To use all functions of this page, please activate cookies in your browser.
my.chemeurope.com
With an accout for my.chemeurope.com you can always see everything at a glance – and you can configure your own website and individual newsletter.
 My watch list
 My saved searches
 My saved topics
 My newsletter
AppletonHartree equationThe AppletonHartree equation, sometimes also referred to as the AppletonLassen equation is a mathematical expression that describes the refractive index for electromagnetic wave propagation in a cold magnetized plasma. The AppletonHartree equation was developed independently by several different scientists, including Edward Victor Appleton, Douglas Hartree and K. Lassen. Additional recommended knowledge
EquationFull EquationThe equation is typically given as follows ^{[1]}: Definition of Termsn = complex refractive index i =
ν = electron collision frequency ω = 2πf f = wave frequency = electron plasma frequency = electron gyro frequency ε_{0} = permittivity of free space μ_{0} = permeability of free space B_{0} = ambient magnetic field strength e = electron charge m = electron mass θ = angle between the ambient magnetic field vector and the wave vector Modes of PropagationThe presence of the sign in the AppletonHartree equation gives two separate solutions for the refractive index ^{[2]}. For propagation parallel to the magnetic field, i.e., , the '+' sign represents the "ordinary mode," and the '' sign represents the "extraordinary mode." For propagation perpendicular to the magnetic field, i.e., , the '+' sign represents a lefthand circularly polarized mode, and the '' sign represents a righthand circularly polarized mode. See the article on electromagnetic electron waves for more detail. Reduced FormsPropagation in a Collisionless PlasmaIf the wave frequency of interest ω is much smaller than the electron collision frequency ν, the plasma can be said to be "collisionless." That is, given the condition , we have , so we can neglect the Z terms in the equation. The AppletonHartree equation for a cold, collisionless plasma is therefore, QuasiLongitudinal Propagation in a Collisionless PlasmaIf we further assume that the wave propagation is primarily in the direction of the magnetic field, i.e., , we can neglect the Y^{4}sin^{4}θ term above. Thus, for quasilongitudinal propagation in a cold, collisionless plasma, the AppletonHartree equation becomes, References 

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "AppletonHartree_equation". A list of authors is available in Wikipedia. 