View source for Field-reversed configuration

{{short description|Magnetic confinement fusion reactor}}
[[File:Field-Reversed Configuration.svg|thumb|300px|Field-reversed configuration: a toroidal electric current is induced inside a cylindrical plasma, making a poloidal magnetic field, reversed in respect to the direction of an externally applied magnetic field. The resultant high-beta axisymmetric compact toroid is self-confined.]]
A '''field-reversed configuration''' ('''FRC''') is a type of [[plasma (physics)|plasma]] device studied as a means of producing [[nuclear fusion]]. It confines a plasma on closed magnetic [[field line]]s without a central penetration.<ref>{{cite book|title=Plasma Physics and Fusion Energy|first=Jeffrey P.|last= Freidberg|publisher=Cambridge University Press|date= 2007|isbn=978-0-521-85107-7}}</ref><ref>{{Cite book |last=Freidberg |first=Jeffrey P. |url=https://archive.org/details/PlasmaPhysicsAndFusionEnergyFreidberg |title=Plasma Physics and Fusion Energy |publisher=Cambridge University Press |year=2015 |page=335 |format=DJVU |author-link=Jeffrey P. Freidberg |access-date=13 May 2023 |via=Internet Archive}}</ref> In an FRC, the plasma has the form of a self-stable torus, similar to a [[smoke ring]].

FRCs are closely related to another self-stable [[magnetic confinement fusion]] device, the [[spheromak]]. Both are considered part of the [[compact toroid]] class of fusion devices. FRCs normally have a plasma that is more elongated than spheromaks, having the overall shape of a hollowed out sausage rather than the roughly spherical spheromak.

FRCs were a major area of research in the 1960s and into the 1970s, but had problems scaling up into practical [[fusion triple product]]s (target combinations of density, temperature and confinement time). Interest returned in the 1990s and {{asof|2019||df=|lc=Y}}, FRCs were an active research area.

==History==
The FRC was first observed in laboratories in the late 1950s during [[Pinch (plasma physics)|theta pinch]] experiments with a reversed background magnetic field.<ref>{{Cite journal |last1=Kolb |first1=A.C. |last2=Dobbie |first2=C.B.|last3=Griem |first3=H.R. |title=Field mixing and associated neutron production in a plasma |date=1 July 1959 |others=The original idea was attributed to the Greek scientist and engineer Nicholas C. Christofilos.
 |journal=Physical Review Letters |volume=3 |issue=1 |pages=5–7 |doi=10.1103/PhysRevLett.3.5|bibcode = 1959PhRvL...3....5K }}{{Subscription required}}</ref> The original idea was attributed to the Greek scientist and engineer [[Nicholas Christofilos|Nicholas C. Christofilos]] who developed the concept of E-layers for the [[Astron (fusion reactor)|Astron]] fusion reactor.<ref>{{Cite book |last=Reinders |first=L. J. |url=https://link.springer.com/content/pdf/bfm:978-3-030-64344-7/1 |title=The Fairy Tale of Nuclear Fusion |publisher=Springer International Publishing |year=2021 |isbn=978-3-030-64343-0 |location=Cham, Switzerland |pages=83 |doi=10.1007/978-3-030-64344-7|s2cid=241339825 }}</ref> 

The first studies were at the [[United States Naval Research Laboratory]] (NRL) in the 1960s. Considerable data were collected, with over 600 published papers.<ref name="Tuszewski">{{Cite journal |last=Tuszewski |first=M. |date=November 1988 |title=Field reversed configurations |url=https://zenodo.org/record/1235740 |journal=[[Nuclear Fusion (journal)|Nuclear Fusion]] |volume=28 |issue=11 |page=2033 |doi=10.1088/0029-5515/28/11/008 |s2cid=122791237|doi-access=free }}</ref> Almost all research was conducted during [[Project Sherwood]] at [[Los Alamos National Laboratory]] (LANL) from 1975 to 1990,<ref>{{Cite journal |vauthors=McKenna KF, Armstrong WT, Barnes DC, Bartsch RR, Chrien RE, Cochrane JC, Klingner PL, Hugrass WN, Linford RK, Rej DJ, Schwarzmeier JL, Sherwood EG, Siemon RE, Spencer RL, Tuszewski M |date=1985 |title=Field-reversed configuration research at Los Alamos |url=https://zenodo.org/record/1235746 |journal=[[Nuclear Fusion (journal)|Nuclear Fusion]] |volume=25 |issue=9 |page=1317 |doi=10.1088/0029-5515/25/9/057 |s2cid=122374822}}</ref> and during 18 years at the Redmond Plasma Physics Laboratory of the [[University of Washington]],<ref>{{Cite web  |title=Web page of the Redmond Plasma Physics Laboratory  |url=http://depts.washington.edu/rppl/index.html  |url-status=dead  |archive-url=https://web.archive.org/web/20150219182128/http://depts.washington.edu/rppl/index.html  |archive-date=2015-02-19  }}</ref> with the large ''s'' experiment (LSX).<ref>{{Cite journal
 |last1=Hoffman |first1=Alan L. |last2=Carey |first2=Larry L. |last3=Crawford |first3=Edward A. |last4=Harding |first4=Dennis G. |last5=DeHart |first5=Terence E. |last6=McDonald |first6=Kenneth F. |last7=McNeil |first7=John L. |last8=Milroy |first8=Richard D. |last9=Slough |first9=John T.
 |last10=Maqueda |first10=Ricardo|last11=Wurden |first11=Glen A. |title=The Large-s Field-Reversed Configuration Experiment |date=March 1993 |journal=Fusion Science and Technology |volume=23 |issue=2 |pages=185–207 |doi=10.13182/FST93-A30147 |bibcode=1993FuTec..23..185H |osti=6514222
}}</ref> 

