Editing Magnetohydrodynamic generator (section)

== Power generation ==

Typically, for a large power station to approach the operational efficiency of [[computer model]]s, steps must be taken to increase the electrical conductivity of the conductive substance. Heating a gas to its plasma state, or adding other easily ionizable substances like the salts of alkali metals, can help to accomplish this. In practice, a number of issues must be considered in the implementation of an '''MHD generator''': generator efficiency, economics, and toxic byproducts. These issues are affected by the choice of one of the three MHD generator designs: the Faraday generator, the Hall generator, and the disc generator.

=== Faraday generator ===
The Faraday generator is named for Michael Faraday's experiments on moving charged particles in the Thames River. 

A simple Faraday generator consists of a wedge-shaped pipe or tube of some non-[[conductive]] material. When an electrically conductive fluid flows through the tube, in the presence of a significant perpendicular magnetic field, a voltage is induced in the fluid. This can be drawn off as electrical power by placing electrodes on the sides, at 90-degree angles to the magnetic field.

There are limitations on the density and type of field used in this example. The amount of power that can be extracted is proportional to the cross-sectional area of the tube and the speed of the conductive flow. The conductive substance is also cooled and slowed by this process. MHD generators typically reduce the temperature of the conductive substance from plasma temperatures to just over 1000&nbsp;°C.

The main practical problem of a Faraday generator is that differential voltages and currents in the fluid may short through the electrodes on the sides of the duct. The generator can also experience losses from the [[Hall effect]] current, which makes the Faraday duct inefficient.{{Citation needed|reason=Needs context for assertion about being "most powerful waste"|date=April 2024}} Most further refinements of MHD generators have tried to solve this problem. The optimal magnetic field on duct-shaped MHD generators is a sort of saddle shape. To get this field, a large generator requires an extremely powerful magnet. Many research groups have tried to adapt superconducting magnets to this purpose, with varying success. 

=== Hall generator ===

[[File:MHD generator (En).png|thumb|right|upright=1.5|alt=Diagram of a Hall MHD generator|Diagram of a Hall MHD generator showing current flows]]
The typical solution has been to use the [[Hall effect]] to create a current that flows with the fluid. (See illustration.) This design has arrays of short, segmented electrodes on the sides of the duct. The first and last electrodes in the duct power the load. Each other electrode is shorted to an electrode on the opposite side of the duct. These shorts of the Faraday current induce a powerful magnetic field within the fluid, but in a chord of a circle at right angles to the Faraday current. This secondary, induced field makes the current flow in a rainbow shape between the first and last electrodes.

Losses are less than in a Faraday generator, and voltages are higher because there is less shorting of the final induced current. 

However, this design has problems because the speed of the material flow requires the middle electrodes to be offset to "catch" the Faraday currents. As the load varies, the fluid flow speed varies, misaligning the Faraday current with its intended electrodes, and making the generator's efficiency very sensitive to its load.

=== Disc generator ===

[[File:Disk MHD generator.png|thumb|right|upright=1.5|alt=Diagram of a Disk MHD generator|Diagram of a disk MHD generator showing current flows]]
The third and, currently, the most efficient design is the Hall effect disc generator. This design currently holds the efficiency and energy density records for MHD generation. A disc generator has fluid flowing between the center of a disc, and a duct wrapped around the edge. (The ducts are not shown.) The magnetic excitation field is made by a pair of circular [[Helmholtz coils]] above and below the disk. (The coils are not shown.)

The Faraday currents flow in a perfect dead short around the periphery of the disk.

The Hall effect currents flow between ring electrodes near the center duct and ring electrodes near the periphery duct.

The wide flat gas flow reduced the distance, hence the resistance of the moving fluid. This increases efficiency.

Another significant advantage of this design is that the magnets are more efficient. First, they cause simple parallel field lines. Second, because the fluid is processed in a disk, the magnet can be closer to the fluid, and in this geometry, magnetic field strengths increase as the 7th power of distance. Finally, the generator is compact, so the magnet is smaller and uses a much smaller percentage of the generated power.

