Editing Magnetohydrodynamic generator (section)

=== Generator efficiency ===

The efficiency of the [[direct energy conversion]] in MHD power generation increases with the magnetic field strength and the [[Spitzer resistivity|plasma conductivity]], which depends directly on the [[Plasma (physics)#Temperature|plasma temperature]], and more precisely on the electron temperature. As very hot plasmas can only be used in pulsed MHD generators (for example using [[shock tube]]s) due to the fast thermal material erosion, it was envisaged to use [[nonthermal plasma]]s as working fluids in steady MHD generators, where only free electrons are heated a lot (10,000–20,000 [[kelvin]]s) while the main gas (neutral atoms and ions) remains at a much lower temperature, typically 2500 kelvins. The goal was to preserve the materials of the generator (walls and electrodes) while improving the limited conductivity of such poor conductors to the same level as a plasma in [[thermodynamic equilibrium]]; i.e. completely heated to more than 10,000 kelvins, a temperature that no material could stand.<ref name="Kerrebrock 1964a">{{cite journal
 |last1=Kerrebrock
 |first1=Jack L.
 |last2=Hoffman
 |first2=Myron A.
 |title=Non-Equilibrium Ionization Due to Electron Heating. Theory and Experiments
 |date=June 1964
 |journal=AIAA Journal
 |volume=2
 |issue=6
 |pages=1072–1087
 |doi=10.2514/3.2497
 |url=http://ayuba.fr/pdf/kerrebrock1964.pdf
 |bibcode=1964AIAAJ...2.1080H
 |access-date=2018-04-11
 |archive-date=2019-08-19
 |archive-url=https://web.archive.org/web/20190819083451/http://ayuba.fr/pdf/kerrebrock1964.pdf
 |url-status=dead
 }}</ref><ref name="Sherman 1966">{{cite journal
 |last1=Sherman
 |first1=A.
 |title=MHD Channel Flow with Non-Equilibrium lonization
 |date=September 1966
 |journal=The Physics of Fluids
 |volume=9
 |issue=9
 |pages=1782–1787
 |doi=10.1063/1.1761933
 |url=http://ayuba.fr/pdf/sherman1966.pdf
 |bibcode=1966PhFl....9.1782S
 |access-date=2018-04-11
 |archive-date=2018-04-12
 |archive-url=https://web.archive.org/web/20180412082322/http://ayuba.fr/pdf/sherman1966.pdf
 |url-status=dead
 }}</ref><ref name="Argyropoulos 1967">{{cite journal
 |last1=Argyropoulos |first1=G. S.
 |last2=Demetriades |first2=S. T.
 |last3=Kentig |first3=A. P.
 |title=Current Distribution in Non-Equilibrium J×B Devices
 |date=1967
 |journal=Journal of Applied Physics
 |volume=38
 |issue=13
 |pages=5233–5239
 |doi=10.1063/1.1709306
 |url=http://ayuba.fr/pdf/argyropoulos1967
 |format=PDF
 |bibcode=1967JAP....38.5233A
}}</ref><ref name="Zauderer 1968">{{cite journal
 |last1=Zauderer |first1=B.
 |last2=Tate |first2= E.
 |title=Electrical characteristics of a linear, nonequilibrium, MHD generator
 |date=September 1968
 |journal=AIAA Journal
 |volume=6
 |issue=9
 |pages=1683–1694
 |doi=10.2514/3.4846
 |url=http://ayuba.fr/pdf/zauderer1968.pdf
 |bibcode=1968AIAAJ...6.1685T
}}</ref>

