Questions tagged [magnetohydrodynamics]
Magnetohydrodynamics or MHD is a magnetized fluid approximation to the kinetic theory describing a gas composed of charged particles.
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Tuning Drifts in Tokamaks
If we managed to make over 50 % of the drifting of the guiding centers of the gyrating particles inside a tokamak to occur into the inwards direction, away from the tokamak walls, would that allow us ...
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Question about code units and physical units (hydrodynamics simulations)
I'm working on a code that implements smoothed particle hydrodynamics (SPH) method for solving the equations of magnetohydrodynamics (MHD) with self-gravity.
In research papers regarding existing ...
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1answer
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What exactly sets the scale in Fusion power plants?
In fusion power plants, larger devices are said to achieve fusion more easily, next step tokamaks like DEMO are even larger than ITER. In a quantitative way, what exactly isn't scale invariant in a ...
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Magnetic cage for keeping plasma around itself
Let's assume that we have an object in vacuum, venting hydrogen plasma around itself. This object has a powerful internal electrical source, connected to a cage of superconducting wire around it, in ...
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Frozen in Magnetic Field Lines
A perfectly conducting fluid undergoes an axisymmetric motion and contains an azimuthal magnetic field $\textbf{B}_θ$ . Show that $ \dfrac{B_θ}{r}$ is conserved
by each fluid element.
Question from ...
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1answer
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Linearization of MHD equations for a cold plasma and low frequencies
I'm trying to convert the next equations for a cold plasma (consider $P=0$ the pressure), for low frequencies and ignoring dissipative effects:
$$\rho \left(\left(\frac{\partial \vec{v} }{\partial t}\...
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1answer
55 views
How to derive Walen's equation? [closed]
This is perhaps a simple math problem, therefore no books ever given detail calculation. Could someone help to give a proof?
We have continuity eqution as
$\frac{\partial\rho}{\partial t} = -\rho\...
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3answers
174 views
Is it possible to have a liquid plasma?
Plasmas are generally thought of an ionized gases, which are conductive and can respond to electric and magnetic fields. However, I was just wondering if it is possible (in theory or in practice) to ...
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Ideal MHD stability with a Fourier analyzed perturbation
I'm learning through the basics of ideal MHD instabilities and the textbook (Friedberg, Plasma Physics and Fusion Energy, 12.4-12.6) writes the linearized momentum equation in terms of the ...
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1answer
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Difference between MHD turbulance and Alfvenic turbulence?
I'm quiet confused in reading literatures involved MHD turbulance and Alfvenic turbulence, it seems they are pointing to the same notion in most of the content. Please explain the difference of them?
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48 views
Will salt water spin if put in place of rotor in induction motor?
If I have a bottle of salt water and put it in place of rotor in induction motor, will the salt water spin ? Why / why not ?
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2answers
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Simplification of Maxwell equations assuming that the induced fields are much weaker than the applied fields
In cases where induced fields are much smaller than the applied fields, are there any terms in the Maxwell equations that can be neglected? I tried to do a simple scaling analysis to come up with a ...
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Magnetic flux ropes - are they stable for topological reasons like fluxon/Abrikosov vortex?
In images of sun's corona there are clear bright lines - nearly 1D stable structures interpreted as magnetic flux ropes, often suggested to have a topological nature e.g. (source):
They have some ...
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What characteristic length should I use to calculate the magnetic Reynolds number?
I am trying to find the braking torque in an eddy current braking system for the setup shown below. I want to consider skin effect for high speed applications. My approach so far has been as follows:
...
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Electric field in frame corotating with sun
I am studying this paper on the solar wind for a class on MHD, but I am perplexed by the line that precedes equation (5):
"
But in a perfectly conducting fluid ${\bf v}$ is parallel to ${\bf B}$ in ...
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Resources in magnetized accretion disk
I'm looking for some resources in magnetized accretion disk. Preferably a book or an article review that starts with un-magnetized accretion disk theory.
While I have some familiarity with accretion ...
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1answer
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What's the timescale for the formation of a coronal mass ejection?
How quickly does the sun form and release a coronal mass ejection?
If we were watching the right part of the sun closely, how long would it take us to go from "nothing seems to be happening" to "...
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1answer
148 views
What is the physical basis for Pedersen and Hall currents in an atmosphere?
