White hole

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https://en.wikipedia.org/wiki/White_hole

In general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy-matter, light and information can escape from it. In this sense, it is the reverse of a black hole, which can be entered only from the outside and from which energy-matter, light and information cannot escape. White holes appear in the theory of eternal black holes. In addition to a black hole region in the future, such a solution of the Einstein field equations has a white hole region in its past. This region does not exist for black holes that have formed through gravitational collapse, however, nor are there any observed physical processes through which a white hole could be formed.

Supermassive black holes (SBHs) are theoretically predicted to be at the center of every galaxy and that possibly, a galaxy cannot form without one. Stephen Hawking and others have proposed that these SBHs spawn a supermassive white hole/Big Bang.

Overview

Like black holes, white holes have properties like mass, charge, and angular momentum. They attract matter like any other mass, but objects falling towards a white hole would never actually reach the white hole's event horizon (though in the case of the maximally extended Schwarzschild solution, discussed below, the white hole event horizon in the past becomes a black hole event horizon in the future, so any object falling towards it will eventually reach the black hole horizon). Imagine a gravitational field, without a surface. Acceleration due to gravity is the greatest on the surface of any body. But since black holes lack a surface, acceleration due to gravity increases exponentially, but never reaches a final value as there is no considered surface in a singularity.

In quantum mechanics, the black hole emits Hawking radiation and so it can come to thermal equilibrium with a gas of radiation (not compulsory). Because a thermal-equilibrium state is time-reversal-invariant, Stephen Hawking argued that the time reversal of a black hole in thermal equilibrium results in a white hole in thermal equilibrium (each absorbing and emitting energy to equivalent degrees).  Consequently, this may imply that black holes and white holes are the same structure, wherein the Hawking radiation from an ordinary black hole is identified with a white hole's emission of energy and matter. Hawking's semi-classical argument is reproduced in a quantum mechanical AdS/CFT treatment, where a black hole in anti-de Sitter space is described by a thermal gas in a gauge theory, whose time reversal is the same as itself.

Origin

A diagram of the structure of the maximally extended black hole spacetime. The horizontal direction is space and the vertical direction is time.

The possibility of the existence of white holes was put forward by Russian cosmologist Igor Novikov in 1964. White holes are predicted as part of a solution to the Einstein field equations known as the maximally extended version of the Schwarzschild metric describing an eternal black hole with no charge and no rotation. Here, "maximally extended" refers to the idea that the spacetime should not have any "edges": for any possible trajectory of a free-falling particle (following a geodesic) in the spacetime, it should be possible to continue this path arbitrarily far into the particle's future, unless the trajectory hits a gravitational singularity like the one at the center of the black hole's interior. In order to satisfy this requirement, it turns out that in addition to the black hole interior region that particles enter when they fall through the event horizon from the outside, there must be a separate white hole interior region, which allows us to extrapolate the trajectories of particles that an outside observer sees rising up away from the event horizon. For an observer outside using Schwarzschild coordinates, infalling particles take an infinite time to reach the black hole horizon infinitely far in the future, while outgoing particles that pass the observer have been traveling outward for an infinite time since crossing the white hole horizon infinitely far in the past (however, the particles or other objects experience only a finite proper time between crossing the horizon and passing the outside observer). The black hole/white hole appears "eternal" from the perspective of an outside observer, in the sense that particles traveling outward from the white hole interior region can pass the observer at any time, and particles traveling inward, which will eventually reach the black hole interior region can also pass the observer at any time.

Just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black-hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other one), and likewise particles from the interior white-hole region can escape into either universe. All four regions can be seen in a spacetime diagram that uses Kruskal–Szekeres coordinates (see figure).

In this spacetime, it is possible to come up with coordinate systems such that if you pick a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge" or Schwarzschild wormhole. Depending on where the space-like hypersurface is chosen, the Einstein-Rosen bridge can either connect two black hole event horizons in each universe (with points in the interior of the bridge being part of the black hole region of the spacetime), or two white hole event horizons in each universe (with points in the interior of the bridge being part of the white hole region). It is impossible to use the bridge to cross from one universe to the other, however, because it is impossible to enter a white hole event horizon from the outside, and anyone entering a black hole horizon from either universe will inevitably hit the black hole singularity.

Note that the maximally extended Schwarzschild metric describes an idealized black hole/white hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region. But because the equations of general relativity are time-reversible – they exhibit Time reversal symmetry – general relativity must also allow the time-reverse of this type of "realistic" black hole that forms from collapsing matter. The time-reversed case would be a white hole that has existed since the beginning of the universe, and that emits matter until it finally "explodes" and disappears. Despite the fact that such objects are permitted theoretically, they are not taken as seriously as black holes by physicists, since there would be no processes that would naturally lead to their formation; they could exist only if they were built into the initial conditions of the Big Bang. Additionally, it is predicted that such a white hole would be highly "unstable" in the sense that if any small amount of matter fell towards the horizon from the outside, this would prevent the white hole's explosion as seen by distant observers, with the matter emitted from the singularity never able to escape the white hole's gravitational radius.

