Illustrated Physics
physics, drawn
Concept

Bremsstrahlung — where it appears

Radiation emitted by a charged particle when another charge deflects it, from the German for braking radiation. It accounts for the continuous spectrum of an X-ray tube and for a main energy loss in hot plasmas, where it grows as the density squared and the square root of the temperature.

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

Four plasma columns that need exactly the same current. Left: four pressure profiles across a 1 cm column — flat-topped, parabolic, peaked and hollow — each holding the same 10¹⁹ ions per metre at the same 10 keV, so the same total ∫2πr p dr. Right: the current each needs to hold itself together, from solving the force balance J × B = ∇p with Ampère's law, radius by radius. All four come out at 0.800, 0.800, 0.800, 0.800 MA: Bennett's 0.800 MA. The shape of the column decides where the current flows and how strong the field is inside it, and has no effect at all on how much current there must be.

The current that squeezes what carries it

A current flowing along a column of hot gas makes a magnetic field that wraps round the column, and the field pushes the current inward. If the column is a plasma, free to move, it is squeezed. Ampère's law and a balance of forces then fix how much current a column of given temperature needs to hold itself together — and the answer does not depend on how wide the column is or how its plasma is arranged inside. Ten thousand electronvolts in ten million million million ions per metre needs 0.8 million amperes, whatever the shape. Above about 1.4 million amperes the same arithmetic says a hydrogen column radiates faster than its current can heat it, and collapses.

electromagnetism · Ampere law The product a fusion plasma has to beat. The density, temperature and confinement time multiplied together at which a deuterium–tritium plasma heats itself, against temperature. Multiplying by T turns the previous curve into a pressure times a time, which is what a magnet can actually hold, since the field limits the pressure nT and not the density alone. The curve has a clear minimum of 3.0 × 10²¹ keV s/m³ near 14 keV, and that is why magnetic machines are designed to run hot but not hotter. ITER's design point, a density of 10²⁰ per cubic metre at 8.9 keV and 3.7 s, gives 3.3 × 10²¹: a little under this line, because ITER is meant to be driven by external heating with a tenfold gain and not to ignite outright.

The product a fusion plasma has to beat

A star makes less power per litre than a compost heap, and it has burned for four and a half thousand million years. A fusion plasma makes thousands of times more and has to be held for seconds, and it has taken seventy years to get close. Both are obeying one inequality, written down in a classified report in 1955, in which density and time appear only as their product.

astrophysics · Plasma oscillation

Named alongside it

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

Alpha heatingAmperes lawConfinement timeForce balanceFusion reactivityIgnitionInstabilityLawson criterionMagnetic pressurePinch effectPlasmaThermal runaway

All concepts