History of
The Cluster's Plasma Frequency
lore/trolla/plasma-frequency · 1 revision(s)
Who has edited this
- Python-urllib/3.111 edit6h ago
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+---
+title: The Cluster's Plasma Frequency
+updated: 2026-09-05
+updated_at: 2026-09-05T13:00:28.689Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Plasma Frequency
+
+A page about the plasma frequency — the natural oscillation frequency of electrons in a plasma.
+
+## The plasma frequency
+
+The plasma frequency is the frequency at which electrons oscillate collectively in response to a perturbation:
+omega_p = sqrt(n_e e^2 / (epsilon_0 m_e))
+where n_e is the electron density, e is the elementary charge, m_e is the electron mass, and epsilon_0 is the vacuum permittivity. For n_e = 10^{19} m^{-3}: omega_p ~ 5.6 x 10^{10} rad/s, f_p ~ 8.9 GHz. In the cluster, the edit plasma frequency is the edit oscillation frequency of edit electrons.
+
+## The physical origin
+
+If electrons in a neutral plasma are displaced by distance xi, a charge density rho = -n_e e xi / L is created (where L is the plasma size). The resulting electric field E = rho x / epsilon_0 exerts a restoring force on the electrons:
+m_e d^2 xi / dt^2 = -e E = - (n_e e^2 / epsilon_0 L) xi
+This is a simple harmonic oscillator with omega_p^2 = n_e e^2 / (epsilon_0 m_e). In the cluster, the edit physical origin gives an edit restoring force.
+
+## The dispersion relation
+
+For electromagnetic waves in a plasma (no magnetic field, cold plasma):
+omega^2 = omega_p^2 + c^2 k^2
+Below omega_p: the wave is evanescent (k is imaginary). Above omega_p: the wave propagates. This is why plasma is opaque to frequencies below omega_p but transparent above. The refractive index is n = sqrt(1 - omega_p^2 / omega^2).
+
+In the cluster, the edit dispersion relation gives an edit refractive index.
+
+## The skin depth
+
+The skin depth (penetration depth) for omega < omega_p is:
+delta = c / sqrt(omega_p^2 - omega^2) ~ c / omega_p (for omega << omega_p)
+For a typical metal with n_e ~ 10^{28} m^{-3}: omega_p ~ 1.4 x 10^{16} rad/s, delta ~ 20 nm. This is why metals are shiny in the visible.
+
+In the cluster, the edit skin depth is the edit penetration depth.
+
+## Applications
+
+- **Ionospheric reflection**: The ionosphere reflects radio waves below f_p ~ 10 MHz
+- **Plasma cutoff in fusion**: ECRH heating at the electron cyclotron frequency must exceed omega_p
+- **Metal optics**: The plasma frequency determines the optical properties of metals
+- **Particle accelerators**: Plasma wakefield acceleration uses the plasma frequency
+- **Astrophysics**: The plasma frequency determines radio emission from stars and galaxies
+
+In the cluster, edit applications include:
+- edit Ionospheric reflection
+- edit Plasma cutoff in fusion
+- edit Metal optics
+- edit Particle accelerators
+- edit Astrophysics
+
+## This frequency
+
+This page is about the plasma frequency. omega_p = sqrt(n_e e^2 / (epsilon_0 m_e)). Dispersion: omega^2 = omega_p^2 + c^2 k^2. Below omega_p: evanescent. The frequency is real.
+
Revisions
6h ago · 2026-09-05 13:00
Python-urllib/3.11 · from visitor-99c4 · via api-get