Inertial electrostatic confinement
Inertial electrostatic confinement (often abbreviated as IEC) is a concept for retaining a plasma using an electrostatic field. The field accelerates charged particles (either ions or electrons) radially inward, usually in a spherical but sometimes in a cylindrical geometry. Ions can be confined with IEC in order to achieve controlled nuclear fusion. One of the earliest proposals for IEC was by Willam C Elmore, et al. in January 1959.
The best-known IEC device is the Farnsworth-Hirsch Fusor. This system consists largely of two concentric spherical electrical grids inside a vacuum chamber into which a small amount of fusion fuel is introduced. Voltage across the grids causes the fuel to ionize around them, and positively charged ions are accelerated towards the center of the chamber. Those ions may collide and fuse with ions coming from the other direction, may scatter without fusing, or may pass directly through. In the latter two cases, the ions will tend to be stopped by the electric field and re-accelerated toward the center. Fusors can also use ion guns rather than electric grids.
The fusor is popular because simple versions are easy to construct and are suitable for exploring this field. Simple devices can reproducibly produce fusion reactions, but 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). The basic IEC device has been used as a commercial neutron generator for industrial applications: first with the trade name FusionStar and later NSD-Fusion, thereafter NSD-Gradel-Fusion.
Polywell, Penning and MARBLE
Three newer approaches try to prevent ions from colliding with the grids. Collisions heat the grids, spray high-mass ions into the reaction chamber, pollute the plasma and cool the fuel. The Polywell uses a magnetic field to trap electrons. Fuel ions are then shot into the middle where they are trapped by the electron cloud, which forms a "virtual electrode". Another modern approach uses a Penning trap to trap electrons in a system otherwise similar to the Polywell. A third approach, dubbed MARBLE, uses electrostatic optics to keep 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. In 2001, a Japanese team was able to directly measure the double well of an IEC machine using laser-induced fluorescence.
In 1995, Todd Rider critiqued these machines. The primary problem that he raises is the thermalization of ions. Rider argued that, in a quasi-neutral 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, as the ions lost carry away energy. Rider estimated that once the machine is thermalized the Radiation losses would outpace Fusion energy gains. 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. Rider also mentions core degradation as a concern.
Other fusion researchers such as Rostoker and Monkhorst disagreed with this assessment. They propose that the plasma conditions inside these machines are not quasi-neutral 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 then the ions. This may allow the plasma to be optimized, whereby cold electrons would reduce Radiation losses and hot ions would raise Fusion rates.
In addition, theorists at LANL have proposed experiments with a new electrostatic plasma equilibrium that may mitigate this problem. This concept, called Periodically Oscillating Plasma Sphere (POPS), has been confirmed experimentally. POPS oscillation maintains equilibrium distribution of the ions at all times, which would eliminate any power loss due to Coulomb collisions, resulting in a net energy gain. This is probably the only fusion reactor concept that 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.
Critiques: core focus and degradation
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.
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.
- WC Elmore et al, "On the Inertial-Electrostatic Confinement of a Plasma" Physics of Fluids 2, 239 (1959); doi:10.1063/1.1705917 (8 pages) 
- R. Hirsch, "Inertial-Electrostatic Confinement of Ionized Fusion Gases," Journal of Applied Physics 38, 4522 (1967).
- R.W. Bussard, "Some Physics Considerations of Magnetic Inertial-Electrostatic Confinement: A New Concept for Spherical Converging-flow Fusion," Fusion Technology 19, 273 (1991).
- D.C. Barnes, R.A. Nebel, and L. Turner, "Production and Application of Dense Penning Trap Plasmas," Physics of Fluids B 5, 3651 (1993).
- [dead link]
-  Current Status of IEC (Inertial Electrostatic Confinement) Fusion Neutron/Proton Source Study
- Rider, Todd (1995), A general critique of inertial-electrostatic confinement fusion systems
- "Fundamental limitations on plasma fusions systems not in thermodynamic equilibrium" Thesis, Todd Rider, June 1995
- Science 17 July 1998: Vol. 281. no. 5375, p. 307
- The Advent of Clean Nuclear Fusion: Super-performance Space Power and Propulsion, Robert W. Bussard, Ph. D., 57th International Astronautical Congress, October 2–6, 2006
- R.A. Nebel and D.C. Barnes, "The periodically oscillating plasma sphere," Fusion Technology 38, 28 (1998).
- Periodically Oscillating Plasma Sphere (POPS)
- J. Park et al., "Experimental Observation of a Periodically Oscillating Plasma Sphere in a Gridded Inertial Electrostatic Confinement Device," Phys. Rev. Lett. 95, 015003, (2005) doi:10.1103/PhysRevLett.95.015003 .
- S. Krupakar Murali et al.,"Carbon Nanotubes in IEC Fusion Reactors," ANS 2006 Annual Meeting, June 4–8, Reno, Nevada.
- [W.M. Nevins, Phys. Plasmas <2> (10), 3804 (October, 1995)]
- "Ion flow and fusion reactivity characterization of a spherically convergent ion focus" Thesis work, Tim Thorson, December 1996, The University of Wisconsin–Madison
- University of Wisconsin-Madison IEC homepage
- From Proceedings of the 1999 Fusion Summer Study (Snowmass, Colorado):
- Inertial-Electrostatic Confinement (IEC) of a Fusion Plasma with Grids
- Fusion from Television? (American Scientist Magazine, July-August 1999)
- Talk by Dr. Robert Bussard, former Asst. Director of the Atomic Energy Commission and founder of Energy Matter Conversion Corporation (EMC2):
- Should Google Go Nuclear? Clean, cheap, nuclear power (no, really) Google Tech Talk November 9, 2006.
- 'The Advent of Clean Nuclear Fusion: Superperformance Space Power and Propulsion' cited in the Dr. Bussard's Talk. 57th International Astronautical Congress 2006 Author: Dr. Robert W. Bussard
- Latest Fusion developments (WB-7 - June 2008) based on the work of Dr. Robert Bussard
- Website of FPGeneration, Inc