Electron cyclotron resonance

Cyclotron resonance refers to the resonant absorption of electromagnetic waves by charged particles (eg by free electrons or electrons in a solid body ), which are in a constant magnetic field. The name is derived from the cyclotron, a particle accelerator; where the particles move with the cyclotron frequency in a circular path.

In the plasma of the electron cyclotron resonance can be used to couple energy into the plasma, so to increase the kinetic energy of the electrons and thus to heat the plasma ( electron cyclotron resonance, ECR, ECR eng. ). This method is applied to ECR ion sources.

In experiments on nuclear fusion, a very high temperature of the ion (different hydrogen isotopes) needed. An additional heating of the ions can be reached among others by means of ion cyclotron resonance heating ( ICR ).

The investigation of the cyclotron resonance of electrons (or "holes" ) of a material is also a method of solid state physics for determining the effective mass of the charge carriers.

The cyclotron resonance of free electrons is the basis of the function of the gyrotron, and also plays a role in the magnetron. Both are powerful microwave generators.

The cyclotron resonance of charged particles in a Penning trap can be used to determine the relationship between mass and charge or charge with knowledge of their mass.

Theoretical basis

No electric field to an electron ( charge -e) in the magnetic field B interacts with the velocity v only the Lorentz force

A free electron follows a circular path or a helical line; The cyclotron frequency is the frequency of revolution of the electron.

In the solid state the velocity is given by the dispersion relation, ie, by the energy and the wave vector

Thus, the electron undergoes a force to the gradient of E is perpendicular to the magnetic field B, and the k-space perpendicular (k ) face. It thus moves on a surface of constant energy. This can of course also include reasons of energy conservation, as a temporally constant magnetic field causes no change in energy of the deflected particle. In the solid state, an electron remains in its movement on the Fermi surface.

Assuming a free electron gas, this results in the classic cyclotron frequency, in which each electron has the same round-trip time. However, this is not the case in the solid state. To obtain a general expression for the current frequency, the mass of the particle, therefore, must be replaced by the effective mass of the particle. This results in

With B - magnetic flux density   - Cyclotron frequency or rotational frequency m * - effective mass of particles ( here: effective electron mass ) e - elementary charge

Cyclotron resonance in solid state physics

A crystal sample at low temperatures ( approximately 4 Kelvin) is located in a static magnetic field B is irradiated with radio waves. The radio waves to accelerate the charge carriers, which are deflected by the magnetic field to spiral tracks. The absorption of the wave is maximal, if the frequency of the radio wave is equal to or a multiple of the cyclotron is:

With a known magnetic field strength can thus read off the effective mass of the charge carrier.

In a semiconductor, the sample must also be irradiated with light whose photon have a sufficiently large energy to raise the electrons in the conduction band.