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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Why is the electric field time independent in the induction equation of the magnetohydrodynamics?
Why does the induction equation of the magnetohydrodynamics assume the electric field $E$ is time $t$ independent or $\frac{\partial E}{\partial t}=0$?
Note: I am querying about the general case ...
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MHD plasma regime clarification
Could you give an intuition about why does MHD requires the following condition in time and spatial scales, please? Thanks.
At scales much larger than the mean free path and gyroradius, and time ...
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Perfect Conducting (PC) and Perfect Insulating (PI) boundary conditions for magnetic induction in MHD problems in cylindrical coordinates
I understand the computational implementation of the PC and PI bcs in cartesian case. In terms of the magnetic field components for PI, we have $B_x = B_y = B_z = 0$, and for PC, we have $B_x = \...
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Magnetic reconnection in MHD theory [closed]
What does the MHD theory predict when two regions with magnetic field of opposed polarization interact? When we take in account the resistivity then we can observe a rearrangement of the topology due ...
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Is it possible to sustain an net electric charge density in a moving conductor? (MHD application)
The conservation of electric charge, deduced from the divergence of the Maxwell-Ampère equation, takes the form:
$$ \nabla \cdot \textbf{J} = -\frac{\partial \rho_e}{\partial t}.$$
For low frequency ...
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Is it worth to study the "Membrane Paradigm" of black holes nowadays? [closed]
I'm very interested in the region near the outer event horizon and its magnetohydrodynamic enviroment physics. For instance, I'm beggining to study the Blandford-Znajek process, and subjects related. ...
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Why Euler equation in Ideal MHD is not identically zero?
In Ideal MHD, we assume the plasma to be force-free:
$$\vec{E} = - \frac{1}{c}\left(\vec{v}\times \vec{B}\right)$$
But the Euler equation of motion is written as:
$$\rho \frac{d\vec{u}}{dt} = \vec{j}\...
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Why do we need a symmetric matrix for the threshold current at a magnetic neutral point?
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I'm reviewing a paper for my final year BS project and I seem to be confused on a step that the author takes. The following part is from the paper itself.
"2.1. The Threshold Current.
From the ...
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Blandford-Znajek process - energy flow reverse and other questions
In the original BZ paper [1] from 1977, the authors invoke a number of facts and conclusions that I do not quite follow. In the hope that someone has read it and was able to grasp all the details, I ...
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Finding velocity field components from electric and magnetic field components in ideal MHD
How can I determine the components of the velocity field ($V_x, V_y, V_z$) using the components of the electric field $(E_x, E_y, E_z)$ and magnetic field $(B_x, B_y, B_z)$, assuming the ideal ...
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Why is it necessary to break conformal invariance of the electromagnetic action to generate seeds for primordial magnetogenesis?
A large number of mechanisms whereby magnetic fields are generated in the early universe involve the breaking of the conformal invariance of the electromagnetic action. Why is it so? What is the ...
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Magnetic pressure explanation and penetration depths
Can I get an explanation of what magnetic pressure is exactly in the context of MHD? From my simple understand, it's essentially just the force that magnetic field lines exert back onto a plasma that ...
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Derivation of pressure balance equation for a toroidal geometry [closed]
Derivation of pressure balance equation in toroidal geometry
$$
\boxed{
\frac{\mathrm{d}p}{\mathrm{d}r} + \frac{\mathrm{d}}{\mathrm{d}r} \left( \frac{B_{\phi}^2}{2\mu_0} \right) + \frac{B_{\theta}}{\...
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Why is electromotive force in magnetohydrodynamics a vector quantity?
In the mean-field dynamo theory in magnetohydrodynamics, I frequently came across a quantity;
$\langle v'\times B' \rangle$, which is termed as the mean electromotive force. I want to know that why is ...
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Gauge fixing in the magnetic induction equation
The magnetic induction equation for a fluid with zero resistivity may be written as
\begin{equation}
\frac{\partial \mathbf{B}}{\partial t} + \nabla \times (\mathbf{B} \times \mathbf{u}) = 0
\end{...
