Ion Plasma Frequency

\[\omega_{pi}=\sqrt{\frac{n_i Z^2 e^2}{\varepsilon_0 m_i}}\]

Variables

omegapi[ωpi]ion plasma angular frequency (rad/s)

niion number density (m⁻³)

Zion charge number

eelementary charge (C)

epsilon0[ε0]vacuum permittivity (F/m)

miion mass (kg)

Description

What is this formula?

The ion plasma frequency formula calculates the natural oscillation frequency of ions in a plasma when they are displaced from charge equilibrium.

Because ions are much heavier than electrons, the ion plasma frequency is usually much lower than the electron plasma frequency.

When to use it

Use this formula when studying low-frequency plasma oscillations, ion dynamics, plasma waves, sheath behavior, fusion plasmas, ionospheric plasmas, and laboratory plasma diagnostics.

Example

A singly ionized hydrogen plasma has:

ni = 1×10^18 m⁻³

Z = 1

e = 1.602×10^-19 C

ε0 = 8.854×10^-12 F/m

mi = 1.673×10^-27 kg

Formula:

ωpi = √((ni*Z²*e²)/(ε0*mi))

Substitution:

ωpi = √((1×10^18 × 1² × (1.602×10^-19)²)/(8.854×10^-12 × 1.673×10^-27))

Result:

ωpi ≈ 1.32×10^9 rad/s

Applications

- Ion plasma oscillations

- Low-frequency plasma waves

- Fusion plasma analysis

- Space plasma physics

- Ionospheric plasma modeling

- Plasma sheath studies

- Laboratory plasma diagnostics