Guiding Center - Gyration

Gyration

If the magnetic field is uniform, the particle velocity is perpendicular to the field, and other forces and fields are absent, then the magnetic Lorentz force is perpendicular to both the velocity and the magnetic field and is constant in magnitude, resulting in particle motion at constant speed on a circular path. This is known as the gyration around the magnetic field. For mass m, charge q, and magnetic field B, the frequency of the circular motion, the gyro-frequency or cyclotron frequency, is

For speed v, the radius of the orbit, called the gyroradius or Larmor radius, is