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Lecture# Magnetohydrodynamics: Modeling and Equations

Description

This lecture introduces the physics of plasmas, focusing on magnetohydrodynamics (MHD). The instructor covers the two-fluid model, MHD equations, conservation of energy, Alfvén's theorem, solar wind, Parker spiral, magnetic reconnection, dynamos, and MHD waves. The lecture discusses the challenges of modeling plasmas, including the impossibility of Maxwell's equations. Various scales, from particle number to spatial dimensions, are explored, with a focus on ITER. The lecture also delves into the equations of state, continuity, and closure in the two-fluid model, emphasizing the conservation of mass. The Alfven theorem, magnetic field dynamics, and collisional effects are discussed in the context of MHD.

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Related concepts (217)

PHYS-325: Introduction to plasma physics

Introduction à la physique des plasmas destinée à donner une vue globale des propriétés essentielles et uniques d'un plasma et à présenter les approches couramment utilisées pour modéliser son comport

Induction equation

In magnetohydrodynamics, the induction equation is a partial differential equation that relates the magnetic field and velocity of an electrically conductive fluid such as a plasma. It can be derived from Maxwell's equations and Ohm's law, and plays a major role in plasma physics and astrophysics, especially in dynamo theory. Maxwell's equations describing the Faraday's and Ampere's laws read: and where: is the electric field. is the magnetic field. is the electric current density.

Coronal seismology

Coronal seismology is a technique of studying the plasma of the Sun's corona with the use of magnetohydrodynamic (MHD) waves and oscillations. Magnetohydrodynamics studies the dynamics of electrically conducting fluids - in this case the fluid is the coronal plasma. Observed properties of the waves (e.g. period, wavelength, amplitude, temporal and spatial signatures (what is the shape of the wave perturbation?), characteristic scenarios of the wave evolution (is the wave damped?), combined with a theoretical modelling of the wave phenomena (dispersion relations, evolutionary equations, etc.

Magnetohydrodynamics

Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in numerous fields including geophysics, astrophysics, and engineering. The word magnetohydrodynamics is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement.

Binary relation

In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets X and Y is a new set of ordered pairs (x, y) consisting of elements x in X and y in Y. It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element x is related to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation.

Plasma stability

The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it. The stability of the system determines if the perturbations will grow, oscillate, or be damped out. In many cases, a plasma can be treated as a fluid and its stability analyzed with magnetohydrodynamics (MHD).

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