Big Bang/Supermassive White Hole

Main article: Big Bang

A view of black holes first proposed in the late 1980s might be interpreted as shedding some light on the nature of classical white holes. Some researchers have proposed that when a black hole forms, a Big Bang may occur at the core/singularity, which would create a new universe that expands outside of the parent universe.

The Einstein–Cartan–Sciama–Kibble theory of gravity extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable. Torsion naturally accounts for the quantum-mechanical, intrinsic angular momentum (spin) of matter.

According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole. In the Einstein–Cartan theory, however, the minimal coupling between torsion and Dirac spinors generates a repulsive spin–spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction prevents the formation of a gravitational singularity. Instead, the collapsing matter on the other side of the event horizon reaches an enormous but finite density and rebounds, forming a regular Einstein–Rosen bridge. The other side of the bridge becomes a new, growing baby universe. For observers in the baby universe, the parent universe appears as the only white hole. Accordingly, the observable universe is the Einstein–Rosen interior of a black hole existing as one of possibly many inside a larger universe. The Big Bang was a nonsingular Big Bounce at which the observable universe had a finite, minimum scale factor.

A 2012 paper argues that the Big Bang itself is a white hole. It further suggests that the emergence of a white hole, which was named a 'Small Bang', is spontaneous—all the matter is ejected at a single pulse. Thus, unlike black holes, white holes cannot be continuously observed; rather, their effects can be detected only around the event itself. The paper even proposed identifying a new group of gamma-ray bursts with white holes.

In 2014, the idea of the Big Bang being produced by a supermassive white hole explosion was explored in the framework of a five dimensional vacuum by Madriz Aguilar, Moreno and Bellini.

 

Fusor

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https://en.wikipedia.org/wiki/Fusor

A homemade fusor

A fusor is a device that uses an electric field to heat ions to nuclear fusion conditions. The machine induces a voltage 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 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 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 a viable concept for large-scale energy production by scientists.

Mechanism

For every volt that an ion of ±1 charge is accelerated across it gains 1 electronvolt in energy, similar to heating a material by 11,604 kelvins in temperature (T = eV / k_B, where T is the temperature in kelvins, eV is the energy of the ion in electronvolts, and k_B is the Boltzmann constant). After being accelerated by 15 kV a singly-charged ion has a kinetic energy of 15 keV, similar to the average kinetic energy at a temperature of approximately 174 megakelvins, a typical magnetic confinement fusion plasma temperature. Because most of the ions fall into the wires of the cage, fusors suffer from high conduction losses. On a bench top, these losses can be at least five orders of magnitude higher than the energy released from the fusion reaction, even when the fusor is in star mode. Hence, no fusor has ever come close to break-even energy output. 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.

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

History

See also: Inertial electrostatic confinement § History

U.S. Patent 3,386,883 – fusor – Image from Farnsworth's patent, on 4 June 1968. This device has an inner cage to make the field, and four ion guns on the outside.

The fusor 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 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 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 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.

Design

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 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 the electrodes needs to be at least 25,000 Volts for fusion to occur.

Work at Farnsworth Television labs

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 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 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, the AEC decided to concentrate funding on large tokamak projects, and reduce backing for alternative concepts.

Recent developments

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 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 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.

Fusion in fusors

Basic fusion

The cross-sections 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 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 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.

Net power

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.

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

where

${\displaystyle P_{\text{fusion}}}$ is the fusion power density (energy per time per volume),

n is the number density of species A or B (particles per volume),

${\displaystyle \langle \sigma v_{A,B}\rangle }$ is the product of the collision cross-section σ (which depends on the relative velocity) and the relative velocity v of the two species, averaged over all the particle velocities in the system,

${\displaystyle E_{\text{fusion}}}$ is the energy released by a single fusion reaction.

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 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.

${\displaystyle P_{\text{out}}=\eta _{\text{capture}}(P_{\text{fusion}}-P_{\text{conduction}}-P_{\text{radiation}}).}$

where:

η is the efficiency,

${\displaystyle P_{\text{conduction}}}$ is the power of conduction losses as energy-laden mass leaves,

${\displaystyle P_{\text{radiation}}}$ is the power of radiation losses as energy leaves as light,

${\displaystyle P_{\text{out}}}$ is the net power from fusion.

John Lawson used this equation to estimate some conditions for net power based on 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 fusors

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 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 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 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 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.

Common considerations

Modes of operation

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.

Fusors have at least two modes of operation (possibly more): star mode and halo mode. Halo mode 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.

Power density

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 the achievable density. This could place an upper limit on the machine's power density, which may keep it too low for power production.

Thermalization of the ion velocities

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 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.

Electrodes

Image showing a different grid design

There are a number of unsolved challenges with the electrodes in 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 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 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 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".

Radiation

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 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 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 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 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.

Safety

There are several key safety considerations involved with the building and operation of 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. See "Neutron Safety FAQ" for additional information.

