioactive tritium , and produces no neutrons in the primary reaction. Fusors have at least two modes of operation (possibly more): star mode and halo mode . Halo mode

13375-414: The only significant energy loss channel is through electron losses proportional to the surface area. He also stated that the density would scale with the square of the field (constant beta conditions), and the maximum attainable magnetic field would scale with the radius. Under those conditions, the fusion power produced would scale with the seventh power of the radius, and the energy gain would scale with

13500-440: The opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances, the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in

13625-441: The order of 100 million K are desirable in practical machines. Due to the extremely high temperatures, fusion reactions are also referred to as thermo nuclear. When atoms are heated to temperatures corresponding to thousands of degrees, the electrons become increasingly free of their nucleus. This leads to a gas-like state of matter known as a plasma , consisting of free nuclei known as ions, and their former electrons. As

13750-403: 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 temperature , making positive ions . The ions are positive and move towards the negative inner cage. Those that miss the wires of the inner cage fly through

13875-445: The particle and the electric field. Since there are no magnetic fields, fusors emit no cyclotron radiation at slow speeds, or synchrotron radiation at high speeds. In Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium , Todd Rider argues that a quasineutral isotropic plasma will lose energy due to Bremsstrahlung at a rate prohibitive for any fuel other than D-T (or possibly D-D or D-He3). This paper

14000-408: The plasma pressure is weak compared to the magnetic pressure . Several models describe magnetic trapping in polywells. 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. The main problem with the fusor

14125-460: The plasma is thermalized . The justification given is that the longer the electrons and ions move inside the polywell, the more interactions they undergo leading to thermalization. This model for the ion distribution is shown in Figure 5. Supporters modeled a nonthermal plasma . The justification is the high amount of scattering in the device center. Without a magnetic field, electrons scatter in this region. They claimed that this scattering leads to

14250-422: The problem becomes more pronounced as the system approaches fusion-relevant operating conditions. As a result of these loss mechanisms, no fusor has ever come close to break-even energy output and it appears it is unable to ever do so. The common sources of the high voltage are ZVS flyback HV sources and neon-sign transformers . It can also be called an electrostatic particle accelerator . The fusor

14375-400: 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. In 1955, Harold Grad theorized that a high-beta plasma pressure combined with a cusped magnetic field would improve plasma confinement. A diamagnetic plasma rejects the external fields and plugs the cusps. This system would be

14500-421: The spherical arrangement of its accelerator grid system. Ions that fail to fuse pass through the center of the device and back into the accelerator on the far side, where they are accelerated back into the center again. There is no energy lost in this action, and in theory, assuming infinitely thin grid wires, the ions can circulate forever with no additional energy needed. Even those that scatter will simply take on

14625-406: The temperature of the grid as well as eroding it. These strikes 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 conduction losses. Hence, no fusor has come close to energy break-even. The Polywell

14750-539: The vacuum chamber. The team then turned to the AEC , then in charge of fusion research funding, and provided them with a demonstration device mounted on a serving cart that produced more fusion than any existing "classical" device. The observers were startled, but the timing was bad; Hirsch himself had recently revealed the great progress being made by the Soviets using the tokamak . In response to this surprising development,

14875-484: The volume. When voltage is applied to the electrodes, the atoms between them will experience a field that will cause them to ionize and begin accelerating inward. As the atoms are randomly distributed to begin, the amount of energy they will gain differs; atoms initially near the anode will gain some large portion of the applied voltage, say 15 keV. Those initially near the cathode will gain much less energy, possibly far too low to undergo fusion with their counterparts on

15000-485: The weak counteracting field that forms when the electrons' trajectories are curved due to the Lorentz force . Landau diamagnetism, however, should be contrasted with Pauli paramagnetism , an effect associated with the polarization of delocalized electrons' spins. For the bulk case of a 3D system and low magnetic fields, the (volume) diamagnetic susceptibility can be calculated using Landau quantization , which in SI units

15125-536: The world of fusors and aiding other amateurs in their projects. The site includes forums, articles and papers done on the fusor, including Farnsworth's original patent, as well as Hirsch's patent of his version of the invention. Nuclear fusion refers to reactions in which lighter nuclei are combined to become heavier nuclei. This process changes mass into energy which in turn may be captured to provide fusion power . Many types of atoms can be fused. The easiest to fuse are deuterium and tritium . For fusion to occur

15250-404: Was originally conceived by Philo T. Farnsworth , better known for his pioneering work in television. In the early 1930s, he investigated a number of vacuum tube designs for use in television, and found one that led to an interesting effect. In this design, which he called the "multipactor", electrons moving from one electrode to another were stopped in mid-flight with the proper application of

15375-442: Was repelled by magnetic fields. In 1845, Michael Faraday demonstrated that it was a property of matter and concluded that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field. On a suggestion by William Whewell , Faraday first referred to the phenomenon as diamagnetic (the prefix dia- meaning through or across ), then later changed it to diamagnetism . A simple rule of thumb

15500-499: Was transferred to SpaceDev , which hired three of the team's researchers. 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?" He also presented and published an overview at the 57th International Astronautical Congress in October 2006. He presented at an internal Yahoo! Tech Talk on April 10, 2007. and spoke on

15625-399: 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 providing (1) x-ray and (2) flux loop measurements that

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