Electron cyclotron resonance

Electron Cyclotron Resonance (ECR) is a phenomenon in which electrons in a magnetic field absorb energy from an electromagnetic wave with a frequency equal to or near their cyclotron frequency. This results in the acceleration of the electrons to high energies, which can then collide with and ionize gas atoms or molecules. Here, the oscillation is taken in terms of wave vector k. Parallel and perpendicular will be used to denote the direction of k relative to the magnetic field Bo. Longitudinal and transverse will be used to denote the direction of k relative to the electric field E. If the oscillating magnetic field B is zero, the wave is electrostatic otherwise electromagnet.

Let us consider the oscillation of electron is perpendicular to the magnetic field Bo. Also assume that the ions are too massive to move at the frequencies involved and form a fixed uniform background of positive charge. We shall neglect the thermal motion so that

The electron equation of motion is

The equation of continuity

The Maxwell's equation are

To solve these equations, the following assumption are made

The oscillating quantities are assumed to be behave sinusoidally as

Using these consideration, equation 1 reduces to

Considering only longitudinal waves. It's x component is

y component is

z component is

Also we can reduce equation 6, 7 and 8 as

If v1z is absent then the electron moves in circular motion. From equation 10

Substituting the value of v1y in equation 9

If w = wc then v1x -> ∞. This condition is called cyclotron resonance which is unstable condition. At this condition, the motion of electron cannot be predicted.

The electron cyclotron frequency plays an important role in many areas of physics, including plasma physics and fusion research, where it is used to heat and confine high-temperature plasmas. The interaction of electrons with high-frequency electromagnetic waves at or near the electron cyclotron frequency can also be used to accelerate charged particles, such as in electron cyclotron resonance ion sources.

Previous note: Electron plasma waves

This note is a part of the Physics Repository.