Later research was at the [[Air Force Research Laboratory]] (AFRL),<ref>{{Cite tech report
 |last1=Kirtley |first1=David |last2=Brown |first2=Daniel L. |last3= Gallimore |first3=Alec D. |last4=Haas |first4=James
 |title=Details on an AFRL Field Reversed Configuration Plasma Device |date=June 2005 |institution=Air Force Research Laboratory
 |url=http://on-the-rag.com/wp-content/uploads/2013/03/GetTRDoc.pdf}}</ref> the Fusion Technology Institute (FTI) of the [[University of Wisconsin-Madison]],<ref>{{Cite web
 |title=Web page of the Fusion Technology Institute, University of Wisconsin-Madison
 |author=<!--Staff writer(s); no by-line.-->
 |url=http://fti.neep.wisc.edu/research/frc
 |access-date=2014-06-08
 |archive-date=2020-05-16
 |archive-url=https://web.archive.org/web/20200516031250/http://fti.neep.wisc.edu/research/frc
 |url-status=dead
 }}</ref> [[Princeton Plasma Physics Laboratory]],<ref>{{Cite journal|date=2012-10-31|title=First operation of the PFRC-2 device|url=http://meetings.aps.org/Meeting/DPP12/Event/176136|journal=Bulletin of the American Physical Society|volume= 57| issue = 12|bibcode=2012APS..DPPPP8051C |last1=Cohen |first1=Samuel }}</ref> and the [[University of California, Irvine]].<ref>{{cite journal
 |last1=Harris
 |first1=W.S.
 |last2=Trask
 |first2=E.
 |last3=Roche
 |first3=T.
 |last4=Garate
 |first4=E.P.
 |last5= Heidbrink
 |first5=W.W.
 |last6=McWilliams
 |first6=R.
 |title=Ion flow measurements and plasma current analysis in the Irvine Field Reversed Configuration
 |date=20 November 2009
 |journal=Physics of Plasmas
 |volume=16
 |issue=11
 |pages=112509
 |publisher=American Institute of Physics
 |url=http://www.physics.uci.edu/~wwheidbr/papers/Harris.pdf
 |doi=10.1063/1.3265961
|bibcode = 2009PhPl...16k2509H |s2cid=103136706
 }}</ref> 

Private companies now study FRCs for electricity generation, including [[General Fusion]], [[TAE Technologies]], and [[Helion Energy]].<ref>{{Cite web
 |last=Poddar
 |first=Yash
 |title=Can Startups Make Nuclear Fusion Possible?
 |date=11 March 2014
 |website=Stanford University
 |url=http://large.stanford.edu/courses/2014/ph241/poddar1/
}}</ref>

The Electrodeless Lorentz Force Thruster (ELF) developed by MSNW was an attempt to design a space propulsion device.<ref>{{cite web|url=https://science.house.gov/imo/media/doc/Pancotti%20Testimony.pdf|title=Testimony before the Space Subcommittee of the House Committee on Science, Space, and Technology United States House of Representatives Hearing on In-Space Propulsion: Strategic Choices and Options June 29, 2017|last1=Pancotti|first1=Anthony|access-date=8 April 2019|archive-date=29 November 2022|archive-url=https://web.archive.org/web/20221129080550/https://science.house.gov/imo/media/doc/Pancotti%20Testimony.pdf|url-status=dead}}</ref> ELF was a candidate in [[NASA]]'s NextSTEP advanced electric propulsion program, along with the X-3 Nested-Channel Hall Thruster and [[VASIMR]]<ref>{{cite web|url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20180007411.pdf|title=NASA's NextSTEP Advanced Electric Propulsion Activities|date=9 July 2018 |publisher=NASA|access-date=8 April 2019}}</ref> before MSNW dissolved.

