# Talk:Magnetohydrodynamics

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## Limits of MHD

"MHD is lacking when electric currents flows through these plasmas and produces filaments, double layers and plasma instabilities."

Aren't filaments essentially a product of the pinch effect, which is MHD? And there are certainly many fluid instabilities. You might be right about double layers. Can you (Iantresman) tell me in three sentences how they form? Art Carlson 06:20, 2005 Jun 8 (UTC)

I removed the offending sentence. Electric current flowing through plasmas, and the formation of "filaments ... and plasma instabilities" are explicitly part of magnetohydrodynamics. The formation of a double layer is an example of breakdown of MHD, but I don't believe that they are actually observed. zowie 19:24, 16 October 2005 (UTC)
I'm not sure I understand your reasoning. (1) What is "explicitly part of magnetohydrodynamics"? (2) If the formation of a double layer is an example of breakdown of MHD, then why can't we say so, as an example? (3) Likewise, aren't field-aligned currents a breakdown of MHD, in which case, why don't we say so. (4) You say that "don't believe that they are actually observed"... do you mean that double layers are not observed, and if so, where? --Iantresman 20:52, 16 October 2005 (UTC)
(1) Electrical currents of all types are allowed in magnetohydrodynamics. That is the whole and entire point of MHD - to deal with the coupling of Maxwell's Equations governing electrical phenomena and the Navier-Stokes Equations governing fluid dynamics. Filament formation and the various instabilities are well known magnetohydrodynamic phenomena; they are predicted by the MHD equations and hence are not examples of the breakdown of the theory.
(2) My bad - transient double layers are worth a mention, especially in the context of magnetic reconnection or electrojet formation. Sorry if I threw out a baby with that particular bathwater. (also, see (4) below).
(3) In the special case of quasi-static, low-beta plasmas (in which all non-magnetic forces are negligible) only field-aligned currents are allowed -- but in high-beta plasmas (in which the plasma gas pressure dominates over the magnetic pressure) non-field-aligned currents are also allowed. The important effect here is the Lorenz force, which is proportional to J x B (where J is the electric current and B is the magnetic field). In quasi-static, low-beta plasmas, J x B must be near zero everywhere, which means that J (if it exists) must be nearly parallel to B -- ie field-aligned. In other systems, the JxB force can be balanced by inertial forces ('mass times acceleration'; non-static) or by other forces (such as a gas pressure gradient or gravity; non-low-beta).
(4) Hmmm... When I typed that I was thinking of non-transient resistive regions in a plasma; but I had a look at some of the review articles in the double layer article (I think you may have linked to them; thanks!), and my mind is changed. I'm used to thinking of double layers as transient phenomena, perhaps related to anomalous resistivity in magnetic reconnection -- but I was surprised to read that relatively stable double layers can form in lab plasmas and are thought (by at least some) to form in astrophysical plasmas as well. So, I stand corrected here. Thanks!
Cheers, zowie 00:51, 17 October 2005 (UTC)
• Is there a contradiction between (1) you say "Electrical currents of all types are allowed in magnetohydrodynamics.", but then in (3) ".. in low-beta plasmas .. only field-aligned currents are allowed". Does this imply that non-field-aligned currents are not allowed in low-beta plasmas, or not described. And if such currents are found, is that a breakdown?
Non-field-aligned currents are simply not force-free; they violate a particular further simplification of MHD. Hmmm... A good analogy: parasitic capacitance violates the assumptions of basic circuit design, because normally one assumes that the circuit traces are perfectly isolated. That doesn't mean Maxwell's Equations are wrong -- just that you can't use that particular simplifying assumption. zowie 15:11, 17 October 2005 (UTC)
• I get the impression from Alfvén that certain currents in certain plasmas, do result in a breakdown of MHD?
The usual MHD equations predict the behavior of the fluid plasma for all finite configurations of electric current. Ideal MHD predicts the formation of ideal current sheets, which are not physical (ideal current sheets are infinitely thin and carry an infinite current density); but they are only singularities of the first kind (integrating across them gives a finite amount of current). Non-ideal MHD does not suffer from that problem, because the plasma resistivity limits the thickness of the sheet.
• And that the electric field across a double layer resulting in beams and jets (electric currents?) are also a breakdown?
One normally assumes that the electric field is zero everywhere (ideal) or near-zero everywhere (non-ideal); double layers are not well described by the normal MHD equations. Of course one may augment them with some kind of anomalous resistivity term that describes double layer formation -- but that is outside the normal theory.
• Do you have access to Alfvén's Cosmic Plasmas (1981)? --Iantresman 13:41, 17 October 2005 (UTC)
I do not have it in my office. I generally work with Priest's books ("Solar MHD" and "Magnetic reconnection").
I'll post (here in the discussion) what I mean by "the usual MHD equations" -- but I want to make sure I have a reference handy, so I don't muck it up by doing it from memory. That way at least we won't be talking past each other. zowie 15:11, 17 October 2005 (UTC)
• Since double layers may generate quite large electric fields, (up to 10^4V in the auroral electrojets), can we say that MHD breaks down when significant non-field aligned electric currents are generated, for example, in in some double layers (ie. oblique double layers)? --Iantresman 15:55, 17 October 2005 (UTC)
• The MHD equations are (from Priest's _Magnetic_Reconnection_):
Mass conservation:
${\displaystyle {\frac {d\rho }{dt}}={\frac {\partial \rho }{\partial t}}+v\cdot y\nabla \rho =-\rho \nabla \cdot v}$ (where ${\displaystyle \rho }$ is the density and ${\displaystyle v}$ is the plasma velocity)
Momentum conservation:
${\displaystyle \rho {\frac {dv}{dt}}=-\nabla p+j\times B+\nabla \cdot S+F_{g}}$ (where ${\displaystyle p}$ the normal gas pressure, ${\displaystyle j}$ is electric current, ${\displaystyle S}$ is the viscous stress tensor [so ${\displaystyle \nabla \cdot S}$ is itself a vector], and ${\displaystyle F_{g}}$ is any externally applied volume force such as gravity) This is very similar to the Navier-Stokes momentum equation for fluids, (which itself is a fancy way of writing "ma=F"), except that it includes the Lorenz force ${\displaystyle j\times B}$ as one of the force terms.
Internal energy conservation:
${\displaystyle \rho {\frac {de}{dt}}+p\nabla \cdot v=\nabla \cdot (\kappa \cdot \nabla T)+(\eta _{e}\cdot j)\cdot j+Q_{v}-Q_{r}}$ (where ${\displaystyle e}$ is the internal energy per unit mass [something like temperature over the molecular mass], ${\displaystyle \kappa }$ is the thermal conductivity tensor [indicating direction and strength of thermal flux, given a direction and strength of thermal gradient], ${\displaystyle \eta _{e}}$ is the electrical resistivity tensor [direction and strength of the electric field given a direction and strength of current flow], and ${\displaystyle Q_{v}}$ and ${\displaystyle Q_{r}}$ are the viscous (friction) heating and radiative loss terms, respectively).
${\displaystyle \nabla \times E=-{\frac {\partial B}{\partial t}}}$ (this is the electric induction equation)
Ampere's Law:
${\displaystyle \nabla \times B=\mu j}$ (here, ${\displaystyle \mu }$ is the permeability of free space; it depends on the system of units you like)
Gauss's Law:
${\displaystyle \nabla \cdot B=0}$ (no magnetic monopoles)
Ohm's Law:
${\displaystyle E=\eta _{e}\cdot j-v\times B}$ (Neglecting ${\displaystyle \eta _{e}}$ is what yields reconnection-free "ideal MHD")
Equation of State (ideal gas law)
${\displaystyle p=\rho {\frac {k_{B}}{\mu _{av}}}T}$ (this is just the familiar PV = nRT, rewritten -- ${\displaystyle \mu _{av}}$ is the average particle mass in the plasma, not to be confused with ${\displaystyle \mu }$, the permeability of free space!)