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Deriving a dispersion relation in Hall MHD for inhomogeneous plasmas
I'm trying to derive the dispersion relation of a drift wave in Hall MHD. The derivation is done in this paper (https://aip.scitation.org/doi/10.1063/1.859752)
The governing equations are something ...
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Determining parameters of magnetohydrodynamic plasma equations
For wide ranges of pressure and temperature, plasma can be described by magnetohydrodynamic (MHD) equations. These equations contains some parameters (resistivity, diffusivity, etc.). I am wondering ...
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Biermann Mechanism [closed]
Biermann mechanism says that due to different masses of electrons and protons, the motion of former leads to the latter. This effect produces non-zero circular currents which induce vertical magnetic ...
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Numerically computing induced magnetic field from current density
Let's say we have current density $J_i$ on a discretized grid with $(N_x \times N_y \times N_z)$ points. What is the best procedure to compute the induced magnetic field $(B_i)$ from the current ...
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Conservation of Momentum violation with Lorentz Force
Note: I am describing this question using cylindrical coordinates $\hat{r}$, $\hat{\theta}$, $\hat{z}$.
I've been looking into how you could slow down a plasma moving downstream in a pipe using ...
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Alfven velocity in space. Maybe too large?
I'm calculating the Alfven velocity in space plasma.
B = 4.2 nT (nanoTesla)
...
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Fluid mechanics - Particular derivative
I've got a problem in MHD where I need to develop the following derivative (where $\vec{B}$ is the magnetic field and $\rho$ the density, both are functions of $(\vec{r},t))$: $$ \frac{\mathrm{d}}{\...
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Is there a relativistic version of Navier-Stokes equations?
Just as the title says, is there a relativistic version of Navier-Stokes equations?
In electromagnetic hydrodynamics it would be very useful to have relativistic version of Navier-Stokes equations, ...
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Magnetic explosions on Sun
They say (in popular videos and articles) that tangled magnetic fields on Sun explode. But i don't understand why and how magnetic fields, tangled or not, explode. Could anyone explain?
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Could I really use bar magnets in space to protect myself from solar wind?
I have read this question:
The magnitude at the magnetic equator is given by the approximation:
$$
\lvert \mathbf{B} \rvert \left( r \right) \approx B_{o} \left( \frac{R_{E}}{r} \right)^{3} \tag{1}
$$...
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Why are Ohm's law and Ampere's law contrasting in Magnetohydrodynamics?
In the Magnetohydrodynamics the electric current is given by the Ampere's law is:
$$\nabla \times \mathbf{B}=\mu_0\mathbf{J}$$
where $\mathbf{B}$ is the magnetic field and $\mathbf{J}$ is the electric ...
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Lorentz's derivation of Lorentz force in 1892
I've found Lorentz's 1892 paper 'La théorie electromagnétique de Maxwell et son application aux corps mouvants' on Wikipedia
(It's in French and I failed to find the English version.)
https://ilorentz....
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Acceleration of fluid in a magnetohydrodynamics vortex
In the following video we see a mercury vortex done by magnetohydrodynamics:
https://youtu.be/au4hbUm4mMo
In the following manuscript they say that the fluid will accelerate according to (14) ${}^1$:
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Magnehydrotostatic equilibrium
in plasma physics the magnetostatic equilibrium is defined as
$$
\vec{j}\times\vec{B}=\nabla p
$$
where $\vec{j}$ is the current density $\vec{B}$ is the magnetic field and $p$ is the pressure. But ...
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Introduction to magnetohydrodynamics
does anybody have any reference books for introduction to magnetohydrodynamics? I want to dive into this topic and I don´t know about any good reference.
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How is the solar magnetic field produced?
I have been trying to understand the magnetic field creation mechanism. I know that its origin is not perfectly understood, but what is currently believed (as I know) is that the magnetic fields ...
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Is it generally accepted that Field Aligned Currents are caused by Force-Free Fields?
I am currently an undergraduate working on a project about FAC (Birkeland Currents) and it seems that most of the sources on the subject are very technical and hard for me to read (particularily ...
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Does magnetic force on a current-carrying thin slab depend on current distribution in the slab?
In Purcell and Morin’s Electricity and Magnetism, the magnetic force on a current-carrying sheet is found by using the fact that the force on a segment of wire with length $l$ would be $IB_{avg}l$, ...