== Applications ==
The primary application is for fusion power generation.

The FRC is also considered for [[deep space exploration]], not only as a possible nuclear energy source, but as means of accelerating a propellant to high levels of [[specific impulse]] (I<sub>sp</sub>) for [[electrically powered spacecraft propulsion|electrically powered spaceships]] and [[fusion rocket]]s, with interest expressed by [[NASA]].<ref>{{Cite book|title=AIP Conference Proceedings|last1=Wessel|first1=F. J.|year=2000|isbn=978-1563969195|volume=504|pages=1425–1430|chapter=Colliding beam fusion reactor space propulsion system|doi=10.1063/1.1290961}}</ref><ref>{{Cite book|title=AIP Conference Proceedings|last1=Cheung|first1=A.|year=2004|volume=699|pages=354–361|chapter=Colliding Beam Fusion Reactor Space Propulsion System|doi=10.1063/1.1649593}}</ref><ref name="NIAC-2012">{{Cite conference|last1=Slough|first1=John|last2=Pancotti|first2=Anthony|last3=Pfaff|first3=Michael|last4=Pihl|first4=Christopher|last5=Votroubek|first5=George|date=November 2012|title=The Fusion Driven Rocket|url=https://s3-us-west-2.amazonaws.com/pnwmsnw/NIAC_PhaseII_FDR.pdf|conference=NIAC 2012|location=Hampton, VA|publisher=NASA Innovative Advanced Concepts}}</ref><ref name="IEPC-2013">{{Cite conference|last1=Slough|first1=John|last2=Pancotti|first2=Anthony|last3=Kirtley|first3=David|last4=Votroubek|first4=George|date=6–10 October 2013|title=Electromagnetically Driven Fusion Propulsion|url=http://www.iepc2013.org/get?id=372|format=PDF|conference=33rd International Electric Propulsion Conference (IEPC-2013)|location=Washington, D.C.|publisher=George Washington University}}</ref><ref name="Slough_Space">{{Cite web|url=http://www.space.com/20609-nuclear-fusion-rocket-mars.html|title=Nuclear Fusion Rocket Could Reach Mars in 30 Days|author=<!--Staff writer(s); no by-line.-->|date=10 April 2013|website=Space.com}}</ref>

==Comparisons==
[[File:A comparison of an FRC and A Spheromak.png|thumb|The Difference Between an FRC and a Spheromak]]
{{Main|Magnetic confinement fusion}}Producing fusion power by confining the plasma with magnetic fields is most effective if the field lines do not penetrate solid surfaces but close on themselves into circles or toroidal surfaces. The mainline confinement concepts of [[tokamak]] and [[stellarator]] do this in a toroidal chamber, which allows a great deal of control over the magnetic configuration, but requires a very complex construction. The field-reversed configuration offers an alternative in that the field lines are closed, providing good confinement, but the chamber is cylindrical, allowing simpler, easier construction and maintenance.<ref>{{Cite journal|last=Ryzhkov|first=Sergei V.|date=2002|title=Features of Formation, Confinement and Stability of the Field Reversed Configuration|url=http://vant.kipt.kharkov.ua/ARTICLE/VANT_2002_4/article_2002_4_73.pdf|journal=Problems of Atomic Science and Technology|series=Plasma Physics|volume=7|issue=4|pages=73–75|issn=1682-9344}}</ref>

Field-reversed configurations and [[spheromak]]s are together known as [[compact toroid]]s. [[Spheromak]]s and FRC differ in that a spheromak has an extra toroidal field. This toroidal field can run along the same or opposite direction as the spinning plasma.<ref>Dolan, Thomas. Magnetic Fusion Technology. Vol. 2. New York City: Springer, 2012. Print.</ref> In the spheromak the strength of the [[Toroidal and poloidal|toroidal]] magnetic field is similar to that of the [[poloidal field]]. By contrast, the FRC has little to no toroidal field component and is confined solely by a poloidal field. The lack of a toroidal field means that the FRC has no [[magnetic helicity]] and that it has a [[Beta (plasma physics)|high beta]]. The high beta makes the FRC attractive as a [[Fusion power|fusion reactor]] and well-suited to [[Aneutronic fusion|aneutronic]] fuels because of the low required magnetic field. Spheromaks have ''β''&nbsp;≈&nbsp;0.1 whereas a typical FRC has ''β''&nbsp;≈&nbsp;1.<ref name="Ono 1999">{{cite journal|last=Ono|first=Y|date=1999|title=New relaxation of merging spheromaks to a field reversed configuration|journal=Nuclear Fusion|volume=39|issue=11Y|pages=2001–2008|bibcode=1999NucFu..39.2001O|doi=10.1088/0029-5515/39/11Y/346|s2cid=250871394}}</ref><ref name=":0">{{Cite journal|last=Momita Okamoto Nomura|date=1987|title=Advanced Fuels in a Field-Reversed Configuration|url=http://www.ans.org/pubs/journals/fst/a_25020|journal=Fusion Science and Technology|volume=11 |issue=2 |pages=436–450 |doi=10.13182/FST87-A25020 |bibcode=1987FuTec..11..436M |access-date=2016-01-05}}</ref>

== Formation ==
[[File:Info-graphic on the Field Reversed Configuration.png|thumb|The Dimensions of an FRC, including the S-parameter]]
In modern FRC experiments, the plasma current that reverses the magnetic field can be induced in a variety of ways.

