# Magnetohydrodynamics

Benchmark Problem for MHD?
I am looking for a benchmark problem for MagnetoHydroDynamics to validate a numerical code.
Nishant Narechania · University of Michigan
Hello Amin, you are welcome. But, I do not have knowledge of MHD in molten metals or arc plasma. I would know more about space plasma applications.
Any suggestions for the boundary conditions of the magnetic field equation in MHD?
There is an equation: dB/dt - curl( v x B) = - curl ( L curl B) for the magnetic field B in MagnetoHydroDynamic domains. For the boundary conditions we have curl B = -mu j (j is the electric current density)
Abdellah Kharicha · Montanuniversität Leoben
no references no text only experience. Well you can find plenty of references in the field of Astrophysical MHD.
What is the relation for entrance length of magnetohydrodynamic flow for rectangular channels?
I need some help to find out empirical relation for entrance length in channel flow in terms of Hartmann number and Reynolds number. As far as I know it is proportional to Ha/Re. I think the following paper has given some relation about this: W. T. SNYDER. "Magnetohydrodynamic flow in the entrance region of a parallel-plate channel." AIAA Journal, Vol. 3.
Janis Priede · Coventry University
In that case you could just take a developed flow profile a few 'diameters' upstream from the bend and forget about the entrance length...
What is the advantage of Hamiltonian mechanics in describing transport and turbulence in magnetized plasma?
I need to know in detail why we prefer to use Hamiltonian mechanics for transport and turbulence in the confined hot plasma rather than using the concept of anomalous diffusion.
Vasily Erofeev · Russian Academy of Sciences
Difference between B,H and M in magnetics
I am somewhat confused with what is B, H and M in magnetism. Can someone explain their equivalence in terms of electrostatics Bio Savart law gives us B (which I suppose is magnetic field). But I have read in many places H is magnetics field and is defined as and we have relation as B=mu0*H where B is magnetic flux density. This is somewhat confusing. It would be really helpful if someone may explain the following case for the following terms magnetic field, magnetic field strength magnetic flux density and magnetization. Also how mu and mu0 are related in each aspect Consider a current carrying conductor in free vacuum. Then at any point Pin free space some B will be felt (I am not giving any name as I am not clear what exactly it is). Now suppose the space is not free space but some gas which poses some restriction to flow of magnetic field’s lines through it then if UI am correct, the magnetic field at same pointy will decrease. Is that factor of reduction mu (permeability of gas.
Daniel Baldomir · University of Santiago de Compostela
In Electrodynamics there are three antisymmetric tensors of second rank B,D and J which have only three independent components. Thus these components can be associated to the three components of one ordinary vector and this mathematical object is named pseudovector because it doesn't transform as one real vector. There are also two fundamenta vectors H and E for the magnetic and electric fields. These basic physical quantities may be defined in vacuum (i.e. without matter) and related with matter trough the quantities M and P which are also two antisymmetric tensors and which can be associated to vectors only for homogeneous and isotropic materials having magnetic or electric dipoles. For M it is possible to have spins instead of classical magnetic dipoles for obtaining magnetic order because it is well known that the Bohr-van Leeuwen forbids to have a spontaneous magnetization M as it is needed for explaining ferromagnetic or antiferromagnetic order. Thus M and P are physically different because there is not a concept as spin for the electric dipoles and therefore for the polarization P, but playing a similar role in classical electrodynamics for taking into account the magnetic or electric dipolar order. Finally we can see that the Lorentz force of electrodynamics use the electric vector field E and the pseudovector magnetic induction B. Therefore both quantities are associated in the same form as do the magnetic field H vector and the electric induction D pseudovector in the definitions of the electromagnetic fields in four dimensions. Two references for presenting this issue much deeper are: 1. J.D.Jackson, Classical Electrodynamics, John Wiley & Sons, third edition 2. D.Baldomir and P.Hammond, Geometry of Electromagnetic Systems, Clarendon Press, 1996.