Commercial applications

Production source
Neutrons
Energy	2.45 MeV
Mass	940 MeV
Electric charge	0 C
Spin	1/2

Main article: Neutron generator

Neutron source

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, 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 a fusor-like device has been 3 × 10¹¹ neutrons per second with the deuterium-deuterium fusion reaction.

Medical isotopes

Commercial startups have used the neutron fluxes generated by fusors to generate Mo-99, an isotope used for medical care.

Magnetized target fusion

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Magnetized Target Fusion (MTF) is a fusion power concept that combines features of magnetic confinement fusion (MCF) and inertial confinement fusion (ICF). Like the magnetic approach, the fusion fuel is confined at lower density by magnetic fields while it is heated into a plasma. As with the inertial approach, fusion is initiated by rapidly squeezing the target to greatly increase fuel density and temperature. Although the resulting density is far lower than in ICF, it is thought that the combination of longer confinement times and better heat retention will let MTF operate, yet be easier to build. The term magneto-inertial fusion (MIF) is similar, but encompasses a wider variety of arrangements. The two terms are often applied interchangeably to experiments.

Fusion concepts

Main article: Fusion power

In fusion, lighter atoms are fused to make heavier atoms. The easiest fuels to do this with are isotopes of hydrogen. Generally these reactions take place inside a plasma. A plasma is a heated gas, where all the electrons have been stripped away; the gas has been fully ionized. The ions are positively charged, so they repel each other due to the electrostatic force. Fusion occurs when two ions collide at high energy, allowing the strong force to overcome the electrostatic force at a short distance. The amount of energy that needs to be applied to force the nuclei together is named the Coulomb barrier or fusion barrier energy. For fusion to occur in bulk plasma, it must be heated to tens of millions of degrees and compressed at high pressures, for a sufficient amount of time. Together, this is termed the triple product (see Lawson criterion). Fusion research focuses on reaching the highest triple product possible.

Magnetic fusion works to heat a dilute plasma (10¹⁴ ions per cm³) to high temperatures, around 20 keV (~200 million C). Ambient air is about 100,000 times denser. To make a practical reactor at these temperatures, the fuel must be confined for long periods of time, on the order of 1 second. The ITER tokamak design is currently being built to test the magnetic approach with pulse lengths up to 20 minutes.

Inertial fusion attempts to produce much higher densities, 10²⁵ ions per cubic cm, about 100 times the density of lead. This causes the reactions to occur extremely quickly (~1 nanosecond). Confinement is not needed; although the heat and particles created by the reactions will cause the plasma to explode outward, the speed this occurs is slower than the fusion reactions.

As of 2018, both of these methods of nuclear fusion are nearing net energy (Q>1) levels after many decades of research, but remain far from practical energy-producing devices.

Approach

While MCF and ICF attack the Lawson criterion problem from different directions, MTF attempts to work between the two. MTF aims for a plasma density of 10¹⁹ cm⁻³, intermediate between MCF (10¹⁴ cm⁻³) and ICF (10²⁵ cm⁻³) At this density, confinement times must be on the order of 1 µs, again intermediate between the other two. MTF uses magnetic fields to slow down plasma losses, and inertial compression is used to heat the plasma.

In general terms, MTF is an inertial method. Density is increased through a pulsed operation that compresses the fuel, heating the plasma, just as compression heats an ordinary gas. In traditional ICF, more energy is added through the lasers that compress the target, but that energy leaks away through multiple channels. MTF employs a magnetic field that is created before compression that confines and insulates fuel so less energy is lost. The result, compared to ICF, is a somewhat-dense, somewhat-hot fuel mass that undergoes fusion at a medium reaction rate, so it only must be confined for a medium length of time.

As the fuel pellet is compressed, the heat and pressure in the plasma grow. The rate of collapse is generally linear, but the pressure is based on the volume, which increases with the cube of the compression. As some point the pressure is enough to stop and then reverse the collapse. The mass of the metal liner around the fuel means this process takes some time to occur. The MTF concept is based on having this dwell time be long enough for the fusion processes to take place.

MTF has advantages over both ICF and low-density plasma fusion. Its energy inputs are relatively efficient and inexpensive, whereas ICF demands specialized high-performance lasers that currently offer low efficiency. The cost and complexity of these lasers, termed "drivers", is so great that traditional ICF methods remain impractical for commercial energy production. Likewise, although MTF needs magnetic confinement to stabilize and insulate the fuel while it is being compressed, the needed confinement time is thousands of times less than for MCF. Confinement times of the order needed for MTF were demonstrated in MCF experiments years ago.

The densities, temperatures and confinement times needed by MTF are well within the current state of the art and have been repeatedly demonstrated. Los Alamos National Laboratory has referred to the concept as a "low cost path to fusion".

