Illustrated Physics
physics, drawn
Concept

Particle beam — where it appears

A stream of charged or neutral particles moving together in nearly one direction at nearly one speed, as in an accelerator, a vacuum tube or a solar flare. A beam carries its own space charge and current, and passing through other charges it can drive waves that slow and spread it.

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

Two pushes that nearly cancel. The forces between two equal charges moving side by side at the same speed, measured in the laboratory, in units of the Coulomb force the same two charges exert at rest, against their speed. Electric repulsion grows as γ, because a moving charge's field is stronger across its motion: 2.29 at β = 0.9, 7.1 at 0.99. The magnetic attraction of two parallel currents grows as γβ² and eats it almost entirely: the net push is γ(1 − β²) = 1/γ — 0.436 at 0.9 and 0.141 at 0.99. Measured in the pair's own frame the push is exactly the Coulomb force at every speed; the difference is not a force that exists in one frame and not another but a difference in how fast the two frames' clocks run while the charges drift apart.

The beam that stops pushing itself apart

A beam of electrons is a crowd of like charges, and a crowd of like charges flies apart. A slow beam does, within centimetres. A fast one hardly does at all: at a gigaelectronvolt the same current travels kilometres before its width doubles. The electric repulsion has not weakened — it has grown, by the factor γ. What has grown faster is a magnetic attraction between parallel currents, which cancels all but 1/γ² of the push. Seen from the beam itself there is no magnetism at all, only Coulomb repulsion acting while the beam's clocks run slow.

relativity · Field transformation Two beams that each stay straight, and wind each other into whirlpools. Phase space of a one-dimensional particle simulation: every dot is an electron, plotted at its position along a periodic box one fastest-growing wavelength long (10.26 v₀/ωₚ) and its velocity, in units of the beam speed. One beam starts at +v₀, the other at −v₀, with a 0.0001 ripple in position. At t = 18/ωₚthe beams are visibly rippled; by 26 the ripple has grown into overturning, and by 40 the two beams have wound round each other into a single vortex, filamented into strands. When growth first stops, at ωₚt = 25.2, the wave's field is 0.56 m v₀ωₚ/e; electrons trapped in it bounce at 0.59 ωₚ, faster than the 0.354 ωₚ at which it was growing, and it traps any electron within ±1.92 v₀ of the wave's speed — zero, by symmetry — so both beams are inside its separatrix; total energy was conserved to 0.31%.

The two beams that unravel each other

A cold beam of electrons, alone, is perfectly stable: disturb it and it rings at its plasma frequency and carries the ringing downstream. Send a second beam through it the other way and the pair is not stable at all. A ripple of the right length grows by a factor of e in less than half a plasma period, takes a third of the beams' drift energy into an electric field, and then winds both beams into a single whirlpool in which their drift is gone. Neither beam can do it. The growth exists only in the pair, and a beam a millionth as dense as the plasma it crosses is enough to start it.

astrophysics · Plasma oscillation

Named alongside it

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

CollidersDispersion relationInstabilityLandau dampingThe Lorentz factorThe Lorentz transformationMagnetic forcePhase spacePinch effectPlasma frequencyPlasma oscillationSpace charge

All concepts