Gyrofrequency and Plasma Frequency

The two fundamental frequencies of a plasma: gyration about field lines and collective electrostatic oscillation.

Cyclotron (Gyro) Frequency

A charged particle in a magnetic field circles the field line at the cyclotron frequency omega_c = |q| B / m. Electrons, being light, gyrate far faster than ions: the electron cyclotron frequency is thousands of times the ion value at the same field. The gyrofrequency sets the timescale of magnetization and defines the cyclotron resonances used for radio-frequency heating.

Plasma Frequency

If electrons are displaced from the ions, the resulting electric field pulls them back and they overshoot, oscillating at the plasma frequency omega_p = sqrt(n q^2 / (epsilon0 m)). It depends only on density and species, not on the magnetic field. The electron plasma frequency is the natural frequency of collective electrostatic response and sets the cutoff below which electromagnetic waves cannot propagate through the plasma.

Ratios That Classify a Plasma

The ratio omega_p / omega_c distinguishes magnetically dominated from inertially dominated behavior. A related length, the inertial skin depth c / omega_p, sets the scale for field penetration and for the Hall term. The Debye length, thermal speed divided by plasma frequency, sets the scale of charge screening. Together these characterize whether a system behaves as a magnetized fluid or a kinetic medium.

Relevance

Heating scheme selection depends directly on these frequencies: electron-cyclotron systems target omega_c e, ion-cyclotron systems target omega_c i, and lower-hybrid schemes sit between them. For Kronos concepts, the Hyperion breeder on-axis field near 8 T and peak field of 16.84 T set the cyclotron layers, while the D-3He burner plug at 26.49 T raises them further; these are design values for machines in simulation.