Devices

FRX-L

In the pioneering experiment, Los Alamos National Laboratory's FRX-L, a plasma is first created at low density by transformer-coupling an electric current through a gas inside a quartz tube (generally a non-fuel gas for testing purposes). This heats the plasma to about 200 eV (~2.3 million degrees). External magnets confine fuel within the tube. Plasmas are electrically conducting, allowing a current to pass through them. This current, generates a magnetic field that interacts with the current. The plasma is arranged so that the fields and current stabilize within the plasma once it is set up, self-confining the plasma. FRX-L uses the field-reversed configuration for this purpose. Since the temperature and confinement time is 100x lower than in MCF, the confinement is relatively easy to arrange and does not need the complex and expensive superconducting magnets used in most modern MCF experiments.

FRX-L is used solely for plasma creation, testing and diagnostics. It uses four high-voltage (up to 100 kV) capacitor banks storing up to 1 MJ of energy to drive a 1.5 MA current in one-turn magnetic-field coils that surround a 10 cm diameter quartz tube. In its current form as a plasma generator, FRX-L has demonstrated densities between (2 and 4)×10¹⁶ cm⁻³, temperatures of 100 to 250 eV, magnetic fields of 2.5 T and lifetimes of 10 to 15 μs. All of these are within an order of magnitude of what would be needed for an energy-positive machine.

FRX-L was later upgraded to add an "injector" system. This is situated around the quartz tube and consists of a conical arrangement of magnetic coils. When powered, the coils generate a field that is strong at one end of the tube and weaker at the other, pushing the plasma out the larger end. To complete the system, the injector was planned to be placed above the focus of the existing Shiva Star "can crusher" at the Air Force Research Laboratory's Directed Energy Lab at the Kirtland Air Force Base in Albuquerque, NM.

FRCHX

In 2007, an experiment called FRCHX was placed on Shiva Star. Similar to FRX-L, it uses a generation area and injects the plasma bundle into the Shiva Star liner compression area. Shiva Star delivers about 1.5 MJ into the kinetic energy of the 1 mm thick aluminum liner, which collapses cylindrically at about 5 km/s. This collapses the plasma bundle to a density around 5×10¹⁸ cm⁻³ and raises the temperature to about 5 keV, producing neutron yields on the order of 10¹² neutrons "per shot" using a D-D fuel. The power released in the larger shots, in the range of MJ, needs a period of resetting the equipment on the order of a week. The huge electromagnetic pulse (EMP) caused by the equipment forms a challenging environment for diagnostics.

Fusion demonstration plant

General Fusion of Canada, in partnership with the UK's Atomic Energy Authority, is to build a demonstration plant at Culham, England, as a precursor to a commercially viable pilot plant. The reaction vessel will be a fast-rotating cylinder of liquid metal (lead, incorporating lithium to harvest the tritium formed through neutron activation) which is formed into a sphere by the action of synchronised pistons driven by steam. Magnetized fusion fuel as plasma is injected into the sphere as it contracts, producing sufficient temperature and pressure for the fusion reaction to take place. The liquid metal is circulated through heat exchangers to provide steam.

Construction is expected to start in 2022, with operations beginning in 2025.

Challenges

MTF is not the first "new approach" to fusion power. When ICF was introduced in the 1960s, it was a radical new approach that was expected to produce practical fusion devices by the 1980s. Other approaches have encountered unexpected problems that greatly increased the difficulty of producing output power. With MCF, it was unexpected instabilities in plasmas as density or temperature was increased. With ICF, it was unexpected losses of energy and difficulties "smoothing" the beams. These have been partially addressed in large modern machines, but only at great expense.

In a general sense, MTF's challenges appear to be similar to those of ICF. To produce power effectively, the density must be increased to a working level and then held there long enough for most of the fuel mass to undergo fusion. This is occurring while the metal liner is being driven inwards. Mixing of the metal with the fusion fuel would "quench" the reaction (a problem that occurs in MCF systems when plasma touches the vessel wall). Similarly, the collapse must be fairly symmetrical to avoid "hot spots" that could destabilize the plasma while it burns.

Problems in commercial development are similar to those for any of the existing fusion reactor designs. The need to form high-strength magnetic fields at the focus of the machine is at odds with the need to extract the heat from the interior, making the physical arrangement of the reactor a challenge. Further, the fusion process emits large numbers of neutrons (in common reactions at least) that lead to neutron embrittlement that degrades the strength of the support structures and conductivity of metal wiring. In typical MCF schemes, neutrons are intended to be captured in a lithium shell to generate more tritium to feed in as fuel, further complicating the overall arrangement. Deuterium-deuterium fusion would, of course, avoid this requirement.

Kopek problem

Another concern for the MTF concept is named the kopek problem. The kopek is the Russian currency unit similar to the penny or cent, with 100 kopeks to the ruble. At an exchange rate of 75 rubles to the US dollar, a kopek is worth little. The name is intended to allude to a tiny value of money.

The problem is that the metal liners used in baseline MTF are consumed during the reaction. In return, the device would generate electricity. However, the value of that electricity is very low, on the order of a few pennies. Thus, in order to generate net positive cash flow, the device has to generate enormous amounts of energy per shot, unrealistically high amounts, or the cost of the fuel assemblies must be tiny, about a kopek.

