Illustrated Physics
physics, drawn
Concept

Storage ring — where it appears

A circular accelerator in which particles circulate at fixed energy for hours, held on their orbit by bending magnets and refocused by others. It is used to collide beams, to make synchrotron light and to measure particles' lifetimes and magnetic moments.

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

A muon's spin lapping its own momentum round a storage ring. Snapshots of a muon circling a storage ring at γ = 29.3, taken every four turns (not to scale in time: the muon is drawn at a different place on the ring for each snapshot so they do not overlap). The dashed arrow is the direction of motion, tangent to the ring; the solid arrow is the spin. On each turn the spin gains 12.3° on the momentum — 2πaγ — so after 29.3 turns it has gained a full lap. That lap takes 4.37 microseconds, and the muon, whose lifetime is stretched from 2.2 to 64.4 microseconds by its speed, lives for about fifteen of them.

The spin that runs ahead of its own motion

A charged particle circling in a magnetic field has two directions that turn: the direction it is moving, and the direction its spin points. If the particle's magnetism were exactly what Dirac's equation first gave — a g-factor of exactly two — the two would turn together at every speed, the spin locked to the motion as a compass needle is locked to a car. The muon's g is not quite two, and its spin creeps ahead by a fixed rate that is the same at a crawl and at 99.94 per cent of the speed of light. That constancy is a delicate cancellation between a magnetic field made stronger by motion and a rotation that exists only because the particle is being turned, and it is what made the most precise measurements of the muon possible — at one magic speed, where the electric fields that steer the particles stop affecting the spin at all.

relativity · Field transformation 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.

Time dilationCyclotron frequencyDecay lengthG factorLarmor precessionThe Lorentz factorThe Lorentz transformationMagnetic momentMean lifeMuonParticle acceleratorPrecession

All concepts