[[Evgeny Velikhov]] first discovered theoretically in 1962 and experimentally in 1963 that an ionization instability, later called the Velikhov instability or [[electrothermal instability]], quickly arises in any MHD converter using [[Plasma (physics)#Magnetization|magnetized]] nonthermal plasmas with hot electrons, when a critical [[Hall effect|Hall parameter]] is reached, depending on the [[degree of ionization]] and the magnetic field.<ref name="Velikhov 1962">
{{cite conference
 | last1 = Velikhov | first1 = E. P.
 | year = 1962
 | title = Hall instability of current carrying slightly ionized plasmas
 | conference = 1st International Conference on MHD Electrical Power Generation
 | location = Newcastle upon Tyne, England
 | id = Paper 47
 | page = 135
}}</ref><ref name="Velikhov 1963">
{{cite conference
 | last1 = Velikhov | first1 = E. P.
 | last2 = Dykhne | first2 = A. M.
 | title = Plasma turbulence due to the ionization instability in a strong magnetic field
 | conference = 6th International Conference on Phenomena in Ionized Gases
 | book-title = Volume IV. Proceedings of the conference held July 8-13, 1963
 | editor = P. Hubert
 | editor2 = E. Crémieu-Alcan
 | location = Paris, France
 | page = 511
 | bibcode = 1963pig4.conf..511V
}}</ref><ref name="Velikhov 1965">
{{cite conference
 | last1 = Velikhov | first1 = E. P.
 | last2 = Dykhne | first2 = A. M.
 | last3 = Shipuk | first3 = I. Ya
 | year = 1965
 | title = Ionization instability of a plasma with hot electrons
 | conference = 7th International Conference on Ionization Phenomena in Gases
 | location = Belgrade, Yugoslavia
 | url = https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19670016557.pdf
}}</ref> This instability greatly degrades the performance of nonequilibrium MHD generators. The prospects of this technology, which initially predicted high efficiencies, crippled MHD programs all over the world as no solution to mitigate the instability was found at that time.<ref>
{{cite journal 
 | last1 = Shapiro | first1 = G. I.
 | last2 = Nelson | first2 = A. H.
 | date = 12 April 1978
 | title = Stabilization of ionization instability in a variable electric field
 | journal = Pis'ma V Zhurnal Tekhnischeskoi Fiziki
 | volume = 4
 | issue = 12
 | pages = 393–396
 | bibcode = 1978PZhTF...4..393S
}}</ref><ref>
{{cite journal 
 | last1 = Murakami |first1 = T.
 | last2 = Okuno |first2 = Y.
 | last3 = Yamasaki | first3 = H.
 | date = December 2005
 | title = Suppression of ionization instability in a magnetohydrodynamic plasma by coupling with a radio-frequency electromagnetic field
 | journal = Applied Physics Letters
 | volume = 86
 | issue = 19
 | pages = 191502–191502.3
 | url = http://ayuba.fr/pdf/murakami2005.pdf
 | doi = 10.1063/1.1926410
 | bibcode = 2005ApPhL..86s1502M
}}</ref><ref name="Petit 2009">
{{cite journal
 | last1 = Petit | first1 = J.-P.
 | last2 = Geffray | first2 = J.
 | date = June 2009
 | title = Non equilibrium plasma instabilities
 | journal = Acta Physica Polonica A
 | volume = 115
 | issue = 6
 | pages = 1170–1173
 | doi = 10.12693/aphyspola.115.1170
 | bibcode = 2009AcPPA.115.1170P
 | citeseerx = 10.1.1.621.8509
}}</ref><ref name="Petit 2013">{{Cite journal
 |last1=Petit |first1=J.-P.
 |last2=Doré |first2=J.-C.
 |title=Velikhov electrothermal instability cancellation by a modification of electrical conductivity value in a streamer by magnetic confinement
 |year=2013
 |journal=Acta Polytechnica
 |volume=53
 |issue=2
 |pages=219–222
 |doi=10.14311/1765
 |url=https://ojs.cvut.cz/ojs/index.php/ap/article/view/1765/1597
|doi-access=free
 |hdl=10467/67041
 |hdl-access=free
 }}</ref>

Without implementing solutions to overcome the electrothermal instability, practical MHD generators had to limit the Hall parameter or use moderately-heated thermal plasmas instead of cold plasmas with hot electrons, which severely lowers efficiency.

As of 1994, the 22% efficiency record for closed-cycle disc MHD generators was held by Tokyo Technical Institute. The peak enthalpy extraction in these experiments reached 30.2%. Typical open-cycle Hall & duct coal MHD generators are lower, near 17%. These efficiencies make MHD unattractive, by itself, for utility power generation, since conventional [[Rankine cycle]] power plants can reach 40%.

However, the exhaust of an MHD generator burning [[fossil fuel]] is almost as hot as a flame. By routing its exhaust gases into a heat exchanger for a turbine [[Brayton cycle]] or steam generator [[Rankine cycle]], MHD can convert [[fossil fuel]]s into electricity with an overall estimated efficiency of up to 60 percent, compared to the 40 percent of a typical coal plant.

A magnetohydrodynamic generator might also be the first stage of a [[gas core reactor]].<ref>{{cite conference|vauthors=Smith BM, Anghaie S, Knight TW|date=2002|title=Gas Core Reactor-MHD Power System with Cascading Power Cycle|conference=ICAPP'02: 2002 International congress on advances in nuclear power plants, Hollywood, FL (United States), 9-13 Jun 2002|id=OSTI: 21167909|osti=21167909}}</ref>