=== 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
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 |issue=6
 |pages=1072–1087
 |doi=10.2514/3.2497
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 }}</ref><ref name="Sherman 1966">{{cite journal
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 |title=MHD Channel Flow with Non-Equilibrium lonization
 |date=September 1966
 |journal=The Physics of Fluids
 |volume=9
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 |pages=1782–1787
 |doi=10.1063/1.1761933
 |url=http://ayuba.fr/pdf/sherman1966.pdf
 |bibcode=1966PhFl....9.1782S
 |access-date=2018-04-11
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 |archive-url=https://web.archive.org/web/20180412082322/http://ayuba.fr/pdf/sherman1966.pdf
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 }}</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
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}}</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 
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 | 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
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{{cite journal
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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> 

=== Material and design issues ===

MHD generators have problems in regard to materials, both for the walls and the electrodes. Materials must not melt or corrode at very high temperatures. Exotic ceramics were developed for this purpose, selected to be compatible with the fuel and ionization seed. The exotic materials and the difficult fabrication methods contribute to the high cost of MHD generators.

MHDs also work better with stronger magnetic fields. The most successful magnets have been [[superconductor | superconducting]], and very close to the channel. A major difficulty was refrigerating these magnets while insulating them from the channel. The problem is worse because the magnets work better when they are closer to the channel. There are also risks of damage to the hot, brittle ceramics from differential thermal cracking: magnets are usually near absolute zero, while the channel is several thousand degrees.

For MHDs, both [[alumina]] (Al<sub>2</sub>O<sub>3</sub>) and [[magnesium peroxide]] (MgO<sub>2</sub>) were reported to work for the insulating walls. Magnesium peroxide degrades near moisture.  Alumina is water-resistant and can be fabricated to be quite strong, so in practice, most MHDs have used alumina for the insulating walls.

For the electrodes of clean MHDs (i.e. burning natural gas), one good material was a mix of 80% CeO<sub>2</sub>, 18% ZrO<sub>2</sub>, and 2% Ta<sub>2</sub>O<sub>5</sub>.<ref name="rohatgi">{{cite journal |last1=Rohatgi |first1=V. K. |title=High temperature materials for magnetohydrodynamic channels |journal=Bulletin of Materials Science |date=February 1984 |volume=6 |issue=1 |pages=71–82 |url=https://www.ias.ac.in/article/fulltext/boms/006/01/0071-0082 |access-date=19 October 2019|doi=10.1007/BF02744172 |doi-access=free }}</ref>

Coal-burning MHDs have highly corrosive environments with slag. The slag both protects and corrodes MHD materials. In particular, migration of oxygen through the slag accelerates the corrosion of metallic anodes. Nonetheless, very good results have been reported with [[stainless steel]] electrodes at 900{{nbsp}}K.<ref name="bogdancks">{{cite journal|vauthors=Bogdancks M, Brzozowski WS, Charuba J, Dabraeski M, Plata M, Zielinski M|title=MHD Electrical Power Generation|journal=Proceedings of 6th Conference, Washington DC|date=1975|volume=2|page=9}}</ref> Another, perhaps superior option is a spinel ceramic, FeAl<sub>2</sub>O<sub>4</sub> - Fe<sub>3</sub>O<sub>4</sub>. The spinel was reported to have electronic conductivity, absence of a resistive reaction layer but with some diffusion of iron into the alumina. The diffusion of iron could be controlled with a thin layer of very dense alumina, and water cooling in both the electrodes and alumina insulators.<ref name="mason">{{cite journal|vauthors=Mason TO, Petuskey WT, Liang WW, Halloran JW, Yen F, Pollak TM, Elliott JF, Bowen HK|title=MHD Electrical Power Generation|journal=Proceedings of 6th Conference, Washington DC|date=1975|volume=2|page=77}}</ref>

Attaching the high-temperature electrodes to conventional copper bus bars is also challenging. The usual methods establish a chemical passivation layer, and cool the busbar with water.<ref name="rohatgi" />

=== Economics ===

MHD generators have not been used for large-scale mass energy conversion because other techniques with comparable efficiency have a lower lifecycle investment cost. Advances in [[combined cycle | natural gas turbines]] achieved similar thermal efficiencies at lower costs, by having the turbine exhaust drive a [[Rankine cycle]] steam plant. To get more electricity from coal, it is cheaper to simply add more low-temperature steam-generating capacity.

