Illustrated Physics
physics, drawn
Concept

Magnetosphere — where it appears

The region around a planet or star dominated by its own magnetic field, shaped by the solar wind into a compressed dayside and a long tail. It traps charged particles into radiation belts, channels them into auroras and is a source of natural radio emission.

Named by 2 essays across one field — 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 The circle of electrons a wave can talk to. Electron velocities along and across the magnetic field, in units of c. Shaded: a horseshoe of 10 keV electrons (speed 0.195c), the shape a beam takes when it is driven down into a strengthening field, with the electrons moving up along the field missing. Curves: the electrons a wave travelling across the field can exchange energy with, for wave frequencies of 0.995, 0.980, 0.960 times the cyclotron frequency. Because a faster electron is heavier and circles more slowly, at Ω/γ, each resonance is a semicircle of radius c√(1 − ω²/Ω²): 0.100, 0.199, 0.280c. A wave at 0.981Ω resonates with the horseshoe's middle.

The radio that only heavier electrons can make

Above every aurora the Earth broadcasts a gigawatt of radio that no one on the ground can hear. It comes out just below the frequency at which electrons circle the field there, and it is a maser — amplified by the electrons themselves. The surprise is what makes the amplifier work. Without relativity it could not: summed over every electron, a wave at the circling frequency is always absorbed. The few per cent by which a fast electron is heavier, and circles more slowly, is not a correction to the mechanism. It is the mechanism.

astrophysics · Radiating charge

Named alongside it

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

Circular polarisationCyclotron frequencyCyclotron motionDipole fieldDispersionGroup velocityGyrofrequencyLandau dampingPlasma frequencyPlasma oscillationPopulation inversionRelativistic mass

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