Are solar/space physics in a mature state where all "easy" problems have been done? Are we reduced merely to reducing data and running models?
Current work in solar physics is dominated by data acquisition, reduction, and numerical modeling. Has the tool between the ears become less important than those catching photons, particles, and those that move electrons around on electrical devices in computers? Is the infrastructure now guiding our research, or are scientific questions guiding the infrastructure we have? To see how we might make real progress and avoid some potential traps in relying on external tools, it might be useful to compare thoughts on the major achievements, questions that have been answered in solar physics since, say 1900, and how these were achieved. I might start it off by saying that the development of the Saha equation allowed us to begin to understand solar spectra for the first time, in a quantitative fashion, for example.
Bo Thidé · Swedish Institute of Space Physics
According to Physics Nobel Laureate Steven Weinberg, physics is a science whose aim is "...not just to describe the world as we find it, but to explain — in terms of a few fundamental principles — why the world is the way it is." Physics adopts a hypothetic-deductive method where advancements are made by making a series of systematic experiments and/or observations of nature and then, after analysis and clever thinking, proposing new extensions or additions to the existing set of laws of physics. Based on these new laws, taken as postulates, we deduce hypotheses about new physical phenomena and make experiments/observations that either falsify or support these hypotheses. An example of this is the hypothesis of the existence of the Higgs particle, that was based on a hypothesis made by Phil Anderson on how EM waves/photons behave when they interact with plasma/plasmons. Anderson's hypothesis, that in turn was based on a hypothesis by Julian Schwinger about massive gauge bosons, could easily have been formulated by a space plasma physicist. According to Sir Rudolf Peierls, a new law/postulate of physics ‘...must firstly leave undisturbed the successes of earlier work and not upset the explanations of observations that had been used in support of earlier ideas. Secondly it must explain in a reasonable manner the new evidence which brought the previous ideas into doubt and which suggested the new hypothesis. And thirdly it must predict new phenomena or new relationships between different phenomena, which were not known or not clearly understood at the time when it was invented.’ Sadly, very little of this creativity seems to be present in current-day space physics.
• Philip G. Judge added an answer:
What does happen with the electric characteristics, when a battery is submitted to a high (time variable or not) magnetic field?
I know, that there are some effects related to magnetohydrodynamics and can change internal resistances, but I'd like to know more about this matter
Philip Judge · National Center for Atmospheric Research
If one considers a wet battery of the old fashioned type as a kind of plasma, with free ions in a background solution, then the addition of slowly varying magnetic fields to the battery will affect the resistance to current flow inside the battery itself, and thereby any external circuit you connect it to. In this case a magnetic field parallel to the direction of normal current flow has no effect. But if you put a magnetic field across this direction it will increase the resistance according to the "magnetization", a parameter (omega*tau) which measures the ion gyrofrequency (omega) times the collision time of the ion with other ions and the solution (tau). The resistance in the direction perpendicular to the magnetic field will go something like (1 + omega*tau)^2. In the liquid state I would expect that tau is very small such that omega*tau is << 1 for most magnetic fields experience on earth. Thus, the magnetic field will have little influence since the ion dynamics is controlled by collisions and not magnetic fields. The clearest explanation of the physics of collisional plasmas is Braginskii's article from 1965 Rev Plasma Phys. 1, p. 205. I hope this helps
• Andrea Di Vita added an answer:
Do turbulent magnetic diffusivities in highly conducting plasmas have a sound physical basis?
In solar physics, it is customary to use magnetic diffusivities which are orders of magnitude larger than kinetic values. But Parker (Space Sci. Rev. 144, 15 2009) points to fundamental difficulties with this concept: the back reaction of the Lorentz force on the plasma frozen to the field on scales above the real diffusion scale can stop the motion of fields through conducting plasma before it reaches the diffusion scale. Under what conditions might a "turbulent diffusivity" be a well grounded concept for highly conducting plasmas, like those in the Sun?
