Editing Inertial electrostatic confinement (section)

==General criticism==
In 1995, Todd Rider critiqued all fusion power schemes using plasma systems not at thermodynamic equilibrium.<ref name="Plasma Physics 1995">{{cite thesis|title="Fundamental limitations on plasma fusions systems not in thermodynamic equilibrium", Thesis (Ph.D), Dept. of Electrical Engineering and Computer Science|author=Todd Rider |publisher=Massachusetts Institute of Technology |date=June 1995 |hdl=1721.1/11412 |url=http://hdl.handle.net/1721.1/11412}}</ref> Rider assumed that plasma clouds at equilibrium had the following properties:
* They were [[plasma (physics)|quasineutral]], where the positives and negatives are equally mixed together.<ref name="Plasma Physics 1995"/>
* They had evenly mixed fuel.<ref name="Plasma Physics 1995"/>
* They were [[isotropy|isotropic]], meaning that its behavior was the same in any given direction.<ref name="Plasma Physics 1995"/>
* The plasma had a uniform energy and temperature throughout the cloud.<ref name="Plasma Physics 1995"/>
* The plasma was an unstructured [[Gaussian surface#Spherical surface|Gaussian sphere]].

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

Other fusion researchers such as [[Nicholas Krall]],<ref name="krall">{{cite journal |last1=Rosenberg |first1=M. |last2=Krall |first2=Nicholas A. |title=The effect of collisions in maintaining a non-Maxwellian plasma distribution in a spherically convergent ion focus |journal=Physics of Fluids B: Plasma Physics |publisher=AIP Publishing |volume=4 |issue=7 |year=1992 |issn=0899-8221 |pages=1788–1794 |bibcode=1992PhFlB...4.1788R |doi=10.1063/1.860034|doi-access=free }}</ref> [[Robert W. Bussard]],<ref name="bussard"/> Norman Rostoker, and Monkhorst disagreed with this assessment. They argue that the plasma conditions inside IEC machines are not quasineutral and have [[plasma (physics)#Thermal vs. non-thermal plasmas|non-thermal]] energy distributions.<ref>{{cite journal |title=Feasibility of a Colliding Beam Fusion Reactor |first=W. M. |last=Nevins |journal=Science |volume=281 |issue=5375 |date=17 July 1998 |pages=307a–307 |bibcode=1998Sci...281..307C |doi=10.1126/science.281.5375.307a |doi-access=}}</ref> 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 [[nuclear fusion|fusion]] rates.<ref name="Bussard6"/>

===Thermalization===
[[File:Thermalized Ion populations.jpg|thumbnail|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 [[plasma (physics)#Thermal vs. non-thermal plasmas|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 [[nuclear fusion|fusion]] energy generated. He focused on a specific type of radiation: [[bremsstrahlung|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.<ref name="Plasma Physics 1995"/>

===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]].<ref name=Nevins1995/>

The core focus problem was also identified in fusors by Tim Thorson at the [[University of Wisconsin–Madison]] during his 1996 doctoral work.<ref name="Tim Thorson 1996"/> 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.<ref>{{cite journal |last=Brillouin |first=Leon |title=A Theorem of Larmor and Its Importance for Electrons in Magnetic Fields |journal=Physical Review |publisher=American Physical Society (APS) |volume=67 |issue=7–8 |date=1945-04-01 |pages=260–266 |issn=0031-899X |bibcode=1945PhRv...67..260B |doi=10.1103/physrev.67.260}}</ref> This limit is commonly referred to as the Brillouin limit or Brillouin density,<ref>"Brillouin limit for electron plasmas confined on magnetic surfaces" Allen H. Boozer Department of Applied Physics and Applied Mathematics Columbia University, New York NY 10027, http://www-fusion.ciemat.es/SW2005/abstracts/BoozerAH_SW.pdf {{Webarchive|url=https://web.archive.org/web/20100404003718/http://www-fusion.ciemat.es/SW2005/abstracts/BoozerAH_SW.pdf |date=2010-04-04}}</ref> this is shown below.<ref name="ReferenceB"/>
:<math>N=\frac{B^2}{2\mu_{0}mc^2}</math>

Where B is the magnetic field, <math>\mu_{0}</math> 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.