# Inertial electrostatic confinement

File:Deuterium Ionized.JPG
A fusor, doing nuclear fusion in star mode

Inertial electrostatic confinement is a branch of fusion research which uses an electric field to heat a plasma to fusion conditions. Electric fields can do work on charged particles (either ions or electrons), heating them to fusion conditions.[1] This is typically done in a sphere, with material moving radially inward, but can also be done in a cylindrical or beam geometry.[2] The electric field can be generated using a wire grid [3] or a non-neutral plasma cloud.[4][5][6]

## Mechanism

For every volt that an ion is accelerated across, it gains 11,604 kelvins. For example, a typical magnetic confinement fusion plasma is 15 keV, or 170 megakelvin. An ion with a charge of one can reach this temperature by being accelerated across a 15,000 V drop. 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.[7][8]

## History

### 1930s

Mark Oliphant adapts Cockcroft and Walton's particle accelerator at the Cavendish Laboratory to create Tritium and Helium-3 by nuclear fusion.[9]

### 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.[10] The idea had been proposed by a colleague.[11] 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.[12] 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.[13][14] 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

File:US3386883 - fusor.png
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.[15] 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.[16] 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[17] and published the design in 1967.[3] 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.[18] 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 was developed by Richard F. Post's group at LLNL.[19][20] 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.[21][22][23] Bussard patented [24] the design and received funding from Defense Threat Reduction Agency, DARPA and, Navy to develop the idea.[25]

### 1990s

Bussard and Nicholas Krall published theory and experimental results in the early nineties.[26][27] In response, Todd Rider at MIT, under Lawrence Lidsky developed general models of the device.[28] Rider argued that the device was fundamentally limited. That same year, 1995, William Nevins at LLNL published a criticism of the polywell.[29] 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 a fusors at the University of Wisconsin–Madison and at the University of Illinois at Urbana–Champaign. Madison's machine was first built in 1995 and the group still produces some of the best IEC research in the world.[30] Dr George H. Miley team at Illinois, built a 25 cm fusor which has produced 10E7 neutrons using deuterium gas [31] and discovered the "star mode" of fusor operation in 1994.[32] 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.[33] In the late nineties, hobbyist Richard Hull began building the first amateur fusors in his home in Virginia.[34] In March 1999, he achieved a neutron rate of 10E5 neutrons per second.[35] Hull and Paul Schatzkin, started fusor.net in 1998.[36] Through this open forum, a community of amateur fusioneers have developed done nuclear fusion using homemade fusors.

### 2000s

Taylor Wilson presenting nuclear work to Barack Obama, February 7, 2012[37]

### MIX

The multipole ion-beam experiment (MIX) accelerated ions and electrons into a negatively charged electromagnet.[38] Ions were focused using Gabor lensing. Researcher had problems with a very thin ion turning region very close to a solid surface [38] where ions could be conducted away.

## General criticism

In 1995, Todd Rider critiqued all fusion power schemes using plasma systems not at thermodynamic equilibrium.[28] Rider assumed that plasma clouds at equilibrium had the following properties:

• They were quasineutral, where the positives and negatives are equally mixed together.[28]
• They had evenly mixed fuel.[28]
• They were isotropic, meaning that its behavior was the same in any given direction.[28]
• The plasma had a uniform energy and temperature throughout the cloud.[28]
• The plasma was an unstructured Gaussian sphere.

Rider argued that if such as 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,[88] Robert W. Bussard,[82] 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.[89] 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.[47]

### 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.

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.[28]

### 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. Overtime 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.[90]

The core focus problem was also identified in fusors by Tim Thorson at the University of Wisconsin–Madison during his 1996 doctoral work.[7] 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.[91] This limit is commonly referred to as the Brillouin limited or Brillouin density,[92] this is shown below.[93]

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

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 [94] 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[45] and Nitrogen-13, medical isotopes, used for PET scans.[95]

## Devices

### Government and commercial

• Los Alamos National Laboratory Researchers developed [96] POPS and penning trap [97]
• 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 2.4E4 neutrons per second.[98]
• Atomic Energy Organization of Iran Researchers at Shahid Beheshti University in Iran have built a 60 cm diameter fusor which can produce 10E7 neutrons per second at 140 kilovolts using deuterium gas.[99]
• ITT Corporation Hirschs original machine was a 17.8 cm diameter machine with 150 Kv voltage drop across it.[3] This machine used ion beams.
• Phoenix Nuclear Labs Has developed a commercial neutron source based off a fusor, achieving 3X10^11 neutrons per second with the deuterium-deuterium fusion reaction.[45]
• 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.[94]

### Amateur

Amateurs mainly build fusors. Listed here are teams or machines which have produced neutrons.

• Richard Hull Since the late nineties, Richard Hull has built several fusors in his home in Richmond, Virginia.[34] In March 1999, he achieved a neutron rate of 10E5 neutrons per second.[35] Hull maintains a list of amateurs who have gotten neutrons from fusors.
• North West Nuclear Consortium This is an organization in Washington state which teaches a class on nuclear engineering principles, to high school students, using a 60 kvolt fusor.[62][63]
• Taylor Wilson In 2008, Taylor Wilson became the youngest person to build a working fusor, at age 14.[105][106]
• Matthew Honickman Was a high school student who built a working fusor in his basement in Rochester, New York.[107]
• Michael Li In 2003, Michael Li built a fusor and won second place [108] in the US's Intel Science Talent Search winning a \$75,000 college scholarship.[109]
• Mark Suppes Built a working fusor and measured electron trapping inside a polywell.[110][111]
• Thiago David Olson Built a 40 kV fusor at age 17, in his home in Rochester, Michigan.[112][113][114]
• Andrew Seltzman Has built several fusors with neutrons detected in 2008.[115]
• Mert Soykan and Ferit Kutay built a 45 kV homemade fusor together in 2013 when they were both 16 years old.
• Conrad Farnsworth of Newcastle, Wyoming produced fusion in 2011 at 17[116][117] and used this to win a regional and state science fair.
• Michael Kovalchick of York Pennsylvania achieved fusion in 2011 with a fusor he built in his family's basement. Kovalchick was the first to record video evidence of rotational electrostatic forces on the fusor inner grid. He used his fusion work to win high school and regional science fairs and a fourth award at the 2012 Intel ISEF. In 2012 at the age of 17, under instruction of a licensed operator, Kovalchick pulled control rods of a fission research reactor to critical and in doing so may have been the youngest person to have directly controlled both nuclear fission and fusion reactors.[118][119][120]
• Jamie Edwards 13 became the youngest fusor builder in March 2014.[121] He received a letter of congratulations from his royal highness, the Duke of York.[69] He also appeared on the late show with David Letterman.

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