When a field-reversed configuration is formed using the [[Pinch (plasma physics)|theta-pinch]] (or inductive electric field) method, a cylindrical coil first produces an axial magnetic field. Then the gas is pre-ionized, which "freezes in" the bias field from a [[Magnetohydrodynamics|magnetohydrodynamic]] standpoint, finally the axial field is reversed, hence "field-reversed configuration." At the ends, reconnection of the bias field and the main field occurs, producing closed field lines. The main field is raised further, compressing and heating the plasma and providing a vacuum field between the plasma and the wall.<ref>{{Cite journal|title = Creation of a high-temperature plasma through merging and compression of supersonic field reversed configuration plasmoids|journal = Nuclear Fusion|date = 2011|volume = 51|issue = 5|doi =  10.1088/0029-5515/51/5/053008|first = J|last = Slough|bibcode = 2011NucFu..51e3008S|pages=053008| s2cid=120579314 }}</ref>

Neutral beams are known to drive current in [[Tokamak]]s<ref>{{Cite journal|title = Approximate expression for beam driven current in tokamak plasmas|journal = Nuclear Fusion|date = 1992-01-01|pages = 143–150|volume = 32|issue = 1|doi = 10.1088/0029-5515/32/1/i12|first = M|last = Taguchi|bibcode = 1992NucFu..32..143T | s2cid=250743246 }}</ref> by directly injecting charged particles. FRCs can also be formed, sustained, and heated by application of neutral beams.<ref name=":0" /><ref>{{Cite journal|title = Fusion reactors based on colliding beams in a field reversed configuration plasma|url = http://inis.iaea.org/Search/search.aspx?orig_q=RN:28039760|date = 1996-01-01|first1 = N.|last1 = Rostoker|first2 = M.|last2 = Binderbauer|first3 = H. J.|last3 = Monkhorst| journal=Fusion Technology | volume=30 | issue=3 | pages=1395–1402 | doi=10.13182/FST96-A11963143 | bibcode=1996FuTec..30.1395R }}</ref> In such experiments, as above, a cylindrical coil produces a uniform axial magnetic field and gas is introduced and ionized, creating a background plasma. Neutral particles are then injected into the plasma. They ionize and the heavier, positively-charged particles form a current ring which reverses the magnetic field.

[[Spheromak]]s are FRC-like configurations with finite toroidal magnetic field. FRCs have been formed through the merging of spheromaks of opposite and canceling toroidal field.<ref>{{Cite journal|title = Recent Advances in the SPIRIT (Self-organized Plasma with Induction, Reconnection, and Injection Techniques) Concept|journal = Journal of Fusion Energy|date = 2006-12-01|issn = 0164-0313|pages = 93–97|volume = 26|issue = 1–2|doi = 10.1007/s10894-006-9043-4|first1 = H.|last1 = Ji|first2 = E.|last2 = Belova|author2-link=Elena Belova (physicist)|first3 = S. P.|last3 = Gerhardt|first4 = M.|last4 = Yamada|bibcode = 2007JFuE...26...93J | s2cid=59377360 }}</ref>