A coal-fueled MHD generator is a type of [[Brayton cycle|Brayton power cycle]], similar to the power cycle of a combustion turbine. However, unlike the combustion turbine, there are no moving mechanical parts; the electrically conducting plasma provides the moving electrical conductor. The side walls and electrodes merely withstand the pressure within, while the anode and cathode conductors collect the electricity that is generated. All Brayton cycles are heat engines. Ideal Brayton cycles also have an ideal efficiency equal to ideal [[Carnot cycle]] efficiency. Thus, the potential for high [[Electrical efficiency|energy efficiency]] from an MHD generator. All Brayton cycles have higher potential for efficiency the higher the firing temperature. While a combustion turbine is limited in maximum temperature by the strength of its air/water or steam-cooled rotating airfoils; there are no rotating parts in an open-cycle MHD generator. This upper bound in temperature limits the energy efficiency in combustion turbines. The upper bound on Brayton cycle temperature for an MHD generator is not limited, so inherently an MHD generator has a higher potential capability for energy efficiency.

The temperatures at which linear coal-fueled MHD generators can operate are limited by factors that include: (a) the combustion fuel, oxidizer, and oxidizer preheat temperature which limit the maximum temperature of the cycle; (b) the ability to protect the sidewalls and electrodes from melting; (c) the ability to protect the electrodes from electrochemical attack from the hot slag coating the walls combined with the high current or arcs that impinge on the electrodes as they carry off the direct current from the plasma; and (d) by the capability of the electrical insulators between each electrode. Coal-fired MHD plants with oxygen/air and high oxidant preheats would probably provide potassium-seeded plasmas of about 4200{{nbsp}}°F, 10 atmospheres pressure, and begin expansion at Mach{{nbsp}}1.2. These plants would recover MHD exhaust heat for oxidant preheat, and for combined cycle steam generation. With aggressive assumptions, one DOE-funded feasibility study of where the technology could go, [[1000 MWe Advanced Coal-Fired MHD/Steam Binary Cycle Power Plant Conceptual Design]], published in June 1989, showed that a large coal-fired MHD combined cycle plant could attain a HHV energy efficiency approaching 60 percent—well in excess of other coal-fueled technologies, so the potential for low operating costs exists.

However, no testing at those aggressive conditions or size has yet occurred, and there are no large MHD generators now under test. There is simply an inadequate reliability track record to provide confidence in a commercial coal-fuelled MHD design.

U25B MHD testing in Russia using natural gas as fuel used a superconducting magnet, and had an output of 1.4 megawatts. A coal-fired MHD generator series of tests funded by the [[United States Department of Energy|U.S. Department of Energy (DOE)]] in 1992 produced MHD power from a larger superconducting magnet at the Component Development and Integration Facility (CDIF) in [[Butte, Montana|Butte]], [[Montana]]. None of these tests were conducted for long-enough durations to verify the commercial durability of the technology. Neither of the test facilities were in large-enough scale for a commercial unit.

Superconducting magnets are used in the larger MHD generators to eliminate one of the large parasitic losses: the power needed to energize the electromagnet. Superconducting magnets, once charged, consume no power and can develop intense magnetic fields 4 teslas and higher. The only [[Losses in electrical systems#Parasitic_loss|parasitic load]] for the magnets are to maintain refrigeration, and to make up the small losses for the non-supercritical connections.

Because of the high temperatures, the non-conducting walls of the channel must be constructed from an exceedingly heat-resistant substance such as [[yttrium]] oxide or [[zirconium]] dioxide to retard oxidation. Similarly, the electrodes must be both conductive and heat-resistant at high temperatures. The AVCO coal-fueled MHD generator at the CDIF was tested with water-cooled copper electrodes capped with platinum, tungsten, stainless steel, and electrically conducting ceramics.

=== Toxic byproducts ===
MHD reduces the overall production of fossil fuel wastes because it increases plant efficiency. In MHD coal plants, the patented commercial "Econoseed" process developed by the U.S. (see below) recycles potassium ionization seed from the fly ash captured by the stack-gas scrubber. However, this equipment is an additional expense. If molten metal is the armature fluid of an MHD generator, care must be taken with the coolant of the electromagnetics and channel. The alkali metals commonly used as MHD fluids react violently with water. Also, the chemical byproducts of heated, electrified alkali metals and channel ceramics may be poisonous and environmentally persistent.