This is the first of three articles about charged particle motion in electromagentics fields and the earths magnetic field. The articles will include simple demonstrations built using the matlab clone scilab and the visualisation tool IBM Open data explorer, both of these are open source applications. The first article will describe a simple scilab based application for modelling charged particle motion. The Lorentz force can be used to model a wide range of systems and phenomena including
- Motion of particles in colliders and their detectors e.g. the CERN Large Hadron Collider
- Understanding the solar interior and atmosphere
- Understanding the charge particles in the ionosphere e.g. the borealis
- Confinement of plasmas for experimental fusion reactors
- Focusing of beams for electron microscopy
The Lorentz force is the force on point charges due to electric and magnetic fields the elctric field gives rise to a linearly increasing force relationship between the charge and the elctric field intensity. The force generated through the magnetic field is such that it is perpendicular to the plane formed by the particle velocity vector and the magnetic field. This explains the action of the vecotor cross product term.
The cross product term can be undersood from the relativistic nature of the elctromagnetic interaction. It is important to remember that the relativistically covariant Maxwell equations and the special theory of relativity enable us to understand the unified nature of the single electromagnetic interaction. When the lorentz transformations are applied to the electric field we have a cross product relationship between the velocity of the particle and the magnetic field it therfore appears that the magnetic interaction is generated by a relativistic effect, an article in the links provides a good description.
The scilab script uses the lorentz force to update the position of a particle in a constant and uniform electromagnetic field. The equations of motion are solved using a simple Euler integration step. When executed, the script starts a number of dialogs in turn requesting the user to
- Define the initial velocity
- Define the b field
- Define the e field
- Provide a tile for the plot
- The plost is drawn
- The user is asked if they want to save the plot, if yes and OK are clicked a file save dialog opens.
The particle mass and charge are hard coded at the start of the script but can be altered if the user requires. Not surprisingly there is a lot of information about the lorentz force and charged particle motion, including some interesting video content on utube, one such link in the useful links section below
Useful Links
Scilab script requires the lorentz force function file
Matlab script requires the lorentz force function file
Scilab home page
IBM Open data explorer
Wikipedia on Lorentz force
Wikibook on the lorentz force
Science world info about the lorentz force
Article about relativistic transformation of electromagnetic fields
Utube demonstration of Lorentz force