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Electron cyclotron resonance

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Electron cyclotron resonance

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

Contents

ω c e = e B m .

where e is the elementary charge and m is the mass of the electron. For the commonly used microwave frequency 2.45 GHz and the bare electron charge and mass, the resonance condition is met when B = 875 G = 0.0875 T. For particles of charge q, rest mass m0 moving at relativistic speeds v, the formula needs to be adjusted according to the special theory of relativity to:

ω c e = q B γ ⋅ m 0

where

γ = 1 1 − ( v / c ) 2 .

In plasma physics

An ionized plasma may be efficiently produced or heated by superimposing a static magnetic field and a high-frequency electromagnetic field at the electron cyclotron resonance frequency. In the toroidal magnetic fields used in magnetic fusion energy research, the magnetic field decreases with the major radius, so the location of the power deposition can be controlled within about a centimeter. Furthermore, the heating power can be rapidly modulated and is deposited directly into the electrons. These properties make electron cyclotron heating a very valuable research tool for energy transport studies. In addition to heating, electron cyclotron waves can be used to drive current. The inverse process of electron cyclotron emission can be used as a diagnostic of the radial electron temperature profile.

In condensed matter physics

Within a solid the mass in the cyclotron frequency equation above is replaced with the effective mass tensor ∥ m ∗ ∥ . Cyclotron resonance is therefore a useful technique to measure effective mass and Fermi surface cross-section in solids. In a sufficiently high magnetic field at low temperature in a relatively pure material

ω c e > 1 / τ ℏ ω c e > k B T

where τ is the carrier scattering lifetime, k B is Boltzmann's constant and T is temperature. When these conditions are satisfied, an electron will complete its cyclotron orbit without engaging in a collision, at which point it is said to be in a well-defined Landau level.

References

Electron cyclotron resonance Wikipedia
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