Rotating magnetic fields have also been used to drive current.<ref>{{Cite journal|title = A review of rotating magnetic field current drive and the operation of the rotamak as a field-reversed configuration (Rotamak-FRC) and a spherical tokamak (Rotamak-ST)|journal = Physics of Plasmas|date = 1999-05-01|issn = 1070-664X|pages = 1950–1957|volume = 6|issue = 5|doi = 10.1063/1.873452|first = Ieuan R.|last = Jones|bibcode = 1999PhPl....6.1950J }}</ref> In such experiments, as above, gas is ionized and an axial magnetic field is produced. A rotating magnetic field is produced by external magnetic coils perpendicular to the axis of the machine, and the direction of this field is rotated about the axis. When the rotation frequency is between the ion and electron gyro-frequencies, the electrons in the plasma co-rotate with the magnetic field (are "dragged"), producing current and reversing the magnetic field. More recently, so-called odd parity rotating magnetic fields<ref>{{Cite journal|title = Ion and electron acceleration in the field-reversed configuration with an odd-parity rotating magnetic field|journal = Physics of Plasmas|date = 2002-05-01|issn = 1070-664X|pages = 2093–2102|volume = 9|issue = 5|doi = 10.1063/1.1459456|author1-link=Alan Herbert Glasser|first1 = A. H.|last1 = Glasser|first2 = S. A.|last2 = Cohen|bibcode = 2002PhPl....9.2093G |url = https://zenodo.org/record/1231858}}</ref><ref name="closure">{{cite journal |last1=Ahsan |first1=T. |last2=Cohen |first2=S. A. |title=An analytical approach to evaluating magnetic-field closure and topological changes in FRC devices |journal=Physics of Plasmas |date=July 2022 |volume=29 |issue=7 |pages=072507 |doi=10.1063/5.0090163|bibcode=2022PhPl...29g2507A |s2cid=251140943 |doi-access=free }}</ref> have been used to preserve the closed topology of the FRC. It was analytically shown that at a very high critical threshold magnitude of 'odd parity' rotating magnetic field, the axisymmetric equilibrium magnetic field lines loses closure and fundamentally changes field topology. <ref name="closure"/>

== Single particle orbits ==
[[File:Particle Trajectory in an FRC.png|thumb|FRC particle trajectory in which a particle starts with cyclotron motion inside the null, transitions to betatron motion, and ends as cyclotron motion outside the null. This motion is in the midplane of the machine. Coils are above and below the figure.]]
FRCs contain an important and uncommon feature: a "magnetic null," or circular line on which the magnetic field is zero. This is necessarily the case, as inside the null the magnetic field points one direction and outside the null the magnetic field points the opposite direction. Particles far from the null trace closed cyclotron orbits as in other magnetic fusion geometries. Particles which cross the null, however, trace not ''cyclotron'' or circular orbits but ''betatron'' or figure-eight-like orbits,<ref>{{Cite journal|last1=Wang|first1=M. Y.|last2=Miley|first2=G. H.|date=1979-01-01|title=Particle orbits in field-reversed mirrors|url=https://iopscience.iop.org/article/10.1088/0029-5515/19/1/005|journal=Nuclear Fusion|language=en|volume=19|issue=1|pages=39|doi=10.1088/0029-5515/19/1/005|s2cid=120544136 |issn=0029-5515|url-access=subscription}}</ref> as the orbit's curvature changes direction when it crosses the magnetic null.

Because the particle's orbits are not cyclotron, models of plasma behavior based on cyclotron motion like [[magnetohydrodynamics]] (MHD) are inapplicable in the region around the null. The size of this region is related to the s-parameter,<ref name=":1" /> or the ratio of the distance between the null and separatrix, and the thermal ion gyroradius. At high-s, most particles do not cross the null and this effect is negligible. At low-s, ~2, this effect dominates and the FRC is said to be "kinetic" rather than "MHD."

==Plasma stability==

At low s-parameter, most ions inside an FRC follow large [[betatron]] [[Orbit (dynamics)|orbits]] (their average [[gyroradius]] is about half the size of the plasma) which are typical in [[accelerator physics]] rather than [[plasma physics]]. These FRCs are very stable because the plasma is not dominated by usual small gyroradius particles like other [[thermodynamic equilibrium]] or [[nonthermal plasma]]s. Its behavior is not described by classical [[magnetohydrodynamics]], hence there are no [[Alfvén waves]] and almost no [[Plasma stability#MHD instabilities|MHD instabilities]] despite their theoretical prediction,{{Citation needed|date=December 2019|reason=removed citation to predatory publisher content}} and it avoids the typical "anomalous transport", i.e. processes in which excess loss of [[particle]]s or [[energy]] occurs.<ref name="FRC1993">{{Cite journal
 |last1=Rostoker 
 |first1=N. 
 |last2=Wessel 
 |first2=F.J. 
 |last3=Rahman 
 |first3=H.U. 
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 |last5=Spivey 
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 |title=Magnetic Fusion with High Energy Self-Colliding Ion Beams 
 |date=22 March 1993 
 |issue=1818 
 |volume=70 
 |journal=Physical Review Letters 
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 |bibcode=1993PhRvL..70.1818R 
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 |pmid=10053394
|s2cid=32950265 
 |url=https://digital.library.unt.edu/ark:/67531/metadc1056327/ 
 }}</ref><ref name="FRC1996">{{Cite journal
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 |last2=Rostoker
 |first2=N.
 |title=Turbulent Transport in Magnetic Confinement: How to Avoid it
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 |journal=Journal of Plasma Physics
 |url=http://journals.cambridge.org/action/displayAbstract?aid=4756616
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|bibcode = 1996JPlPh..56..451B |s2cid=122582085
 |url-access=subscription
 }}</ref><ref name="CBFR_APS">{{Cite conference|last1=Rostoker |first1=N. |last2=Binderbauer |first2=M. W. |last3=Wessel |first3=F. J. |last4=Monkhorst |first4=H. J. |title=Colliding Beam Fusion Reactor |conference=Invited Paper, Special Session on Advanced Fuels APS-DPP |publisher=American Physical Society |url=http://fusion.ps.uci.edu/papers/complete.pdf |archive-url=https://web.archive.org/web/20020126193629/http://fusion.ps.uci.edu/papers/complete.pdf |url-status=dead |archive-date=2002-01-26 }}</ref>