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Taylor's hypothesis in turbulence
Reading about Taylor's hypothesis for converting spatial to temporal scales and vice-versa, I understand that if $V$ is the bulk speed of the fluid then we could use:
$$\ell = V \cdot \tau$$
To ...
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Conservative form of the vector diffusion equation
For some reason I am unable to find a source on the internet about this. I think I have an answer, but I want to be doubly sure about this. All I could find (here), is that for an incompressible fluid,...
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What are the assumptions made in ideal MHD?
So my understanding is that in ideal magnetohydrodynamics (MHD), we assume a conductivity of infinity, and that makes the electric field in a comoving frame equal to zero. As I was watching one ...
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Drift of neutral particles in plasmas
I'm learning about $\mathbf{E}\times \mathbf{B}$ drifts in plasmas. The drift speed is given by $\mathbf{v}=\mathbf{E}\times \mathbf{B}/B^2$. Chen (in Introduction to Plasma Physics and Controlled ...
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Plage regions data
Plages are phenomena of stellar activity.
Where can I find openly-accessible data of plage regions of the Sun with other parameters such as faculae region, magnetic field, etc?
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Do drifting particles violate Alfvén's theorem?
According to this Wikipedia article, Alfvén's theorem states that "in a fluid with infinite electric conductivity, the magnetic field is frozen into the fluid and has to move along with it". ...
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How to yield the relativistic equations of motion for a particle in a plasma non-dimensionless
The relativistic equations equations of motion for the ions are:
$$
\frac{d\vec{p}}{dt} \ = \ q (\vec{E}+ \vec{u} \times \vec{B}), \ \vec{p} \ = \ m \gamma\vec{v}
$$
In many papers discussing test ...
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Transition from inertial to kinetic range in Solar wind turbulence
Most papers studying the turbulence in the solar wind present figures showing the power spectral density (PSD) of the magnetic field. The inertial range, with a power law index of ~ -5/3, is followed ...
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Do numerical MHD codes contain particles?
Does an MHD code contain charged particles, or does one just numerically solve the MHD equations? Also, can you suggest a good introductory book/paper to learn the basics of MHD codes?
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Why does the transverse Alfven mode not undergo wave steepening and hence resulting in shock waves?
Initial Question:
I am currently working through the second edition of Introduction to Plasma Physics by Donald A. Gurnett & A. Bhattacharjee
In section 8.3.8 on page 304, they state that:
.. on ...
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Has any one seen an application of the virial theorem (say with magnetic fields) for non-self gravitating system?
Here is the version of the theorem I am most familiar with - consider an ideal magneto-fluid with density $\rho$, bulk velocity field $\mathbf v$, with magnetic field $\mathbf B$ and (isotropic gas) ...
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Why don't the Earth's oceans generate a magnetic field?
Many questions have been asked here about why the Earth has a magnetic field, e.g.,
What is the source of Earth's magnetic field?
How does Earth's interior dynamo work?
How can an ...
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Alfven waves in the ionosphere
I was given the following problem/question as a part of my homework in physics:
It is raining with thunder in Australia, and the lightnings generate transverse Alfven waves in the ionospheric plasma. ...
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How do I show that an energy minimising magnetic field subject to constraints is force-free?
I want to use the fact that a magnetic field can be written in the form
$$ \textbf{B} = \pmb{\nabla}u \times \pmb{\nabla}v $$
to show that if $\textbf{B}$ minimises the magnetic energy
$$ E = \int_V\...
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Wave drag in the interstellar medium
In Earth's atmosphere, an object moving at supersonic or near-supersonic speed experiences wave drag due to the formation of shock waves around the object's leading edge. At high speeds, wave drag is ...
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Crash course in fluid dynamics
I am teaching myself magnetohydrodynamics and have never taken a class on fluid dynamics before. It seems like knowing some fluid dynamics will help me understand MHD faster, so I was looking for a ...
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Basic questions about Alfven waves in solar corona
I'm a mathematician trying to understand a paper in mathematical physics (Alfven Reflection and Reverberation in the Solar Atmosphere, by Paul Cally), and although I understand most of the pde theory ...
