9887

Cold Wave Plasma Dispersion

This Demonstration solves for the dielectric tensor in the cold plasma wave dispersion relation, which determines the frequency as a function of wavenumber for waves independent of temperature in a plasma. All frequencies are normalized to the electron plasma frequency. The variable is the wavenumber in units of . In the graph, is scaled to and is scaled to , where is the electron plasma frequency.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The variable is the atomic number of the ions (1–30 in this Demonstration).
Change " min", " max", " min", and " max" to vary the area of the dispersion plot being solved for (i.e., acts as the bounds for the solution to the dielectric tensor).
The variable "angle" refers to the angle that the wave makes with the magnetic field in degrees.
The variable "max recursions" defines the precision of the plot, but a higher value takes longer.
For computational reasons, the cyclotron frequency cannot be set to 0, so it is bound between .01 and 1 times the electron plasma frequency.
The red curves correspond to the solutions found by taking the plus sign in the plasma dispersion equation and the blue correspond to the solutions found by taking the minus sign.
References
[1] R. J. Goldston, "Low-Frequency Waves in a Magnetized Plasma," Introduction to Plasma Physics, London: Institute of Physics Publishing, 1995 pp. 285–308.
[2] P. M. Bellan, "Cold Plasma Waves in a Magnetized Plasma," Fundamentals of Plasma Physics, New York: Cambridge University Press, 2006 pp. 206–241.
For more information on plasma waves, see the Wikipedia entry for "Plasma waves".
For more information on dispersion relations in general, see the Wikipedia entry for "Dispersion relation".
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+