{{asof|2000}}, several remaining instabilities are being studied:
* The [[Plasma stability#Resistive Wall Modes|tilt and shift modes]]. Those instabilities can be mitigated by either including a passive stabilizing conductor, or by forming very [[oblate spheroid|oblate]] plasmas (i.e. very elongated plasmas),<ref>{{Cite journal | doi = 10.1063/1.2360912| title = Equilibrium and stability studies of oblate field-reversed configurations in the Magnetic Reconnection Experiment| journal = Physics of Plasmas| volume = 13| issue = 11| pages = 112508| year = 2006| last1 = Gerhardt | first1 = S. P.| last2 = Belova | first2 = E.|author2-link=Elena Belova (physicist)| last3 = Inomoto | first3 = M.| last4 = Yamada | first4 = M.| last5 = Ji | first5 = H.| last6 = Ren | first6 = Y.| last7 = Kuritsyn | first7 = A.| url = http://w3.pppl.gov/~hji/paper/Gerhardt06.pdf|bibcode = 2006PhPl...13k2508G }}</ref> or by creating a self-generated toroidal field.<ref>{{Cite conference
 |last=Omelchenko 
 |first=Yu. A. 
 |title=Stabilization of the FRC Tilt Mode by a Self-Generated Toroidal Field 
 |date=27–29 March 2000 
 |conference=Sherwood 2000 International Fusion/Plasma Theory Conference 
 |location=UCLA, Los Angeles, California 
 |publisher=General Atomics Fusion Energy Research 
 |url=https://web.gat.com/pubs-ext/sherwood00/Omelchenko.pdf 
 |url-status=dead 
 |archive-url=https://web.archive.org/web/20141216062225/https://web.gat.com/pubs-ext/sherwood00/Omelchenko.pdf 
 |archive-date=2014-12-16 
}}</ref> The tilt mode has also been stabilized in FRC experiments by increasing the ion gyroradii.<ref name=":1">{{Cite journal | doi = 10.1088/0029-5515/28/6/016| title = Observation of tilt stability of field reversed configurations at large s| journal = Nuclear Fusion| volume = 28| issue = 6| pages = 1121| year = 1988| last1 = Slough | first1 = J. T. | last2 = Hoffman | first2 = A. L. | s2cid = 121761596}}</ref>
* The [[magnetorotational instability]]. This mode causes a rotating elliptical distortion of the plasma boundary, and can destroy the FRC when the distorted plasma comes in contact with the confinement chamber.<ref>{{Cite journal | doi = 10.1088/0741-3335/26/8/004| title = Experimental study of the equilibrium of field-reversed configurations| journal = Plasma Physics and Controlled Fusion| volume = 26| issue = 8| pages = 991–1005| year = 1984| last1 = Tuszewski | first1 = M. |bibcode = 1984PPCF...26..991T | s2cid = 250861012}}</ref> Successful stabilization methods include the use of a quadrupole stabilizing field,<ref>{{Cite journal | doi = 10.1103/PhysRevLett.51.1042| title = Quadrupole Stabilization of the n=2 Rotational Instability of a Field-Reversed Theta-Pinch Plasma| journal = Physical Review Letters| volume = 51| issue = 12| pages = 1042| year = 1983| last1 = Ohi | first1 = S.| last2 = Minato | first2 = T.| last3 = Kawakami | first3 = Y.| last4 = Tanjyo | first4 = M.| last5 = Okada | first5 = S.| last6 = Ito | first6 = Y.| last7 = Kako | first7 = M.| last8 = Gotô | first8 = S.| last9 = Ishimura | first9 = T.| last10 = Itô | first10 = H.|bibcode = 1983PhRvL..51.1042O }}</ref><ref>{{Cite journal | doi = 10.1063/1.864298| title = Suppression of the n=2 rotational instability in field-reversed configurations| journal = Physics of Fluids| volume = 26| issue = 6| pages = 1626–1629| year = 1983| last1 = Hoffman | first1 = A. L. |bibcode = 1983PhFl...26.1626H }}</ref> and the effects of a rotating magnetic field (RMF).<ref>{{Cite journal | doi = 10.1103/PhysRevLett.94.185001| title = Stabilization of Interchange Modes by Rotating Magnetic Fields| journal = Physical Review Letters| volume = 94| issue = 18| year = 2005| last1 = Guo | first1 = H.| last2 = Hoffman | first2 = A.| last3 = Milroy | first3 = R.| last4 = Miller | first4 = K.| last5 = Votroubek | first5 = G.|bibcode = 2005PhRvL..94r5001G | pmid=15904379 | page=185001}}</ref><ref>{{Cite journal|doi=10.1103/PhysRevLett.85.1444 |pmid=10970525 |title=Enhanced Confinement and Stability of a Field-Reversed Configuration with Rotating Magnetic Field Current Drive |journal=Physical Review Letters |volume=85 |issue=7 |pages=1444–7 |year=2000 |last1=Slough |first1=J. |last2=Miller |first2=K. |url=http://depts.washington.edu/rppl/papers/Slough_PRL.pdf |bibcode=2000PhRvL..85.1444S |url-status=dead |archive-url=https://web.archive.org/web/20121017031629/http://depts.washington.edu/rppl/papers/Slough_PRL.pdf |archive-date=2012-10-17 }}</ref>

