Ion Cyclotron Frequency

What is this formula?

The ion cyclotron frequency formula calculates the angular frequency at which ions rotate around magnetic field lines under the influence of the Lorentz force.

Because ions are much heavier than electrons, ion cyclotron frequencies are significantly lower than electron cyclotron frequencies.

When to use it

Use this formula when studying magnetized plasmas, ion motion, plasma confinement systems, ion cyclotron resonance heating, fusion devices, and space plasma physics.

Example

A singly ionized ion moves in a magnetic field of:

B = 0.15 T

Using:

Z = 1

e = 1.602×10^-19 C

mi = 1.673×10^-27 kg

Formula:

ωci = (Z*e*B)/mi

Substitution:

ωci = (1 × 1.602×10^-19 × 0.15)/(1.673×10^-27)

Result:

ωci ≈ 1.44×10^7 rad/s

Applications

- Fusion plasma confinement

- Ion cyclotron resonance heating

- Magnetized plasma diagnostics

- Space plasma analysis

- Tokamak and stellarator physics

- Charged particle dynamics

- Plasma wave propagation