Plasma Zoo: Gyromotion in Three Dimensions

Motions of charged particles in electromagnetic fields are important in understanding the behaviors of plasmas in space. In Plasma Zoo, we present visualizations of particle motions in simple electromagnetic field configurations.

Consider a magnetic field which fills a region of space with uniform intensity and direction. Here we represent that magnetic field (designated with the letter 'B') as a cyan (light green) arrow, its direction representing the direction of the field vector.

One of the more fundamental motions of charged particles in a magnetic field is gyro-motion, or cyclotron motion. If a charged particle is moving in a magnetic field, the particle experiences a force perpendicular to the direction of the charge motion and the field. This direction is determined by the Right-Hand Rule (Wikipedia).

In the simplest case, this curves the particle path into a circle. The direction of the force also depends on the charge of the particle, with negative particles (labelled '-') being directed in circles in a sense opposite to positive particles (labelled '+'). If we view along the direction the magnetic field is pointing, we will see that the positive particles gyrate anti-clockwise while the negative particles gyrate clockwise.

In this visualization, we have two charged particles, with the same mass and speed, one positive and one negative, moving in a 3-dimensional space. Similar to the resuts we see in Plasma Zoo: Gyromotion in Two Dimensions, we see that the two charged particles, starting out in the same direction, have their trajectories bent into circles and traverse the circular path in opposite directions.

The magnetic field is uniform and directed perpendicular to the plane. In this case, the circular path of the particle becomes a helical path.

Important Note: The example here shows particles with the same speed and mass. If the masses are different (for example, a positive proton has about 1836 times more mass than an electron), the radius of the gyromotion will be proportionally larger for the same speed.