Illustrated Physics
physics, drawn
Concept

Plasma frequency — where it appears

The natural frequency at which the electrons of a plasma oscillate about its ions, ωp = √(ne²/ε₀m). Waves below it cannot propagate and are reflected, which is why the ionosphere reflects short-wave radio and why metals reflect visible light.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A click that arrives sorted by pitch. Arrival time against frequency for a broadband pulse travelling 40 megametres along a magnetic field line through a plasma of 1e+8 electrons per cubic metre in a field of 300 nanotesla — the magnetosphere, roughly. The gyrofrequency is 8.4 kilohertz and the plasma frequency 90 kilohertz, so this is the regime where a right-hand circularly polarised wave travels happily below both of them. It does not travel at one speed. The group velocity is 2c√ω(ω_c − ω)^(3/2)/(ω_p ω_c), which is zero at zero frequency and zero again at the gyrofrequency and peaks in between — at 2.10 kilohertz here, which is a quarter of the gyrofrequency, found by searching the drawn function rather than quoted. Everything either side of that peak is slower, so the curve has a nose: 3.21 s at 500 Hz, 2.20 s at 2000 Hz, 3.59 s at 5000 Hz. The branch below the nose is the classic whistler — a lightning stroke in one hemisphere reaching a receiver in the other as a note gliding downward over about a second, which is what gave the phenomenon its name — and the branch above it arrives as a rising tone at the same time. Both are observed, and a recording that shows the two joined at the nose is how the gyrofrequency along the path is read off directly. Read the other way it is an instrument: the product of the delay and the square root of the frequency is 79 s·Hz^½ here, nearly constant across the low end of the band, and it measures the electron content of a path through the magnetosphere that nothing else could reach.

The whistle that arrives sorted

A lightning stroke in one hemisphere reaches a receiver in the other as a note gliding downward over about a second. Nothing dispersed the sound; there was no sound. A radio pulse travelled forty megametres along a magnetic field line through a plasma whose group velocity depends on frequency, and arrived with its frequencies separated by up to three seconds.

astrophysics · Plasma oscillation Snell's law with space and time exchanged. Two constructions on the same diagram of frequency against wavenumber, with the light lines of a medium of index 1 and of index 1.5. On the left, a boundary in space: the wave crosses a still surface, the frequency is conserved, and the horizontal line at the incident frequency meets the new medium's line at a wavenumber 1.5 times larger — the familiar shortening of the wavelength. On the right, a boundary in time: the whole medium changes at once, the wavenumber is conserved, and the vertical line at the incident wavenumber meets the new medium's line at a frequency 0.667 times the old one. The vertical line also meets the new line's negative-frequency branch, which is a wave running backwards: a reflection in time. A spatial boundary reflects into the same frequency and a temporal one into the same wavelength.

The reflection that needs no surface

Change the refractive index of a whole medium at one instant and a wave already travelling through it splits in two, one part running on and one running back, though there is no surface anywhere for it to reflect from. A boundary in time is Snell's law with space and time exchanged: the wavelength is kept and the frequency changes, momentum is conserved and energy is not.

optics · Refraction

Named alongside it

The objects these essays reach for when they reach for this one.

Boundary conditionCircular polarisationDispersionDispersion relationEnergy conservationGroup velocityGyrofrequencyMagnetosphereMomentum conservationNoethers theoremPermittivityPhase matching

All concepts