It's usually more convenient to combine Faraday's Law, Ampere's Law, and Ohm's Law to eliminate the ${\displaystyle j}$ and ${\displaystyle E}$ terms -- then you get the magnetic induction equation:

${\displaystyle {\frac {\partial B}{\partial t}}=\nabla \times (v\times B)-\nabla \times (({\frac {\eta _{e}}{\mu }})\nabla \times B)}$, which describes time evolution of the magnetic field in terms only of the velocity field and the resistivity. This makes it obvious why "ideal MHD" is so "ideal": turning off the resistivity completely eliminates one of two reasons why the magnetic field can change. The left-hand term describes the magnetic field being carried around by bulk motion; the right-hand term describes the decay of the magnetic field. Incidentally, keeping the ${\displaystyle \eta _{e}}$ inside that first curl operator is important for the physics you're interested in -- double-layer formation.
If the resistivity is constant across the whole plasma, then ${\displaystyle \eta _{e}}$ is just a constant and the right hand side gets even more simple -- ${\displaystyle \nabla \times \nabla \times B}$ is just ${\displaystyle \nabla ^{2}B}$, and you get the old, familiar RHS of the diffusion equation. That diffusion term is what prevents the formation of current sheet singularities in resistive MHD: in an very thin current sheet, ${\displaystyle \nabla ^{2}B}$, would be very large so ${\displaystyle {\frac {\partial B}{\partial t}}}$ would also be very large -- in the corrective direction.
If the resistivity varies in space, you can't commute it through the outer ${\displaystyle \nabla }$, so you get additional terms that describe evolution of the magnetic field near an anomalously resistive area (such as a double layer or condensed region or whatever). The equations above can't predict that change in resistivity -- that is external to the system of equations. In that sense, the system "fails" near double layers: you have to put in more information about the resistivity of the plasma that isn't present in the original equations.

Anyway, the upshot of all of this stuff is that the physical equations don't fail simply because resistivity varies or there are field-aligned electric fields or whatever. Some idealizations may fail, but the fluid approach (informed by the underlyling particle kinematics) remains sound. I suppose it would be useful to list explicitly the assumptions most people use when working in this field ("assumptions of MHD") but I'm all out of steam for now. zowie 17:57, 17 October 2005 (UTC)

