Gyroradius & Cyclotron Frequency
The helical orbital radius (Larmor radius r_L) and angular frequency (cyclotron frequency ω_c) of a charged particle orbiting a magnetic field line.
Governing formula
r_L = (m v_⊥) / (|q| B), ω_c = (|q| B) / m
SI unit
m (Larmor Radius) & rad/s (Cyclotron Frequency)
In depth
Lorentz forces bend moving charged particles into circular orbits perpendicular to magnetic fields. Heavy ions have much larger gyroradii than light electrons, dictating plasma transport and magnetic confinement geometry.
Examples in the real world
Ion cyclotron resonance heating (ICRH) tuning radiofrequency waves to match ion gyromotion frequencies in tokamaks.