Two potential solutions to the kopek problem have been identified; the use of "hotspot ignition" (also explored in traditional ICF) appears to allow a great increase in energy release compared to energy input, thus addressing the problem from the gain side. The other is to attempt to recycle some of the components, or in the case of fluid-wall systems, not lose any material in the first place.

 

Inertial electrostatic confinement

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Inertial_electrostatic_confinement

A fusor, exhibiting nuclear fusion in star mode

Inertial electrostatic confinement, or IEC, is a class of fusion power devices that use electric fields to confine the plasma rather than the more common approach using magnetic fields found in magnetic fusion energy (MFE) designs. Most IEC devices directly accelerate their fuel to fusion conditions, thereby avoiding energy losses seen during the longer heating stages of MFE devices. In theory, this makes them more suitable for using alternative aneutronic fusion fuels, which offer a number of major practical benefits and makes IEC devices one of the more widely studied approaches to fusion.

As the negatively charged electrons and positively charged ions in the plasma move in different directions in an electric field, the field has to be arranged in some fashion so that the two particles remain close together. Most IEC designs achieve this by pulling the electrons or ions across a potential well, beyond which the potential drops and the particles continue to move due to their inertia. Fusion occurs in this lower-potential area when ions moving in different directions collide. As it is the motion provided by the field that creates the energy levels needed for fusion, not random collisions with the rest of the fuel, the bulk of the plasma does not have to be hot and the systems as a whole work at much lower temperatures and energy levels than MFE devices.

One of the simpler IEC devices is the fusor, which consists of two concentric metal wire spherical grids. When the grids are charged to a high voltage, the fuel gas ionizes. The field between the two then accelerates the fuel inward, and when it passes the inner grid the field drops and the ions continue inward towards the center. If they impact with another ion they may undergo fusion. If they do not, they travel out of the reaction area into the charged area again, where they are re-accelerated inward. Overall the physical process is similar to the colliding beam fusion, although beam devices are linear instead of spherical. Other IEC designs, like the polywell, differ largely in the arrangement of the fields used to create the potential well.

A number of detailed theoretical studies have pointed out that the IEC approach is subject to a number of energy loss mechanisms that are not present if the fuel is evenly heated, or "Maxwellian". These loss mechanisms appear to be greater than the rate of fusion in such devices, meaning they can never reach fusion breakeven and thus be used for power production. These mechanisms are more powerful when the atomic mass of the fuel increases, which suggests IEC also does not have any advantage with aneutronic fuels. Whether these critiques apply to specific IEC devices remains highly contentious.

Mechanism

For every volt that an ion is accelerated across, its kinetic energy gain correspond to increase of temperature of 11,604 kelvins (K). For example, a typical magnetic confinement fusion plasma is 15 keV, which corresponds to 170 megakelvin (MK). An ion with a charge of one can reach this temperature by being accelerated across a 15,000 V drop. This sort of voltage is easily achieved in common electrical devices; a typical cathode ray tube operates at perhaps 1/3 this range.

In fusors, the voltage drop is made with a wire cage. However high conduction losses occur in fusors because most ions fall into the cage before fusion can occur. This prevents current fusors from ever producing net power.

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

History

1930s

Mark Oliphant adapts Cockcroft and Walton's particle accelerator at the Cavendish Laboratory to create tritium and helium-3 by nuclear fusion.

1950s

This picture shows the anode/cathode design for different IEC concepts and experiments.

Three researchers at LANL including Jim Tuck first explored the idea, theoretically, in a 1959 paper. The idea had been proposed by a colleague. The concept was to capture electrons inside a positive cage. The electrons would accelerate the ions to fusion conditions.

Other concepts were being developed which would later merge into the IEC field. These include the publication of the Lawson criterion by John D. Lawson in 1957 in England. This puts on minimum criteria on power plant designs which do fusion using hot Maxwellian plasma clouds. Also, work exploring how electrons behave inside the biconic cusp, done by Harold Grad group at the Courant Institute in 1957. A biconic cusp is a device with two alike magnetic poles facing one another (i.e. north-north). Electrons and ions can be trapped between these.

1960s

U.S. Patent 3,386,883 - Schematic from Philo Farnsworth 1968 patent. This device has an inner cage to make the field, and four ion guns on the outside.

In his work with vacuum tubes, Philo Farnsworth observed that electric charge would accumulate in regions of the tube. Today, this effect is known as the multipactor effect. Farnsworth reasoned that if ions were concentrated high enough they could collide and fuse. In 1962, he filed a patent on a design using a positive inner cage to concentrate plasma, in order to achieve nuclear fusion. During this time, Robert L. Hirsch joined the Farnsworth Television labs and began work on what became the fusor. Hirsch patented the design in 1966 and published the design in 1967. The Hirsch machine was a 17.8 cm diameter machine with 150 kV voltage drop across it and used ion beams to help inject material.