Thanks for all that, very impressive. Have you thought about transferring it to the MHD page proper? I can certainly recomend Alfvén's Cosmic Plasmas. As the man who devloped MHD, he will explain far better than I can, some of the points I am trying to convey, and you'd understand it far better than I can. His other book, co-authored with Carl-Gunne Fälthammar is Cosmical Electrodynamics (2nd Ed. 1963) is also recommended. --Iantresman 23:29, 17 October 2005 (UTC)
Well, not so impressive maybe -- but plenty tedious, which is why most folks prefer to wave their hands under simplifying assumptions! :-) You're probably right -- the equations and usual assumptions should be present. But I won't have time to look at it again for a few more days. Anyone else want to see this stuff in the article itself? zowie 23:58, 17 October 2005 (UTC)
There is a good reason that MHD is commonly treated with suspicion: it is often applied to plasmas where the assumptions of a locally thermal plasma do not hold. In particular, fusion, space and astrophysical plasmas are often so collisionless that the collisions can be ignored, and there is no reason for the plasma to be thermal. The question is usually not whether MHD can rigourously be applied (it cannot) but whether it still describes the qualitative physics, and approximates the quantitative physics (MHD is still usually pretty useful). For example, field aligned electric fields arise in collisionless plasmas due to kinetic effects, and it is usually difficult to even get the large scale physics correct with a fluid model (the Aurora is a case in point). Even large scale structures like the Earth's bow shock are only approximately resolved by MHD. Beams in collisionless plasmas can add a fair amount of pressure and move things around. But on the other hand, (fast) magnetic reconnection is now believed to be well modelled by Hall MHD (as long as you are interested in overall shape and timescales and not the details of particle acceleration).
So there probably needs to be a section on where MHD is valid, and why MHD is still useful even when not strictly valid.--Dashpool 17:09, 19 May 2006 (UTC)
Hmm, Dashpool -- do you have a good reference on Hall MHD and astrophysical magnetic reconnection? At least in the solar physics community I hear no clear consensus on how reconnection proceeds. People talk of anomalous resistivity and possible accelerating mechanisms to make the jump from Sweet-Parker type reconnection to faster modes like Petschek reconnection, but there's still an ongoing debate over things like why the energy scaling law appears linear in magnetic field strength (rather than quadratic). Pevtsov et al (2001?) observed the linear scaling law over a huge number of orders of magnitude -- something like 12 orders of magnitude in total magnetic flux, in astrophysical systems from solar bright points to quasars. Schrijver et al (2004?) did an interesting study where they examined forward models of coronal plasmas and tried to match the morphology of the observed corona. Longcope (several references over the last few years) seems to think, like me, that most of the energy is released NOT near the reconnection site but farther away. I've been modeling solar MHD systems using a simple ad-hoc anomalous resistivity that turns on when the current density gets too high -- but I don't think that anyone (yet) has a clear and unambiguous understanding of why and when such a resistivity should happen. zowie 15:24, 22 May 2006 (UTC)
You've probably already seen it, but can I suggest: Hall effects on magnetic relaxation, Turner, Leaf, IEEE Transactions on Plasma Science (ISSN 0093-3813), vol. PS-14, Dec. 1986, p. 849-857. --Iantresman 17:57, 22 May 2006 (UTC)
Probably I need to add some caveats and reduce the force of the statement I made earlier: even if I think an answer is emerging, there is still substantial controversy about reconnection mechanisms, and probably wikipedia isn't the place for picking a winner. Shay+Drake JGR 2001 is a good example of the school of thought I'm thinking about wrt Hall reconnection. I'm not sure that the energy scaling law you mentioned conclusively rules out fluid models of reconnection: Pevstov even mentions in his conclusion that he thinks models involving heating via Alfvén modes (mostly just MHD physics) might explain the power law dependence. Why do you think this scaling rules out reconnection models based on the Hall effect? I'm not sure that Hall MHD is inconsistent with energy release 'far from the reconnection region' either: geometrical effects are important. Also, the question is whether Hall MHD predicts global structures/timescales, rather than details. I think the best information on reconnection comes from plasmas which are well characterised, with in-situ measurements, and for these plasmas there is strong evidence for Hall MHD scaling. For example, the MRX (magnetic reconnection experiment) people presented results at the ICPP conference last week showing very good agreement with timescales expected from Hall MHD. Measurements from WIND in the magnetotail support the existence of quadrupole fields expected in Hall MHD reconnection (Oieroset, Nature 412, p414, 2001). The question of why and when anomalous resistivity arises is avoided in Hall MHD, because the (global) physics becomes insensitive to the resistivity mechanism. My view is that that reconnection in relatively simple scenarios is becoming fairly well understood, and that the problem is to understand the complex systems: but a Hall MHD simulation of a decent chunk of the corona would be difficult, and I don't know of any references on Hall MHD for solar plasmas. From the point of view of writing the article, maybe we could say "resistive MHD simulations usually find rates of reconnection far lower than those observed in systems with low collisionality, but there is evidence that the two-fluid MHD model can predict the rate of magnetic reconnection in many of these systems.". --Dashpool 16:39, 28 May 2006 (UTC)
that wording sounds fine to me. Thanks very much for the Shay & Drake reference (And thanks, Ian, for the Leaf reference as well). To clarify, I can't really opine over the role of the Hall effect on reconnection rates, since I haven't thought much about it -- I just wanted to find a place where I could read more about the physics... Kind regards, zowie 17:21, 28 May 2006 (UTC)
I have reorganised the Ideal MHD section to try to make it more logical and explain the various limitations clearly, and separate out the ideas about current sheets. Dashpool 14:56, 9 July 2006 (UTC) I have removed some material (the writeup on infinitely thin current sheets seemed spurious), and removed some of the references to individual physicists. We just need to explain the physics here, rather than the (in fact, uncontroversial) viewpoints of individuals.Dashpool 15:19, 9 July 2006 (UTC)

## Voltage at Waterloo Bridge in trivia

Would someone do this calculation? I did it about forty years ago at school and remember the answer as one volt, but when I do it now I get a couple of orders of magnitude less. However I am now rusty on these things and they have changed to SI units, so someone should recheck my calculation. Assume that the water is flowing at one metre per second and the river is 200 metres wide. In London the earth’s magnetic field is 55,000 nanotesla and the dip angle is 67 degrees (it is zero at the equator and 90 degrees at the magnetic poles). You then have to invoke Fleming's right hand contortion to get the direction. JMcC 11:07, 20 June 2006 (UTC)

Also, how could Wollaston do this measurement when he had (according to his main article) already been dead for more than two decades? --83.233.10.87 (talk) 20:38, 23 September 2009 (UTC)

he must've been a very persistent researcher! Bob Emmett (talk) 05:35, 21 March 2010 (UTC)

## Magnetohydrodynamics, Electrohydrodynamics, and Electrokinetics

What's the difference? — Omegatron 20:22, 26 June 2006 (UTC)

To get things going:

• "In more precise terms, EHD is the study of fluid flow behavior under the influence of electric fields. Electrohydrodynamics is, in essence, the mirror of electrokinetics, which is concerned with the thrust effect generated by these non-conducting media on the electric field generating apparatuses. As expected, the terms electrohydrodynamics and electrokinetics can be easily interchanged depending on the aspect used to describe the same system. For convenience, this section contains information concerning the hydrodynamic aspect of the apparatuses." [1]
• "Electrohydrodynamics deals with fluid motion induced by electric fields." [2]
• "Electrokinetics involves study of motion of liquid or particles under the action of electric field." [3]
• "Magnetohydrodynamics (MHD). This is the theory of the macroscopic interaction of electrically conducting fluids with a magnetic field." [4]
• "Magnetohydrodynamics (or MHD for short) is the study of the interaction between a magnetic field and a plasma treated as a continuous medium" [5]]
• "[magnetohydrodynamics] , study of the motions of electrically conducting fluids and their interactions with magnetic fields." [6]

