Illustrated Physics
physics, drawn
Concept

Particle accelerator — where it appears

A machine that raises charged particles to high energy with electric fields and steers them with magnetic ones. Its size is set by how strong its magnets are and by how much energy the particles radiate when bent, which limits circular electron machines.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

The orbits of an electron in a travelling wave. The possible motions of an electron in a plasma wave whose phase moves at γₚ = 10 and whose field is 0.2 of the cold wave-breaking field, drawn as its energy against its position in the wave over two wavelengths — the level curves of H = γ − βₚ u − ε cos ψ, which the electron's motion conserves. Inside the separatrix (thick) an electron is trapped: it slides back and forth through the wave, gaining energy while it outruns the wave and losing it while the wave outruns it. The separatrix reaches γ = 99 at its top, near 4γₚ²ε = 80, starting from electrons moving at the wave's own speed. Outside it, electrons that are too slow are overtaken by the wave and those that are fast enough outrun it; neither gains energy on average.

The wave an electron rides to a gigaelectronvolt

A laser pulse fired into a thin plasma pushes its electrons aside and leaves them oscillating behind it, a wave of charge travelling at nearly the speed of light. The field in that wave is a thousand times stronger than any metal accelerator can hold, and an electron caught in it at the right moment is carried along like a surfer, gaining a gigaelectronvolt in a few centimetres. Then it outruns the wave. The distance it can ride, and the energy it can gain, are both set by how nearly the wave keeps pace with it — which is to say, by relativity.

relativity · Relativistic dynamics The speed that stops while the energy keeps coming. The speed of an electron, as a fraction of the speed of light, against the kinetic energy given to it, from special relativity (solid) and from Newton's ½mv² (dashed); dots at the five energies Bertozzi used in 1964. Newton's speed passes the speed of light at a quarter of a megaelectronvolt and is 7.7 times it at 15 MeV. Relativity's speed is 0.863 c at 0.5 MeV, 0.967 c at 1.5 MeV, 0.9948 c at 4.5 MeV and 0.99946 c at 15 MeV. Between 1.5 and 15 MeV the energy grows tenfold and the speed by three and a half per cent. The energy does not stop arriving; the speed stops answering it.

The speed that stops while the energy keeps coming

In 1964 William Bertozzi gave electrons energies from half a megaelectronvolt to fifteen, timed them over eight and a half metres, and caught them in an aluminium disc to measure the heat they brought. By Newton the fastest should have crossed in under four nanoseconds, seven times faster than light. They took twenty-eight, and so did the slower ones, more or less. The heat, meanwhile, rose in proportion to the energy put in. The experiment is famous for showing that nothing outruns light, but its sharper result is the second half: the energy did arrive, all of it, carried at very nearly the same speed.

relativity · Relativistic dynamics Two clocks that slow together. For a muon circling a 1.45 T magnetic field, its mean life as the laboratory measures it and the time it takes to go round once, against its Lorentz factor γ, on logarithmic scales. Time dilation stretches the life to γ × 2.197 μs: 6.6 μs at γ = 3, 64.4 μs at γ = 29.3, the muon g − 2 experiments' value. The orbit grows with the momentum, so the revolution takes γ times longer too: 15.3 ns at γ = 3, 149 ns at γ = 29.3. The two lines are parallel. Their ratio, the number of turns in one mean life, is 431 at every energy — set by the field and the muon's own properties, eBτ/2πm, with γ cancelled out.

The turns a muon makes at any energy

A muon lives two microseconds, and in a storage ring it lives longer the faster it goes, because its clock runs slow. Its orbit runs slow too: a faster muon carries more momentum, bends less in the same field and takes longer to go round. The two slowings are the same factor of gamma, so they cancel. A muon in a 1.45 tesla ring makes 431 turns in a mean life whether it is moving at nine-tenths of the speed of light or at nine nines, and the only way to more turns is a stronger magnet. The same cancellation is why the first cyclotrons stopped working near twenty million electronvolts.

relativity · Time dilation

Named alongside it

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

The Lorentz factorCalorimetryCyclotron frequencyDecay lengthGroup velocityKinetic energyMean lifeMomentumMuonPhase velocityPlasmaPlasma frequency

All concepts