Simultaneously, a key plasma physics text was published by Lyman Spitzer at Princeton in 1963. Spitzer took the ideal gas laws and adapted them to an ionized plasma, developing many of the fundamental equations used to model a plasma. Meanwhile, magnetic mirror theory and direct energy conversion were developed by Richard F. Post's group at LLNL. A magnetic mirror or magnetic bottle is similar to a biconic cusp except that the poles are reversed.

1980s

In 1980 Robert W. Bussard developed a cross between a fusor and magnetic mirror, the polywell. The idea was to confine a non-neutral plasma using magnetic fields. This would, in turn, attract ions. This idea had been published previously, notably by Oleg Lavrentiev in Russia. Bussard patented the design and received funding from Defense Threat Reduction Agency, DARPA and the US Navy to develop the idea.

1990s

Bussard and Nicholas Krall published theory and experimental results in the early nineties. In response, Todd Rider at MIT, under Lawrence Lidsky developed general models of the device. Rider argued that the device was fundamentally limited. That same year, 1995, William Nevins at LLNL published a criticism of the polywell. Nevins argued that the particles would build up angular momentum, causing the dense core to degrade.

In the mid-nineties, Bussard publications prompted the development of fusors at the University of Wisconsin–Madison and at the University of Illinois at Urbana–Champaign. Madison's machine was first built in 1995. George H. Miley's team at Illinois built a 25 cm fusor which has produced 10⁷ neutrons using deuterium gas and discovered the "star mode" of fusor operation in 1994. The following year, the first "US-Japan Workshop on IEC Fusion" was conducted. This is now the premier conference for IEC researchers. At this time in Europe, an IEC device was developed as a commercial neutron source by Daimler-Chrysler Aerospace under the name FusionStar. In the late nineties, hobbyist Richard Hull began building amateur fusors in his home. In March 1999, he achieved a neutron rate of 10⁵ neutrons per second. Hull and Paul Schatzkin started fusor.net in 1998. Through this open forum, a community of amateur fusioneers have done nuclear fusion using homemade fusors.

2000s

Despite demonstration in 2000 of 7200 hours of operation without degradation at high input power as a sealed reaction chamber with automated control the FusionStar project was cancelled and the company NSD Ltd was founded. The spherical FusionStar technology was then further developed as a linear geometry system with improved efficiency and higher neutron output by NSD Ltd. which became NSD-Fusion GmbH in 2005.

In early 2000, Alex Klein developed a cross between a polywell and ion beams. Using Gabor lensing, Dr. Klein attempted to focus plasma into non-neutral clouds for fusion. He founded FP generation, which in April 2009 raised $3 million in financing from two venture funds. The company developed the MIX and Marble machine, but ran into technical challenges and closed.

In response to Riders' criticisms, researchers at LANL reasoned that a plasma oscillating could be at local thermodynamic equilibrium; this prompted the POPS and Penning trap machines. At this time, MIT researchers became interested in fusors for space propulsion and powering space vehicles. Specifically, researchers developed fusors with multiple inner cages. In 2005, Greg Piefer founded Phoenix Nuclear Labs to develop the fusor into a neutron source for the mass production of medical isotopes.

Robert Bussard began speaking openly about the Polywell in 2006. He attempted to generate interest  in the research, before passing away from multiple myeloma in 2007. His company was able to raise over ten million in funding from the US Navy in 2008 and 2009.

2010s

Bussard's publications prompted the University of Sydney to start research into electron trapping in polywells in 2010. The group has explored theory, modeled devices, built devices, measured trapping and simulated trapping. These machines were all low power and cost and all had a small beta ratio. In 2010, Carl Greninger founded the north west nuclear consortium, an organization which teaches nuclear engineering principles to high school students, using a 60 kvolt fusor. In 2012, Mark Suppes received attention, in Brooklyn for a fusor. Suppes also measured electron trapping inside a polywell. In 2013, the first IEC textbook was published by George H. Miley.

Designs with cage

Fusor

The best known IEC device is the fusor. This device typically consists of two wire cages inside a vacuum chamber. These cages are referred to as grids. The inner cage is held at a negative voltage against the outer cage. A small amount of fusion fuel is introduced (deuterium gas being the most common). The voltage between the grids causes the fuel to ionize. The positive ions fall down the voltage drop towards the negative inner cage. As they accelerate, the electric field does work on the ions, heating them to fusion conditions. If these ions collide, they can fuse. Fusors can also use ion guns rather than electric grids. Fusors are popular with amateurs, because they can easily be constructed, can regularly produce fusion and are a practical way to study nuclear physics. Fusors have also been used as a commercial neutron generator for industrial applications.

No fusor has come close to producing a significant amount of fusion power. They can be dangerous if proper care is not taken because they require high voltages and can produce harmful radiation (neutrons and X-rays). Often, ions collide with the cages or wall. This conducts energy away from the device limiting its performance. In addition, collisions heat the grids, which limits high power devices. Collisions also spray high-mass ions into the reaction chamber, pollute the plasma and cool the fuel.