Ok, nevermind about MHD. I see the difference now. EHD and electrokinetics are not clear though. — Omegatron 23:29, 26 June 2006 (UTC)

I don't forget gravitoelectrodynamics [7]--Iantresman 23:46, 26 June 2006 (UTC)
That's not really related. These three are all involved with electrically conducting fluids. — Omegatron 23:56, 26 June 2006 (UTC)

## Image on the MHD page

I think a picture without a scale and a legend (what is plotted?) is really not something that should be on wikipedia USferdinand 21:38, 16 January 2007 (UTC)

## Ideal MHD equations

I think a form of the ideal MHD equations should be on the MHD page. The references to the single equation pages is confusing. In fact, the momentum equation page does not have the differential equation, and the Ampere's Law page only refers to the integrated form of the equation. I am fine with the Priest equations even though I prefer the divergenceless form of the MHD equations.

${\displaystyle {\partial \rho \over \partial t}+\nabla \cdot (\rho \mathbf {u} )=0}$

${\displaystyle {\partial \rho \mathbf {u} \over \partial t}+\nabla \cdot (\rho \mathbf {u} \mathbf {u} +(p+{B^{2} \over 8\pi })\mathbf {I} -{\mathbf {B} \mathbf {B} \over 4\pi })=\mathbf {F} }$

${\displaystyle {\partial \mathbf {B} \over \partial t}+\nabla \cdot (\mathbf {u} \mathbf {B} -\mathbf {B} \mathbf {u} )=0}$

where ${\displaystyle \rho }$ is density, t is time, B is the magnetic field, u is fluid velocity, and F is the forces by unit volume (such as ${\displaystyle \rho \mathbf {g} }$ for the gravity).

Also a reference to the divergenceless nature of B should be added. A entry on numerical MHD (8-wave formulation) is, in my opinion, needed. USferdinand 21:54, 16 January 2007 (UTC)

Comment from another person: I concur that these equations should be on the MHD page. Also, the third equation above is commonly referred to as "the induction equation", not Ampere's Law; it is derived from Faraday's Law. Ampere's Law does not specify the time dependence of the magnetic field in terms of the other variables, which is necessary to describe the evolution of the full system. --Brianwelsch (talk) 02:55, 14 May 2010 (UTC)

I agree that these equations should be on this page as well. Preferably in SI units, and I'd suggest an adiabatic equation of state (no thermal conduction). Freidberg's Ideal MHD book has them in the appropriate forms. I would say also that avoiding dyadic tensors as much as possible is probably best since the conventions among plasma physicists aren't always used in other fields. Maybe I'll put them up, one of these months. Spacehippy (talk) 05:22, 25 March 2011 (UTC)

I just added the ideal MHD equations from Ideal Magnetohydrodynamics by Jeffrey P. Freidberg. The style and explanation are not quite there yet, so some expansion and revisions are still needed. I should be able to come back to this soon. Spacehippy (talk) 23:08, 25 March 2011 (UTC)

I would like to list the equations all together in a (1) ... (6) style (compare german wiki). Any objections? Skangaroo (talk) 14:48, 27 April 2015 (UTC)

## References

I erased the reference to "Magnetohydrodynamics (MHD)": - I) Its author has poor credentials in the field: a search for ("Petit,JP" MHD) by Google Scholar yields a ten of answers with only 3 citations in all (whereas a same search for the other authors quoted in the list of references typically yields hundreds of citations). - II) The scope of the referenced article is very specific, limited to shock wave anihilation by lorentz force field. —Preceding unsigned comment added by 137.138.5.237 (talk) 11:18, 7 August 2008 (UTC)

## Question about the text at Hall MHD

I looked through the page and I found the following statement at Hall MHD which I could not really understand: The most important difference is that in the absence of field line breaking, the magnetic field is tied to the electrons and not to the bulk fluid. I guess someone either wanted to talk about reconnection ("breaking" of field lines) or is talking about the slowing down ("braking" of the field lines). Anyway, can the person who wrote this make a better statement? Tusenfem (talk) 18:21, 5 February 2009 (UTC)

Two-fluid MHD and Hall MHD are actually very similar, and the terms are sometimes used interchangeably. Extended MHD and collisionless MHD are also related to each other and Two-fluid/Hall MHD. A few of these sections should probably be combined. Spacehippy (talk) 05:27, 25 March 2011 (UTC)

## Busted references

Hi, I just noticed footnote number 7 has linkrotted. Not sure what the original paper was being referenced. —Preceding unsigned comment added by 76.118.178.33 (talk) 01:32, 1 December 2009 (UTC)

Fixed it. --Art Carlson (talk) 09:48, 1 December 2009 (UTC)

## What's the point of Fig. 1?

It is beautiful, but neither cited nor described. Also I suspect it is fundamentally irrelevant as a tutorial guide, since it is an MHD simulation of a collisionless plasma. Maybe such a thing is useful in some practical sense, but it would be wrong to give the impression that such a plasma should be approached in this manner as a matter of principle. —Preceding unsigned comment added by Hugh Hudson (talkcontribs) 13:49, 21 April 2010 (UTC)

## I was planning to rearrange some stuff

- The history section needs to go near the top. It will improve the flow of the article.
- I was planning to make some additions to the geophysics section.

