Lecture

Plasma Waves in MHD Model

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the general formulation of ideal MHD waves, starting from the ideal MHD equations and adding small perturbations to a uniform and static equilibrium. The linearized system of equations is obtained by applying Fourier transform to derive the wave dispersion relation. The lecture discusses the choice of geometry for MHD waves and focuses on transverse waves like the shear Alfvén wave, which is non-compressional. The dispersion relation for the shear Alfvén wave is derived, and its importance in fusion plasmas and space observations is highlighted. Additionally, the lecture explores ideal MHD waves with a longitudinal component, deriving the dispersion relation for compressional waves. The conclusion summarizes the different types of ideal MHD waves and their representation through the wave dispersion relation surface.

In MOOC

Plasma Physics: Introduction

Plasma, the fourth state of matter, is by far the most abundant form of known matter in the universe. Its behavior is very different from the other states of matter we are usually familiar with. To understand it, a rigorous formalism is required. This is essential not only to explain important astrophysical phenomena, but also to optimize many industrial and medical applications and for achieving fusion energy on Earth. This physics course, taught by world-renowned experts of the field, gives you the oppor

Official source

Quiz

Related concepts (32)

Longitudinal wave

Longitudinal waves are waves in which the vibration of the medium is parallel to the direction the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure.

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.

Fusion power

Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices designed to harness this energy are known as fusion reactors. Research into fusion reactors began in the 1940s, but as of 2023, no device has reached net power. Fusion processes require fuel and a confined environment with sufficient temperature, pressure, and confinement time to create a plasma in which fusion can occur.

Magnetic reconnection

Magnetic reconnection is a physical process occurring in electrically conducting plasmas, in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection involves plasma flows at a substantial fraction of the Alfvén wave speed, which is the fundamental speed for mechanical information flow in a magnetized plasma. The concept of magnetic reconnection was developed in parallel by researchers working in solar physics and in the interaction between the solar wind and magnetized planets.

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).

Related lectures (64)

Electromagnetic Waves in Plasmas

Covers the behavior of electromagnetic waves in non-magnetized plasmas and the simplification of equations for non-collisional plasmas.

Burning Plasmas: Fast Ions Role MOOC: Plasma Physics: Applications

Explores burning plasma specifics, fast ions role, losses, MHD modes, turbulence, Alfvén waves interaction, and burn stability.

Heating and Current Drive by Waves MOOC: Plasma Physics: Applications

Explores the use of waves for heating and current drive in tokamaks, focusing on ICRH and LH waves, their mechanisms, and antenna features.

MHD Equilibrium: Equations and Applications MOOC: Plasma Physics: Introduction

Covers the equations for static ideal MHD equilibrium and force-free and force-balanced equilibria in plasma physics.

MHD Equilibrium & Stability