POPS

In examining non-thermal plasma, workers at LANL realized that scattering was more likely than fusion. This was due to the coulomb scattering cross section being larger than the fusion cross section. In response they built POPS, a machine with a wire cage, where ions are moving at steady-state, or oscillating around. Such plasma can be at local thermodynamic equilibrium. The ion oscillation is predicted to maintain the equilibrium distribution of the ions at all times, which would eliminate any power loss due to Coulomb scattering, resulting in a net energy gain. Working off this design, researchers in Russia simulated the POPS design using Particle-in-cell code in 2009. This reactor concept becomes increasingly efficient as the size of the device shrinks. However, very high transparencies (>99.999%) are required for successful operation of the POPS concept. To this end S. Krupakar Murali et al., suggested that carbon nanotubes can be used to construct the cathode grids. This is also the first (suggested) application of carbon nanotubes directly in any fusion reactor.

Designs with fields

Several schemes attempt to combine magnetic confinement and electrostatic fields with IEC. The goal is to eliminate the inner wire cage of the fusor, and the resulting problems.

Polywell

The polywell uses a magnetic field to trap electrons. When electrons or ions move into a dense field, they can be reflected by the magnetic mirror effect. A polywell is designed to trap electrons in the center, with a dense magnetic field surrounding them. This is typically done using six electromagnets in a box. Each magnet is positioned so their poles face inward, creating a null point in the center. The electrons trapped in the center form a "virtual electrode"  Ideally, this electron cloud accelerates ions to fusion conditions.

Penning trap

Penning trap cross-section. Axis is vertical. Electrons orbit the center under DC electrostatic (blue) and DC magnetic (red) confinement. In this diagram the confined particles are positive; to confine electrons, the electrodes' polarities must be swapped.

A Penning trap uses both an electric and a magnetic field to trap particles, a magnetic field to confine particles radially and a quadrupole electric field to confine the particles axially.

In a Penning trap fusion reactor, first the magnetic and electric fields are turned on. Then, electrons are emitted into the trap, caught and measured. The electrons form a virtual electrode similar to that in a polywell, described above. These electrons are intended to then attract ions, accelerating them to fusion conditions.

In the 1990s, researchers at LANL built a Penning trap to do fusion experiments. Their device (PFX) was a small (millimeters) and low power (one fifth of a tesla, less than ten thousand volts) machine.

Marble

MARBLE (multiple ambipolar recirculating beam line experiment) was a device which moved electrons and ions back and forth in a line. Particle beams were reflected using electrostatic optics. These optics made static voltage surfaces in free space. Such surfaces reflect only particles with a specific kinetic energy, while higher-energy particles can traverse these surfaces unimpeded, although not unaffected. Electron trapping and plasma behavior was measured by Langmuir probe. Marble kept ions on orbits that do not intersect grid wires—the latter also improves the space charge limitations by multiple nesting of ion beams at several energies. Researchers encountered problems with ion losses at the reflection points. Ions slowed down when turning, spending much time there, leading to high conduction losses.

MIX

The multipole ion-beam experiment (MIX) accelerated ions and electrons into a negatively charged electromagnet. Ions were focused using Gabor lensing. Researcher had problems with a very thin ion-turning region very close to a solid surface where ions could be conducted away.

Magnetically insulated

Devices have been proposed where the negative cage is magnetically insulated from the incoming plasmas.

General criticism

In 1995, Todd Rider critiqued all fusion power schemes using plasma systems not at thermodynamic equilibrium. Rider assumed that plasma clouds at equilibrium had the following properties:

• They were quasineutral, where the positives and negatives are equally mixed together.
• They had evenly mixed fuel.
• They were isotropic, meaning that its behavior was the same in any given direction.
• The plasma had a uniform energy and temperature throughout the cloud.
• The plasma was an unstructured Gaussian sphere.

Rider argued that if such system was sufficiently heated, it could not be expected to produce net power, due to high X-ray losses.

Other fusion researchers such as Nicholas Krall, Robert W. Bussard, Norman Rostoker and Monkhorst disagreed with this assessment. They argue that the plasma conditions inside IEC machines are not quasineutral and have non-thermal energy distributions. Because the electron has a mass and diameter much smaller than the ion, the electron temperature can be several orders of magnitude different than the ions. This may allow the plasma to be optimized, whereby cold electrons would reduce radiation losses and hot ions would raise fusion rates.

Thermalization

This is an energy distribution comparison of thermalized and non-thermalized ions

The primary problem that Rider has raised is the thermalization of ions. Rider argued that, in a quasineutral plasma where all the positives and negatives are distributed equally, the ions will interact. As they do, they exchange energy, causing their energy to spread out (in a Wiener process) heading to a bell curve (or Gaussian function) of energy. Rider focused his arguments within the ion population and did not address electron-to-ion energy exchange or non-thermal plasmas.