Please let me know if the changes are alright. I will check back soon. ShashankSawant (talk) 16:55, 23 April 2011 (UTC)

MAGNETO-HYDRO-DYNAMIC (MHD) POWER GENERATION

1 INTRODUCTION In magneto hydrodynamic power generation heat directly covered into electrical energy. The basic principle of MHD generation is the same as that of conventional electrical generator i.e. the motion of a conductor through a magnetic field induces an e.m.f. in it. In steam power plant the heat released by the fuel is converted into mechanical energy by means of a thermo-cycle and mechanical energy is then used to derive the electric generator. Thus two stages of energy conversion are involved in which the heat to mechanical energy conversion has inherently very low efficiency. Also, the rotating machine has its associated losses and maintenance problem. In MHD generation, electrical energy is directly generated from hot combustion gases produced by the combustion of the fuel without moving parts.MHD generator is a heat engine operating on a turbine cycle and transforming the internal energy of gas directly into electrical energy. So an MHD generator is a device for converting heat energy of a fuel directly into electrical energy without a conventional electric generator.

   In an MHD generator, electrically conducting gas at a very high temperature is passed at high velocity through a strong magnetic field at right angles to the direction of flow, thereby generating electrical energy.  The energy is then collected from stationary electrodes placed on the opposite sides of channel as shown in Fig.1. .  The current so obtained is direct is direct current dc which can be converted into a.c. by using an inverter.

Figure 1


In this method ionized gas is produced by heating the gas to a high temperature. On heating of a gas, the outer electrons escape out from its atoms or molecules. The particles acquire an electric charge and the gases passes into the state of plasma. However, to achieve thermal ionization of products of combustion of fossil fuel inert gases, extremely high temperatures are necessary. Air becomes highly ionized at temperature of 5000oC. To have a reasonable value of electrical conductivity of gases at temperature around 2000oK to 3000oK by reasonable ionization, the gases are seeded with additives of easily ionizing materials (alkali metals) such as cesium or potassium.

2 WORKING PRINCIPLE OF MHD POWER GENERATION

             In MHD power generation conversion process depends upon Faraday’s low of electromagnetic induction, which states that when a conductor and a magnetic field move relative to each other, a voltage is induced in the conductor.  This induced voltage produces an electric current.  The conductor may be solid, liquid or gas. In MHD generator solid conductors are replaced by hot ionized gas.  The hot ionized gas (3000oC) is passed through the MHD duct across which a strong magnetic field is applied.  Since the gases are hot and ionized they form an electrically conducting medium moving in a magnetic field, thus a voltage is generated.  The power generated by MHD generator is in the direct current form.  Now if the electrodes are placed in a suitable position then generated current can be extracted.

Figure 2


Consider a particle, having a charge q moving towards right with velocity v, and a perpendicular magnetic field with flux density B is applied. A magnetic force F acts on the charged particle and given by

                 =q ( x )                                                                                          ……. (1.1)


Now, particle is replaced by ionized gas molecules, moving with velocity V, the positive ions would be accelerated towards plate P1 and negative ions would be accelerated towards plate P2. If the plates are connected through a resistance a current would flow through resistance. Thus, mechanical energy is converted into electrical energy. If an electric field E is also present then equation (1.1) becomes

                   = q {( + ) x  }                                                                              …. (1.2)

In MHD generator, the velocity   is the vector sum of gas velocity V are particle drift velocity u.  Therefore,  =  +


Then = q (E + x + x ) .... (1.3) Let E + x =E’ then = q (E’+ x ) …….. (1.4)

                                            Figure 3


Consider the Fig .2 the movement of gas in x direction, magnetic field B is in y direction and force on the particle in z direction. When the current I is flowing through load resistance RL, then electric intensity between the plates is = - ……. (1.5) Where V is the voltage across load RL and‘d’ is the distance between the plates. Total electric field ’Z = Z +B ’Z = - + V ’Z = (BVd – V) ……. (1.6)

The electromagnetic field EZ and B acting on the moving gas produce the same force on the ions as the electromagnetic field E’Z and B produce on a gas with zero average velocity. Open circuit voltage EO=BVd …….. (1.7) If Rg is the internal resistance of the generator, then maximum power output is obtained when Rg= R¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬L P = E0I =IR¬g I= I2Rg …..(1.8)

I =

P= Rg

Put Rg = RL then

           Pmax   =                                                                                               …..(1.9)


Also, Rg = …..(1.10)

Where: σ= Conductivity of gas

                                A=       Area of the plate


Then from equation (1.7) and (1.10)

           Pmax    =                        ...…. (1.11)


Maximum power per unit volume = …… (1.12)

Also, put the value of Eo from equation (1.7) in (1.9)

Pmax = …... (1.13)

MHD system is reversible process. If instead of resistance an emf greater that Eo is applied (when the switch is at position 1) in opposite to the direction of the flow of above current, energy would be supplied to the gas, the particles of the gas would be accelerated. So, the rejected gas is at a higher velocity than the inlet gas. The reaction forces push the MHD engine in negative x direction. Now the electrical energy is converted into mechanical energy

       3    MHD SYSTEMS


Magneto hydrodynamic conversion systems can operate in either open or closed cycles. In an open cycle system, the working fluid is used on the once through basis. The working fluid after generating electrical energy is discharged to the atmosphere through a stack. In the closed cycle, system the working fluid is continuously recalculated; however, the discharged working fluid is reheated and returned to the converter. In an open cycle system the working fluid is air. In closed cycle systems helium or argon is used as the working fluid. In open-cycle systems, the hot combustion gases offer seeding can be used directly as the working fluid, in closed cycle system helium or argon is used as the working fluid. In open-cycle systems, the hot combustion gases offer seeding, can be used directly as the working fluid, in closed cycle systems, however, heat is transferred from the combustion gases to the working fluid by means of a heat exchanger. A higher working temperature and a better thermal efficiency are thus possible in open cycles, provided suitable construction materials are available Thus the MHD systems can be classified broadly as follows:- 1) Open cycle systems. 2) Closed cycle systems. This may be further sub classified as : (i) Seeded inert gas systems, and (ii) Liquid metal systems These are described in the following sections. 3.1 OPEN-CYCLE SYSTEMS

