Illustrated Physics
physics, drawn
Concept

Plasma beta — where it appears

The ratio of a plasma's gas pressure to its magnetic pressure, deciding which of the two shapes the motion. It is 10⁻³ in the solar corona, where the field dictates everything, and 10⁴ at the base of the convection zone, where the field is carried about like a dye — a range of eight orders of magnitude within one star.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

One magnitude, and a direction that turns the wrong way. The force per unit area a magnetic field of 0.01 tesla exerts on a surface, drawn for surface normals at 0°, 30°, 45°, 60°, 90° to the field. The short grey arrows are the normals; the long coloured ones are the tractions. Every traction has the same length, 40 pascals, because the magnitude of T·n does not depend on the orientation of n at all — and the direction is the normal reflected in the field rather than carried round with it, so as the surface turns one way the force turns the other. A surface cutting across the field is pushed (the magnetic pressure); a surface cutting along it is pulled (the magnetic tension); and at 45° the traction lies in the surface, which is a shear and is neither.

The same force whichever way the surface faces

A magnetic field's stress is usually described as a pressure across the lines with a tension along them, as though it were two effects. It is one. The force per unit area is B²/2μ₀ on every surface however it is oriented, and only the direction changes — the surface normal reflected in the field, so that turning the surface one way turns the force the other. At 45° neither name applies.

astrophysics · Flux freezing Three speeds, drawn against direction. The phase speed of the three magnetohydrodynamic waves against the angle between the wavevector and the field, drawn as a polar diagram with the field horizontal and the sound speed 0.6 times the Alfvén speed. Along the field the two magnetosonic branches take the values of the sound speed and the Alfvén speed themselves and swap which is which as the ratio crosses one; across the field the slow branch vanishes entirely and the fast branch runs at the quadrature sum. The shear branch is the figure-of-eight, v_A cos θ, and it is the only one of the three whose speed contains no thermodynamic quantity — no pressure, no temperature, no sound speed. It does not know what the gas is made of.

The wave that does not know what the gas is made of

Give the magnetic tension of a bent field line an inertia and it becomes a string. The wave that runs along it goes at the same speed at every wavelength, compresses nothing anywhere, and has a speed containing no temperature, no pressure and no sound speed — it is the only wave in classical physics that is indifferent to what the medium is. Its energy travels along the field whatever direction the wave was sent in.

astrophysics · Flux freezing Circles that go nowhere, and a current across the line. Gyrating ions in a uniform magnetic field pointing out of the page, with 60 guiding centres drawn from a density that falls by a factor of e every 3 gyroradii to the right, and Maxwellian speeds. Every ion goes round clockwise and none of the circles moves. Of the circles that cross the dashed vertical line, those centred to its left cross it moving down and those centred to its right cross it moving up; in this sample 11 cross moving down and 7 moving up, a count a sample this small could turn either way. Because there are more circles on the left, the ions at the line move downwards on average over every speed and phase, at exactly the thermal speed squared over the gyrofrequency times L, 0.33 thermal speeds, computed by averaging over speeds and phases and checked against that value. It is a current, carried by circles whose centres are still.

The current no particle carries

A magnetised plasma holds its own pressure against the field only if a current flows across the pressure gradient, and the fluid equations say exactly how much. Follow the particles in a uniform field and none of them is going anywhere; every guiding centre is still. The current is real all the same. It is made of circles that are more crowded on one side of a line than the other, and when the field is not uniform, the drifts that do move the guiding centres flow the wrong way.

electromagnetism · Magnetism

Named alongside it

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

PlasmaFlux freezingMagnetic energyMagnetic pressureMagnetic tensionAlfven waveAnisotropyBuoyancyCoronal heatingDiamagnetic currentDiamagnetismDispersion relation

All concepts