There are three components of a conductivity tensor in atmospheric electrodynamics: the parallel conductivity along the direction of the magnetic field, the Pedersen conductivity (in the direction of ...
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138 views
Can't prove that Fast Magnetosonic Wave's proper speed is given by the following formula
So, suppose a magnetosonic disturbance, it is proven that (You can also see it in Richard Fitzpatrick's Plasma Physics online text), that the Fast Magnetosonic Wave is equal to
\begin{equation}
\dfrac{...
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What is the shape of Basset forces?
Does anybody here know something about Basset force?
Just on the Wikipedia entry I found that,
In a body submerged in a fluid, unsteady forces due to acceleration of that body with respect to the ...
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What is the most general form of the momentum equation in MHD?
The momentum equation for an electrically neutral, conducting, nonpermeable fluid has the form (Jackson, 1962):
$$
\rho \frac{d \mathbf v}{d t} = - \nabla p + \mathbf J \times \mathbf B + \mathbf F_v ...
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2answers
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How many amperes are flowing in the Earth's core?
To my surprise I couldn't find any estimate on how many amperes of electrical current are flowing in total in the Earth's core to be able to create the magnetic field strength $5\cdot 10^{-5}$ T on it'...
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How wide would the current be?
I recently saw the sketch of the magnetohydrodynamic drive of the YAMATO 1 and it occurs to me that one of my teacher has told me the current would, even when traveling in a plane, stay in a line and ...
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How do I estimate the probability of a Carrington-level coronal mass ejection (CME) hitting the Earth?
I have seen some material which estimates the probability of Earth being struck by a Carrington-level CME over some time into the future. These estimates seem to be derived from historical data of CME ...
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1answer
221 views
Rigorous derivation of Faraday's induction
When deriving Faraday's law of induction, one needs to calculate the time derivative of the flux $\Phi = \int_{S(t)} \vec{B} \cdot \vec{n} \;dS$, where $S(t)$ is the surface over which we define this ...
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The production of cosmic jets [duplicate]
For cosmic jets produced in gamma ray bursts or quasars, I've read that you have to assume a "Force-free magnetosphere" in order to explain these phenomena through electromagnetism. From my ...
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Under which angles does the solar wind leave the Sun and arrive at it's desination?
As the sun emits charged particles outwards, those particles will travel long distances to reach far away points in the solar system. They could be influenced by other bodies, electromagnetic fields, ...
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2answers
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Can localized fluid perturbations be accelerated by pressure gradients?
I would like to know if there are any examples in fluid dynamics (or continuum dynamics) of small perturbations (or waves, solitons, or other "localized" solutions of the fluid) being accelerated in ...
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Does a conservative form of the Chew-Goldberger-Low MHD equations exist?
I wonder if is it possible to bring Chew-Goldberger-Low MHD equations to a conservative form? Conservative form of the system of equations of ideal MHD with isotropic pressure is well known and can be ...
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3answers
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Why do charged particles follow magnetic field lines?
This may seem like a dumb question, but I can't think of the answer. The context I am curious about is the solar wind. Specifically particles flowing out of coronal holes and following the magnetic ...
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Dependence of the magneto-rotational instability (MRI) on thermal relaxation?
The MRI is the most efficient driver of turbulence in accretion discs (as measured by the effective scalar stress). The magnetic field, being properly coupled to the gas (weak coupling), connects the ...
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Geometry of magnetic field lines in plasmas/MHD
So I'm trying to gain an intuitive grasp of plasmas and magnetohydrodynamics.
There's a couple of questions I have.
What does it means magnetic field lines are frozen into "plasmas"? Is it that ...
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3answers
479 views
Is magnetic reconnection reconcilable with magnetic field lines neither starting nor ending?
According to Maxwell's equations, magnetic fields are divergence-free: $\nabla \cdot \mathbf{B} = 0$. If I understand this correctly, this means that magnetic field lines do not start or end. How can ...
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What is a weak solution of the MHD equations?
Many papers concerning solutions to the magnetohydrodynamics (MHD) equations (eg. Osher, 1984) say that one is generally interested in finding weak solutions.
Sometimes they are even called global ...
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Cosmology: collisionless vs collisional fluids?