              The arrangement of the systems is shown schematically in Fig (3).  In this system, fuel used may be oil through an oil tank or gasified coal through a coal    gasification plant.  The hot gases from combustor is ten seeded with a small amount of an ionized alkali metal (cesium or potassium), to increase the electrical conductivity of the gas. The seed material, generally potassium carbonate, is injected into the combustion chamber; the potassium is then ionized by the hot combustion gases at temperatures of roughly (2300 to 27000 C)
To attain such high temperatures, the compressed air used to burn the coal (or other fuel) in the combustion chamber, must be preheated to at least 1100oC.  A lower preheat temperature would be adequate if the air were enriched in oxygen. An alternative is to use compressed oxygen alone for combustion of the fuel, little or no preheating is then required

Figure 4 Schematic of an open cycle MHD Generator

The additional cost of the oxygen might be balanced by the savings on the preheated.  The hot, pressurized working fluid leaving the combustor flows through a convergent-divergent nozzle similar to a rocket nozzle. In passing through the nozzle, the random motion energy of the molecules in the hot gas is largely converted into directed, mass motion energy.  Thus, the gas emerges from the nozzle and enters the MHD generator unit at a high velocity.  The MHD generator is a divergent channel (or duct) made of a heat-resistant alloy (e.g.Inconel) with external water cooling.  The hot gas expands through the rocket like generator surrounded by powerful magnet.  During the motion of the gas the positive and negative ions move to the electrodes and constitute an electric current. The magnetic field direction, which is at right angles to the fluid flow, would be perpendicular to the plane of paper.  A number of oppositely located electrode pairs are inserted in the channel to conduct the electric current generated to an external load.  The electrodes pair may be connected in various ways (see below).  An MHD generator, unlike a conventional generator, produced direct current; this can be converted into commonly used alternating current by means of an inverter.


The arrangement of the electrode connection is determined by the need to reduce losses arising from the Hall Effect. By this effect, the magnetic field acts on the MHD- generated (Faraday) current and produces a voltage in the flow direction of the working fluid rather than at right angles to it. The resulting current in an external load is then called the Hall current Various electrode connection schemes have been proposed to utilize the Faraday current while minimizing the Hall current. A better, but more complicated, alternative is to connect each electrode pair across a separate load, as in Fig (4 ).

Figure 5 MHD electrode connections to minimize Hall current

 Another possibility is to utilize the Hall current only; each electrode pair is short-circulated outside the generator, and the load is connected between the electrodes at the two ends of the MHD generator (Fig 5   )

Figure 6 Use of Hall current in MHD generator


As the working fluid travels along the MHD generator and its energy is converted into electricity, its temperature falls. When the gas temperature reaches about 19000 C, the extent of ionization of the p potassium is insufficient to maintain an adequate electrical conductivity. This places a lower limit on the useful operating temperature of the MHD system. The large residual heat available from the hot discharge working gas can then be utilized in several ways. For example, it conserves to preheat the combustion air by way of a heat exchanger similar to the regenerator in a gas turbine. At this stage, some 25 to 35 percent of the heat energy in the working fluid should have been converted into electrical energy. The still hot gas leaving the air preheated would be used in waste heat (heat exchanger) boiler to produce steam for operating a turbine generator. In this way, another 25 to 30 percent of the initial heat should be recovered as electrical energy in combined cycle system. The seed material is recovered for successive use in seed recovery apparatus. Prior to the discharge of the working gas (as flue gas) from the steam boiler to the atmosphere the fly ash from the coal fuel must be removed. However, instead of discharging the flyash, as is usually done, it may have to be treated for recovery of the seed material which is mixed with ash. Unless the sulfur in the coal has been removed (i.e. in a fluidized bed combustor), the original potassium carbonate seed will have been converted into potassium sulphate. This must be extracted from the flyash and reconverted by chemical reactions into potassium carbonate. The removal of residual sulfur by the potassium carbonates seed eliminates need for desulfurization of the flue gas, but nitrogen oxides are not removed. When oxygen alone is used for combustion of the coal (or other fossil fuel), the problem of nitrogen oxide formation does not arise. However, if nitrogen (from air) is resent, the nitrogen oxide contents of the combustion gases will be high because of the required high temperature of the working fluid. Consequently, a controlled combustion procedure is used to reduce the nitrogen oxide level in the discharge flue gas. The air supplied to the combustion chamber is not sufficient to permit complete fuel burning, combustion of the unburned fuel gases is then completed by introducing additional air at a later stage, beyond the MHD generator. The lower combustion temperature is accompanied by a decrease in the nitrogen oxide concentration. For efficient practical realization an MHD system must have the following features; 1. Air super heating arrangement to heat the gas to around 25000C, (the inlet temperature of MHD is about 25000C), so that the electrical conductivity of the gas is increased. 2. The combustion chamber must have low heat losses. 3. Arrangement to add a low ionization potential seed material to the gas to increase its conductivity. 4. Water cooled but electrically insulating expanding duct with long life electrodes. 5. Seed recovery apparatus- necessary for both environmental and economic reasons.

        3.2.   Closed-cycle systems


Two general types of closed cycle MHD generators are being investigated. In one type, electrical conductivity is maintained in the working fluid by ionization of a seed material, as in open-cycle systems; and in the other, a liquid metal provides the conductivity. The carrier is usually a chemical inert gas, although a liquid carrier has been used with a liquid metal conductor. The working fluid is circulated in closed loop and is heated by the combustion gases using a heat exchanger. Hence, the heat sources and the working fluid are independent. The working fluid is helium or argon with cesium seeding 1. Seeded inert gas system. In a closed cycle system the carrier gas (argon/helium) operates in a form of Brayton cycle. The gas is compressed and heat is supplied by the source at essentially constant pressure; the compressed gas ten expands in the MHD generator and its pressure and temperature fall. After leaving the generator, heat is removed from the gas by a cooler, this is the heat rejection stage of the cycle. Finally the gas is recompressed and returned for reheating.