Andrea Di Vita · Università degli Studi di Genova
Dear Bian, I have been impressed by your words 'independent of the resistivity '. I wonder if the critical size of physically relevant regions (e.g. near X-points) can be comparable either to ion Larmor size or to collisionless ion skin depth. In both cases MHD fails, and is to replaced by Hall MHD. The relevance of electrical resistivity to the estimate of the current thickness becomes questionable.
How about the magnétostrophic approximation?
I'm working on the dynamo effect action on the Earth's inner core. When we wrote the equations (Navier stokes and induction equation) and we took the asymptotic case we found an equilibrium between the magnetic forces, Coriolis and the gradient of pressure. My question is: is there a unique solution for this case, and where can I find it?
Abdessamed Medelfef · University of Science and Technology Houari Boumediene
Thanx for your help
In a plasma, is it correct to assume elctrostatics and formulate a debye sphere?
Plasma contains many charged particles at very high temperatures. So, the different particles produce electro-magnetic fields, which fall off rather slowly compared to the electrostatic fields and more effective. So, is it correct to assume electrostatics and formulate a debye sphere?
Johannes Gruenwald · Karl-Franzens-Universität Graz
Yes it is. If you can define a Debye length then you can find (per definition) a Debye sphere.
From frequency to k-space
If a satellite measures magnetic fluctuations, e.g. in the solar wind, taylors frozen in theorem is usually well satisfied (wave speed << plasma speed) and one can go instantly from freq. to k-space with the transformation k = (2 pi f) / (v sin(psi) ), where psi is the angle between plasma velocity and background magnetic field. So far so good. But how do you determine or at least approximate your trasnformation if taylors frozen in theorem is not that well satisfied? I wonder what happens if the plasma speed vpl is of the same order as alfven speen va (vpl~va). Lets say the fluctuations dB are much smaller than background field B, so that at least dva<<va. What possible interpretations are then possible for your measured P(f)? e.g.: We assume there are only alfven waves propagating parallel to the background field, then the sampling v=vpl+va. The k we see is then a mixture of k_parallel*sin(psi)+k_perp*cos(psi), where psi is the angle between v and B. Is that right? What other possibilities are there? How does that look like for kinetic alfven waves?
Yuriy Voitenko · Belgian Institute for Space Aeronomy
Whistlers have higher frequencies, so an interference of spatial and time variations is possible (both k and w can contribute to measured f). This should be checked using solar wind parameters in the Doppler-shifted whistler dispersion (which is equal to f). BTW I joint the RG network today, just accidentally :)
Why is Xe in the atmospheres of Earth and Mars much heavier than the solar Xe, but Kr in the atmospheres of the planets is similar to the solar Kr ?
The noble gas evidence in meteorites.
Johannes Gruenwald · Karl-Franzens-Universität Graz
Oh, then I misunderstood your question (and again learned something new) - thank you for the paper. :)
• Shailendhra Karthikeyan asked a question:
Is there anyone working on enhancement of heat transfer in liquid metal flows in the presence of magnetic field?
I am working on enhancement of heat transfer in laminar oscillatory flow of liquid metals under the influence of a uniform magnetic field. But, most of the works in the literature are on turbulent flow conditions as in the case of nuclear reactors.
• Charles E Seyler added an answer:
How to calculate the dependence of the tearing mode 'Delta' parameter on the mode frequency?
In tearing-mode theory, how to calculate the dependence of the 'Delta' parameter on the mode frequency in the resistive layer?
Charles Seyler · Cornell University
In resistive MHD without equilibrium flow the tearing mode is a purely growing mode and does not have a real frequency. The growth rate (imaginary frequency gamma) depends on delta-prime as gamma^(5/4). If electron inertia dominate resistivity the scaling is different and goes as delta-prime~gamma^(1/2).