I try to understand the difference between collisionless and collisional fluids in cosmology. My first question is the following.
In the context of FLRW cosmology, we suppose that the Universe can ...
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What causes the twisting of flux loops, leading to coronal mass ejections?
I understand that the loop twisting is the ultimate originator of the CMEs but what causes this twisting? The expansion of the loops is caused by a magnetic pressure differential between the top and ...
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3answers
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What is a magnetic flux rope and how does it differ from magnetic flux tubes?
I am currently taking a course on solar physics and it appears the terminology in solar physics is either needlessly verbose or I am just missing something. What is a flux rope and what is a flux ...
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What's the difference between “Ohmic dissipation”, “Joule heating”, “ion drag” and “resistive heating”?
The following terms are sometimes used to refer to ... more or less ... the same thing by different people and in different contexts (electronic circuits vs. plasma physics, etc.):
Ohmic dissipation
...
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How is the MHD magnetic field time evolution equation transformed to the vector potential time evolution equation?
Starting from the time evolution equation of the magnetic field for incompressible MHD (magnetohydrodynamics)
$$\frac{\partial \vec{B}}{\partial t} = \nabla \times (\vec{v} \times \vec{B}) + \frac{\...
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1answer
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ϕ-component of equation of moition: proving a relationship [closed]
I have the following velocity vector (in spherical polars):
\begin{equation}
\textbf{v} = u \hat{\textbf{r}} + v_{\phi}\hat{\boldsymbol\phi}
\end{equation}
Where $u(r) = u$ and $v_{\phi} (r) = v_{\phi}...
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0answers
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Faraday induction for seawater flow system
Magnetic flow meters use Faraday induction to produce a voltage across a channel in which a conductive fluid is flowing. The basic relationship (using convenient geometry so that the cross products ...
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Interpretation of Mass Continuity Equation in MHD [duplicate]
I'm writing up my final-year dissertation and I'm required to give, as part of the introduction, an analysis of all the equations (and their terms) of which I use. Embarrassingly, whilst of course ...
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1answer
199 views
Why doesn't magnetic forces on current carrying wire depends on relative velocity?
We know that magnetic field arises due to relative velocity of charged particle . Electrons in wire move at very slow drift velocity but relativistic variation of magnetic field doesn't seem to apply ...
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Alternative air transportation and magneto-aerodynamics
Firstly, I am not a big fan of UFOs, however, a flying saucer makes me think if is there another, comparatively agile way to travel through the air without jets, turbines or propellers (balloons are ...
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158 views
Magnetic fields in plasma at equilibrium
I'm wondering if it is possible to have a plasma reach an equilibrium state where no more entropy is produced but it still has frozen-in magnetic field lines. The problem is the field lines have a ...
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How to solve the following set of equations (magnetohydrodynamics with anomaly term)?
Let's have system of equations:
$$
\tag 1 [\nabla \times \mathbf E^{(1)}(\mathbf r , t) ] = -\frac{\partial \mathbf B^{(1)}(\mathbf r , t)}{\partial t} ,
$$
$$
\tag 2 [\nabla \times \mathbf B^{(1)}(\...
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1answer
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Electrical Resistance of Spherical, Contacting Colloids
So, I work a lot with Magneto-Rheological (MR) fluids - which are essentially electrolyte solutions with suspended, paramagnetic colloids/particles. Once a magnetic field is applied to such a fluid, ...
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Why do we deal only with large scale magnetic fields in astrophysics, and not electric fields?
In astrophysics there is a lot going on about strong, large scale magnetic fields: in stars (prominences), magnetic dynamos, compact accretors collimating jets, etc. There's even a special ...
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MHD Flow in a channel with and external B field and circuitry determining E. Different circuits and Ohm's law
I was wondering if someone can explain why E is the way it is in cases 2,3,4 in page 9 of these notes ?
In case 2 "Short Circuit", do I just have to assume that for a perfect conductor E = 0 for ...
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Why does this equation refer to magnetic tension?
The force density in a plasma, according to MHD, is $$ \mathbf{F} = -\nabla P -\nabla(\frac{B^2}{2\mu_0}) + \frac{1}{\mu_0}(\mathbf{B}\cdot\nabla)\mathbf{B} $$
where first term is the thermal ...