                                         Figure 7 A closed cycle MHD system


A closed cycle MHD system is shown in Fig (6). The complete system has three distinct but interlocking loops. On the left is the external heating loop. Coal is gasified and the gas (having a high peak value of about 5.35 MJ/Kg and at a temperature of about 5250C) is burnt in a combustor to provide heat. In the primary heat exchanger, is burnt in a combustor to provide heat. In the primary heat exchanger, this heat is transferred to a carrier gas argon/helium (working fluid) of the MHD cycle. The combustion products after passing through the air preheated (to recover a part of the heat of combustion products) and purifier (to remove harmful emissions) are discharged to atmosphere. Because the combustion system is separate from the working fluid, so also are the ash and flue gases. Hence, the problem of extracting the seed material from flyash does not arise. The flue gases are used to preheat the incoming combustion arise and then rerated for the flyash and sulpher-dioxide, removal, if necessary, prior to discharge through a stack to the atmosphere.

The loop in the centre is the MHD loop. The hot argon gas is seeded with cesium and resulting working fluid is passed through the MHD generator at high speeds. The D.C. power out of MHD generator is converted to A.C. by the inverter and is then fed into the grid.

The loop shown on the right hand side in figure is the steam loop for further recovery of the heat of working fluid and converting this heat into electrical energy in the diffuser the working fluid is slowed down to a low subsonic speed. Then hot fluid enters a secondary heat exchanger, which serves as a waste heat boiler to generate steam. This steam is partly utilized to drive a turbine generator and for driving a turbine which runs the argon (or helium) compressor. The output of the generator is also fed to the main grid. The working fluid is returned back to primary heat exchanger after passing through compressor and inters cooler.

A closed cycle system can provide more useful power conversion at lower temperature (around 19000 K as compared to 25000 K for open cycle system). The somewhat lower operating temperatures of a closed cycle, MHD converter than of an open cycle system have an advantage in permitting a wider choice of materials. On the other hand, the lower temperature of the working fluid also means a lower thermal efficiency. Furthermore temperatures in the combustion chamber are still high, and special construction materials are required for the primary heat exchanger. Moreover the working fluid must be kept absolutely pure. The electrical stability of the flow in the generator poses problems because the gas is subjected to electrical fields approaching breakdown conditions.

The closed cycle MHD using rare gases as working fluid is developed and it is the most promising system among all. Generally, the heat source used is gas cooled nuclear reactor. 2. Liquid Metal System. When a liquid metal provides the electrical conductivity, an inert gas (i.e. argon or helium) is a convenient carrier. The carrier gas is pressurized and heated by passage through a (primary) heat exchanger within the combustion chamber. The hot gas is then incorporated into the liquid metal, usually hot sodium, to form the working fluid. The latter then consists of gas bubbles uniformly dispersed in an approximately equal volume of liquid sodium

                                 Figure 8 Closed-cycle MHD Generator


The working fluid is introduced into the MHD generator through a nozzle in the usual ways; the carrier gas then provide the required high directed velocity of the electrical conductor ( i.e. the liquid metal) After passing through the generator, the liquid metal is separated from the carrier gas. Part of the heat remaining in the gas is transferred to water in a (secondary) heat exchanger to produce steam for operating a turbine generator. Finally the carrier gas is cooled, compressed, and returned to the combustion chamber for reheating and mixing with the recovered liquid metal. The working fluid temperature is usually around 8000, as the boiling point of the sodium, even under moderate pressure, is below 9000

The lower operating temperature ten another MHD conversion systems may be advantageous from the material standpoint, but the maximum thermal efficiency is lower. A possible compromise might be to use liquid lithium, with a boiling point near 13000C, as the electrical conductor. Lithium is much more expensive than sodium, but losses in a loosed system be small. The closed cycle liquid metal system has the basic advantage of high electrical conductivity. However, liquids being practically incompressible, high Velocities cannot be produced by expansion as in the case of gas. In order to achieve reasonable velocities, either in low efficiency jet pumps or a two-phase system with vapour bubbles can be used. Even though liquid metal are excellent conductors, their vapours are poor electrical conductors. Thus there are several partial problems which have to be solved before liquid metal MHD systems can be commercially exploited. These systems are also appropriate for being coupled to nuclear reactors and the temperature range of interest to the liquid meal MHD (8000K- 13000K) is similar to liquid metal fast breeder reactors.

A liquid metal MHD cycle is illustrated in Fig (9), in which liquid potassium after being heated in breeder reactor is passed through a nozzle to increase its velocity. The vapour formed due to nozzle action are separated in the separator and condensed and then pumped back to the reactor as shown. Then the liquid metal with high velocity attained is passed through MHD generator to produce D.C. power. The liquid potassium coming out to MHD generator is passed through the conventional stem plant, where in the heat exchanger the heat of liquid potassium is utilized to generate steam to run steam turbine generator.

                           Figure 9 Closed cycle MHD generator using liquid metal as
Working fluid coupled with steam generator


4 MHD Design Problems and Developments The experiments have been demonstrated for the scientific feasibility of MHD generation, but the efficiencies attained so far have been relatively low and the life of the equipment has been short. Some of the matters requiring resolution before MHD generation can become economically practical are outlined below.

The combustor, MHD-generator channel, electrodes, and air preheated are exposed to corrosive combustion gases at very high temperatures, materials must be developed to permit an adequate operating life for the components. The ash (or slag) residue from the burning coal is carried over with the combustion gases and tends to cause erosion of exposed surfaces. However, deposition of the slag on such surfaces may provide some protection. Another problem is separation of the seed material (as potassium sulfate) from the flyash and its reconversion into its original (carbonate) form.

The difficulties associated with slag and seed recovery can be eliminated by using a fuel gas derived from coal rather than coal itself, in the combustor (open cycle system). An ash free low heat value fuel gas, made from coal at a moderate cost and treated for sulfur removal would make a suitable fuel for MHD conversion combustion. Burning of gas in preheated air should provide adequate working fluid temperatures.