==Experiments==

{| border="1" class="wikitable"
|+ Selected field reverse experiments, pre-1988<ref name="Tuszewski"/>
! Year
! Device
! Location
! Device length<br/> (meter)
! Device diameter<br/> (meter)
! B-field<br/> (tesla)
! Fill pressure<br/> (pascal)
! Confinement<br/> (seconds)
! Studied
|-
| 1959||-||[[United States Naval Research Laboratory|NRL]]||0.10||0.06||10.00||13.33||2.E-06||Annihilation
|-
| 1961||Scylla I||[[Los Alamos National Laboratory|LANL]]||0.11||0.05||5.50||11.33||3.E-06||Annihilation
|-
| 1962||Scylla III||[[Los Alamos National Laboratory|LANL]]||0.19||0.08||12.50||11.33||4.E-06||Rotation
|-
| 1962||Thetatron||[[Culham Centre for Fusion Energy|Culham]]||0.21||0.05||8.60||13.33||3.E-06||Contraction
|-
| 1962||||Julich{{what|date=December 2022}}||0.10||0.04||6.00||30.66||1.E-06||Formation, tearing
|-
| 1963||||[[Culham Centre for Fusion Energy|Culham]]||0.30||0.10||5.00||6.67||6.E-06||Contraction
|-
| 1964||0-PII||Garching{{what|date=December 2022}}||0.30||0.05||5.30||13.33||1.E-06||Tearing, contraction
|-
| 1965||Pharos||[[United States Naval Research Laboratory|NRL]]||1.80||0.17||3.00||8.00||3.E-05||Confinement, rotation
|-
| 1967||Centaur||[[Culham Centre for Fusion Energy|Culham]]||0.50||0.19||2.10||2.67||2.E-05||Confinement, rotation
|-
| 1967||Julietta||Julich||1.28||0.11||2.70||6.67||2.E-05||Tearing
|-
| 1971||E-G||Garching||0.70||0.11||2.80||6.67||3.E-05||Tearing, rotation
|-
| 1975||BN||[[Kurchatov Institute|Kurchatov]]||0.90||0.21||0.45||0.27 - 1.07||5.E-05||Formation
|-
| 1979||TOR||[[Kurchatov Institute|Kurchatov]]||1.50||0.30||1.00||0.27 - 0.67||1.E-04||Formation
|-
| 1979||FRX-A||LASL||1.00||0.25||0.60||0.53 - 0.93||3.E-05||Confinement
|-
| 1981||FRX-B||LANL||1.00||0.25||1.30||1.20 - 6.53||6.E-05||Confinement
|-
| 1982||STP-L||Nagoya||1.50||0.12||1.00||1.20||3.E-05||Rotation
|-
| 1982||NUCTE||Nihon||2.00||0.16||1.00||||6.E-05||Confinement, rotation
|-
| 1982||PIACE||Osaka||1.00||0.15||1.40||||6.E-05||Rotation
|-
| 1983||FRX-C||LANL||2.00||0.50||0.80||0.67 - 2.67||3.E-04||Confinement
|-
| 1984||TRX-1||MSNW||1.00||0.25||1.00||0.67 -2.00||2.E-04||Formation, confinement
|-
| 1984||CTTX||Penn S U||0.50||0.12||0.40||13.33||4.E-05||Confinement
|-
| 1985||HBQM||U Wash||3.00||0.22||0.50||0.53 - 0.93||3.E-05||Formation
|-
| 1986||OCT||Osaka||0.60||0.22||1.00||||1.E-04||Confinement
|-
| 1986||TRX-2||STI||1.00||0.24||1.30||0.40 - 2.67||1.E-04||Formation, confinement
|-
| 1987||CSS||U Wash||1.00||0.45||0.30||1.33 - 8.00||6.E-05||Slow formation
|-
| 1988||FRXC/LSM||LANL||2.00||0.70||0.60||0.27 - 1.33||5.E-04||Formation, confinement
|-
| 1990||LSX||STI/MSNW||5.00||0.90||0.80||0.27 - 0.67||||Stability, confinement
|}

