An Introduction to Magnetohydrodynamics

By L. Driel-Gesztelyi. 2004

1,298 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9499ebcf1cb969917f291536b2266aad29058bc7

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In Astronomy and Astrophysics

Citations in the corpus

Astrophysical magnetic fields and nonlinear dynamo theory (2004, background): “ in electric contact with the block through a thin lubricating ﬁlm of mercury. The asymptotic theory of Herzenberg [170] assumed that a/d ≪ 1; for excellent reviews of the Herzenberg dynamo see Refs. [129,177]. Using numerical simulations [174], it has been shown that Eq. (4.3) remains reasonably ac”
A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics (2010, background): “For further discussion of these parameters and their typical values, we refer the reader to [2,26,45].”
An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number (2017, neutral): “1 m in a laboratory), the induced magnetic ﬁeld is usually found to be negligible by comparison with the imposed magnetic ﬁeld, [3].”
MAGNETO-HYDRODYNAMIC (MHD) PUMP FABRICATED WITH CERAMIC TAPES (2002, background): “The field is generally known as Magneto Hydro Dynamics (MHD), and it deals with the conversion of electromagnetic energy into mechanical work in fluid media [1,2].”
On the Limits of Validity of the Low Magnetic Reynolds Number Approximation in MHD Natural-Convection Heat Transfer (2006, methodology): “A common technique in all these studies was the simplification of the magnetic induction equation through the low-Rm (or quasi-static) approximation [20, 21].”
Global Solutions for Incompressible Viscoelastic Fluids (2008, methodology): “The existence results we obtain in this paper, together with the methods, are valid in many related systems, such as those for general polymeric materials [5, 19], magnetohydrodynamics (MHD) [9], liquid crystals [10, 24], and the free interface motion in mixture problems [38].”
Dust in magnetic fusion devices (2011, background): “plasma processing devices [48], liquid metal film MHD flows [49] and arc welding [50, 51], where dust particles and droplets are often observed.”
Micro-magnetofluidics: interactions between magnetism and fluid flow on the microscale (2011, methodology): “The ratio between Lorentz force and inertial force is called the interaction parameter (Davidson 2011):”
On the convergence rate of grad-div stabilized Taylor–Hood to Scott–Vogelius solutions for incompressible flow problems (2011, background): “These equations are commonly used in metallurgical industries to heat, pump, stir and levitate liquid metals [5].”
Helicon-type radiofrequency plasma thrusters and magnetic plasma nozzles (2019, neutral): “…L of the gradient of the physical parameters, i.e., |∇| ∼ 1∕L , being often (32) ( ⋅ ∇) = − ∇p − ∇B2∕2 0 + ( ⋅ ∇) ∕ 0, (33)∇ ( p + B2 2 ) = 0, (34)p + B 2 2 = B2 v 2 , 1 3 Reviews of Modern Plasma Physics (2019) 3:3 Page 43 of 61 3 used for considering the physics qualitatively (Davidson 2001).”
Wave turbulence in incompressible Hall magnetohydrodynamics (2006, methodology): “Indeed, both quantities obey the same Lagrangian equation, which is for Ω, dΩ dt = Ω · ∇V. (2.9) By applying Helmholtz’s law (see, e.g., Davidson 2001) to Hall MHD, we see that the generalized vorticity lines are frozen into the plasma (see, e.g., Sahraoui et al. 2003).”
On Global Dynamics of Three Dimensional Magnetohydrodynamics: Nonlinear Stability of Alfvén Waves (2016, background): “, [4], but there is no rigorous mathematical explanation for the phenomena.”
Fluid Mechanics of Liquid Metal Batteries (2017, background): “Introductions and overviews of the topic of magnetoconvection have been provided in texts dedicated to the subject [110] as well as texts on the more general topic of magnetohydrodynamics [111].”
Dynamo Models of the Solar Cycle (2005, neutral): “…then be combined into a single evolution equation for the magnetic field B, known as the magnetohydrodynamical (MHD) induction equation (see, e.g., Davidson, 2001): ∂B ∂t = ∇× (u×B− η∇×B), (1) where η = c2/4πσe is the magnetic diffusivity (σe being the electrical conductivity), in general only a…”