A more advanced concept is to use hydrogen gas made from coal and water. When this s burned in (compressed) oxygen, the product would be high temperature steam. After seeding and passage as working fluid through the MHD generator, the steam would be used to drive a turbine-generator, thus avoiding the need for a waste-heat boiler.

The power output of an MHD generator is theoretically proportional to the square of the magnetic field strength (Equation 12.6.17) hence a strong magnetic field is desirable. Conventional electro-magnets, in which the field is generated by direct current passing through water-cooled copper coils, have been used in MHD studies. Such magnets would not be partial for large scale MHD power generation because they would require very large current, will be necessary. Magnets of this type are being developed for use of MHD generators.

5 ADVANTAGES OF MHD POWER GENERSTION

MHD power generation offers several advantages over other conventional methods of power generation. Some of these are given below: 1. Since high temperatures are involved, operation efficiency is high. 2. No moving part, so more reliable 3. Lesser thermal pollution. 4. Conceptually such generators are simpler. 5. As there is no limitation to the size of the duct, so high capacity generators are possible. 6. The wall can be cooled below temperature of working gas. 7. Direct conversion of heat into electrical energy results in elimination of the gas turbine (compared with a gas turbine power plant) and both the boiler and turbine (compared with a conventional steam power plant) and thus is reduction of energy losses. 8. Ability of reaching the full power level instantly. 9. The more efficient heat utilization reduces the amount of heat discharged to environments and thus the cooling water requirements are reduced. 10. The capital costs of the MHD plants are estimated to be competitive with those of coal fired steam power plants. 11. The overall costs of the MHD power generation are also estimated to be lower (roughly 20%) than those of conventional power plants. This is because of higher efficiency of MHD power generation. 12. The reduced fuel consumption that is obtained because of higher efficiency or better fuel utilization, offer additional economic and social benefits and also lead to conservation of energy sources. 13. All kinds of heat sources such as coal, oil, gas, solar and nuclear can be used with MHD generators. 14. MHD generators have low specific weight, rapid start, high power density and compact. In spite of the several inherent advantages the MHD system has not been accepted commercially because numerous technological advancements are needed prior to its commercialization. Most of these are related to material problems caused by high temperature and highly corrosive and abrasive environment. The MHD channel operates under extreme conditions of temperature. Development of MHD programmes has been undertaken by different countries during the last two decades. In India also considerable studies have been carried out in this field by a team of scientists under the National Council of Science and Technology. The department of Science and Technology of Govt. of India has sponsored research and development programmes on coal based MHD power generation. Bhabha Atomic Research Centre in collaboration with Bharat Heavy Electricals Ltd and Institute of High Temperature Russia is also executing Research and Development programmes in this field Russia has constructed pilot plant of 75 MW installed capacity, 25 MW is provided by the MHD Generator. The fuel used in natural gas. The plant is designated as “U-25”. A 5-15 MW thermal input pilot plant is being setup in India at Tiruchirapalli. This plant uses fluidized bed combustion. Major countries involved with MHD activities are Russia, USA, Japan, Australia, China, India, Italy, Israel, Poland etc. Besides the use of MHD system for commercial electrical power generation, it has got other special uses. A Major effort was made in USA to use MHD as the conversion system in a nuclear electrical system for space craft’s. MHD conversion has also been considered for ship propulsion, air born applications, hypersonic wind tunnel experiments and for many other defense applications. — Preceding unsigned comment added by Gaurav1021 (talkcontribs) 08:52, 27 June 2011 (UTC)

## Magnetic Drug Targeting

Ferrofluids have nothing to do with MHD, so it's a bad example of applications for MHD. — Preceding unsigned comment added by 82.130.106.41 (talk) 15:19, 20 October 2011 (UTC)

## Engineering -- controversial items

Regarding these two sentences in the "Engineering" section:

  Two widely-reported new applications for MHD drives are the hydrino reactor developed by Dr. Randell Mills of BlackLight Power in Cranbury, N.J., and the Energy Catalyzer, or E-Cat, developed by electrical engineer Andrea Rossi of Miami, Fla. Both of these inventors' devices can produce enormous amounts of heat that theoretically can then be converted to electricity by a MHD drive.


I'm actually hoping that such LENR devices will eventually be shown to be revolutionary energy devices, but the present sentences appear to state, without reservation, that these devices "can produce enormous amounts of heat." In fact, (as of this writing) such claims are quite controversial.

Also, the two sentences appear just before a sentence regarding coal-powered MHD abrasion problems -- seems out of place to me.

Dfgriggs (talk) 14:50, 26 March 2014 (UTC)

## How can a plasma be a fluid?

Consider:

... is the study of the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes. ...

If the four states of matter are solid, fluid, gas and plasma, why are plasmas considered fluids? --Mortense (talk) 16:16, 9 July 2014 (UTC)

The four states of matter are solid, liquid... --Musaran (talk) 21:16, 23 July 2014 (UTC)
The four states of matter are solid, liquid, gas, and plasma. Fluid is a broader concept that encompasses anything that can flow. That usually includes liquid, but in aerodynamics gas is a fluid, in geophysics the solid parts of the earth can behave as fluids over sufficiently long period of time. Zyxwv99 (talk) 21:59, 23 July 2014 (UTC)

## Define J

Isn't J just ρ v ? If so, this should be said when J is intrduced. 89.217.22.3 (talk) 16:13, 8 November 2014 (UTC)

## MHD sensor

Principle of MHD sensor for angular velocity measurement

If {{Sensors}} is not directly related to Magnetohydrodynamics why is MHD sensor, which redirects to Magnetohydrodynamics, included on {{Sensors}}? Peter Horn User talk 03:04, 24 October 2016 (UTC)

MHD sensor is listed as an navigation instrument. Peter Horn User talk 03:20, 24 October 2016 (UTC)
Okay, I see. Isambard Kingdom (talk) 03:24, 24 October 2016 (UTC)
Image added for good measure. Peter Horn User talk 11:37, 24 October 2016 (UTC)

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