Electron cyclotron resonance
![Example of cyclotron resonance between a charged particle and linearly polarized electric field (shown in green). The position vs. time (top panel) is shown as a red trace and the velocity vs. time (bottom panel) is shown as a blue trace. The background magnetic field is directed out towards the observer. Note that the circularly polarized example below assumes there is no Lorentz force due to the wave magnetic field acting on the charged particle. This is equivalent to saying that the charged particle's velocity orthogonal to the wave magnetic field is zero.](/Images/godic/202501/11/Cyclotron-Resonance-Motion_Linearly-Pol-Fields_Freq-1.0_Efield-1.0_fps-20_Image-Res-100_Image-Size-610x6101536.gif")
![Example of cyclotron resonance between a charged particle and circularly polarized electric field (shown in green). The position vs. time (top panel) is shown as a red trace and the velocity vs. time (bottom panel) is shown as a blue trace. The background magnetic field is directed out towards the observer. Note that the circularly polarized example below assumes there is no Lorentz force due to the wave magnetic field acting on the charged particle. This is equivalent to saying that the charged particle's velocity orthogonal to the wave magnetic field is zero.](/Images/godic/202501/11/Cyclotron-Resonance-Motion_Circularly-Pol-Fields_Freq-1.0_Efield-1.0_fps-20_Image-Res-100_Image-Size-610x6101536.gif")
Electron cyclotron resonance is a phenomenon observed in plasma physics, condensed matter physics, and accelerator physics. An electron in a static and uniform magnetic field will move in a circle due to the Lorentz force. The circular motion may be superimposed with a uniform axial motion, resulting in a helix, or with a uniform motion perpendicular to the field, e.g., in the presence of an electrical or gravitational field, resulting in a cycloid. The angular frequency (ω = 2πf ) of this cyclotron motion for a given magnetic field strength B is given (in SI units) by