{| border="1" class="wikitable"
|+ Selected field reverse configurations, 1988 - 2011<ref>{{Cite journal|last=Steinhauer|first=Loren C.|date=July 2011|title=Review of field-reversed configurations|url=http://aip.scitation.org/doi/10.1063/1.3613680|journal=Physics of Plasmas|language=en|volume=18|issue=7|pages=070501|doi=10.1063/1.3613680|bibcode=2011PhPl...18g0501S |issn=1070-664X|url-access=subscription}}</ref>
! Device
! Institution
! Device type
! Electron density
! Max ion or electron
! FRC diameter
! Length/diameter
|-
|  || || ||10<sup>20</sup> / Meter<sup>3</sup>||Temperature [eV]||[Meter]||
|-
| Spheromak-3||Tokyo University||Merging spheromak ||5.0 – 10.0||20 – 100 ||0.40||1.0
|-
| Spheromak-4||Tokyo University||Merging spheromak ||||10 – 40 ||1.20 - 1.40||0.5 – 0.7
|-
| Compact Torus Exp-III||[[Nihon University]]||Theta-pinch ||5.0 – 400.0 ||200 – 300 ||0.10 - 0.40|| 5.0 – 10.0
|-
| Field-Reversed Exp Liner||[[Los Alamos National Laboratory|Los Alamos]]||Theta-pinch ||1,500.0 – 2,500.0 ||200 – 700 ||0.03 - 0.05|| 7.0 – 10.0
|-
| FRC Injection Exp||[[Osaka University]]||Translation trapping||3.0 – 5.0 ||200 – 300 ||0.30 - 0.40||7.0 – 15.0
|-
| Swarthmore Spheromak Exp||Swarthmore||Merging spheromak ||100||20 – 40 ||0.40||1.5
|-
| Magnetic Reconnection Exp||Princeton ([[Princeton Plasma Physics Laboratory|PPPL]])||Merging spheromak ||5.0 – 20.0 ||30||1.00||0.3 – 0.7
|-
|[[Princeton field-reversed configuration experiment]] (PFRC)||Princeton ([[Princeton Plasma Physics Laboratory|PPPL]])||Rotating B-field||0.05 – 0.3 ||200 – 300 ||0.06||
|-
|[[Translation Confinement Sustainment experiment|Translation Confinement Sustainment]]||[[University of Washington]]||Rotating B-field||0.1 – 2.5 ||25 – 50 ||0.70 - 0.74||
|-
|[[Translation Confinement Sustainment experiment|Translation Confinement Sustainment-Upgrade]]||[[University of Washington]]||Rotating B-field|| 0.4 – 1.5 ||50 – 200 ||0.70 - 0.74||1.5 – 3.0
|-
| Plasma Liner Compression||MSNW||Translation trapping||||||0.20||
|-
| Inductive Plasma Accelerator||MSNW||Merging collision||23.0 – 26.0 ||350||0.20||
|-
| Inductive Plasma Accelerator-C||MSNW||Merging compression||300.0||1200 - 2000||0.2||10.0
|-
| Colorado FRC||[[University of Colorado]]||Merging spheromak ||||||||
|-
| Irvine Field Reverse Configuration||[[University of California, Irvine|UC Irvine]]||Coaxial source||150.0||10||0.60||
|-
| C-2||[[Tri Alpha Energy, Inc.]]||Merging collision||5.0 – 10.0||200 – 500 ||0.60 - 0.80||3.0 – 5.0
|-
| [[Star Thrust Experiment|STX]]||[[University of Washington]]||Rotating B-field||0.5||40||0.4||6
|-
|[[Prairie View Rotamak]]
|Prairie View A&M
|Rotating B-field
|0.1
|10-30
|0.4
|2
|}

==Spacecraft propulsion==
Field-reversed configuration devices have been considered for spacecraft propulsion. By angling the walls of the device outward, the plasmoid can be accelerated in the axial direction and out of the device, generating thrust.

==References==
{{Reflist|30em}}

== External links ==
* Google techtalks: [https://www.youtube.com/watch?v=XuAV315__OE ''Nuclear Fusion: Clean Power for the Next Hundred Centuries'']
* University of Washington [https://web.archive.org/web/20110529013024/http://depts.washington.edu/rppl/programs/frc_intro.html " FRC Introduction"]

{{Fusion power}}
{{Nuclear technology}}

[[Category:Magnetic confinement fusion]]