This spreading of energy causes several problems. One problem is making more and more cold ions, which are too cold to fuse. This would lower output power. Another problem is higher energy ions which have so much energy that they can escape the machine. This lowers fusion rates while raising conduction losses, because as the ions leave, energy is carried away with them.

Radiation

Rider estimated that once the plasma is thermalized the radiation losses would outpace any amount of fusion energy generated. He focused on a specific type of radiation: X-ray radiation. A particle in a plasma will radiate light anytime it speeds up or slows down. This can be estimated using the Larmor formula. Rider estimated this for D-T (deuterium-tritium fusion), D-D (deuterium fusion), and D-He3 (deuterium-helium 3 fusion), and that breakeven operation with any fuel except D-T is difficult.

Core focus

In 1995, Nevins argued that such machines would need to expend a great deal of energy maintaining ion focus in the center. The ions need to be focused so that they can find one another, collide and fuse. Over time the positive ions and negative electrons would naturally intermix because of electrostatic attraction. This causes the focus to be lost. This is core degradation. Nevins argued mathematically, that the fusion gain (ratio of fusion power produced to the power required to maintain the non-equilibrium ion distribution function) is limited to 0.1 assuming that the device is fueled with a mixture of deuterium and tritium.

The core focus problem was also identified in fusors by Tim Thorson at the University of Wisconsin–Madison during his 1996 doctoral work. Charged ions would have some motion before they started accelerating in the center. This motion could be a twisting motion, where the ion had angular momentum, or simply a tangential velocity. This initial motion causes the cloud in the center of the fusor to be unfocused.

Brillouin limit

In 1945, Columbia University professor Léon Brillouin, suggested that there was a limit to how many electrons one could pack into a given volume. This limit is commonly referred to as the Brillouin limit or Brillouin density, this is shown below.

${\displaystyle N={\frac {B^{2}}{2\mu _{0}mc^{2}}}}$

Where B is the magnetic field, ${\displaystyle \mu _{0}}$ the permeability of free space, m the mass of confined particles, and c the speed of light. This may limit the charge density inside IEC devices.

Commercial applications

Since fusion reactions generates neutrons, the fusor has been developed into a family of compact sealed reaction chamber neutron generators for a wide range of applications that need moderate neutron output rates at a moderate price. Very high output neutron sources may be used to make products such as Molybdenum-99^[39] and Nitrogen-13, medical isotopes used for PET scans.

Devices

Government and commercial

• Los Alamos National Laboratory Researchers developed POPS and penning trap 
• Turkish Atomic Energy Authority In 2013 this team built a 30 cm fusor at the Saraykoy Nuclear Research and Training center in Turkey. This fusor can reach 85 kV and do deuterium fusion, producing 2.4×10⁴ neutrons per second.
• ITT Corporation Hirschs original machine was a 17.8 cm diameter machine with 150 kV voltage drop across it. This machine used ion beams.
• Phoenix Nuclear Labs has developed a commercial neutron source based on a fusor, achieving 3×10¹¹ neutrons per second with the deuterium-deuterium fusion reaction for 132 hours of continuous operation.
• Energy Matter Conversion Inc Is a company in Santa Fe, which has developed large high powered polywell devices for the US Navy.
• NSD-Gradel-Fusion sealed IEC neutron generators for DD (2.5 MeV) or DT (14 MeV) with a range of maximum outputs are manufactured by Gradel sárl in Luxembourg.
• Atomic Energy Organization of Iran Researchers at Shahid Beheshti University in Iran have built a 60 cm diameter fusor which can produce 2×10⁷ neutrons per second at 80 kilovolts using deuterium gas.

Universities

• Tokyo Institute of Technology has four IEC devices of different shapes: a spherical machine, a cylindrical device, a co-axial double cylinder and a magnetically assisted device.
• University of Wisconsin–Madison – A group at Wisconsin–Madison has several large devices, since 1995.
• University of Illinois at Urbana–Champaign – The fusion studies laboratory has built a ~25 cm fusor which has produced 10⁷ neutrons using deuterium gas.
• Massachusetts Institute of Technology – For his doctoral thesis in 2007, Carl Dietrich built a fusor and studied its potential use in spacecraft propulsion. Also, Thomas McGuire studied multiple well fusors for applications in spaceflight.
• University of Sydney has built several IEC devices and also low power, low beta ratio polywells. The first was constructed of Teflon rings and was about the size of a coffee cup. The second has ~12" diameter full casing, metal rings.
• Eindhoven Technical University
• Amirkabir University of Technology and Atomic Energy Organization of Iran have investigated the effect of strong pulsed magnetic fields on the neutron production rate of IEC device. Their study showed that by 1-2 Tesla magnetic field it is possible to increase the discharge current and neutron production rate more than ten times with respect to the ordinary operation.
• The Institute of Space Systems at the University of Stuttgart, is developing IEC devices for plasma physics research and also as an electric propulsion device, the IECT (Inertial Electrostatic Confinement Thruster).