Illustrated Physics
physics, drawn
Concept

Force-free field — where it appears

A magnetic field whose currents flow everywhere along the field lines, so that the field exerts no force on them. Such fields are the relaxed states of twisted plasmas, but by the virial theorem none can be confined to a finite region without something outside to anchor it.

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

The field a pinch gives up relaxing into. The axial and azimuthal field across a cylinder of conducting plasma in the minimum-energy state at fixed helicity, Bz = J₀(λr) and Bθ = J₁(λr), drawn for λa = 1.5 and λa = 3. Solid lines are the axial field and dashed lines the azimuthal field. Both satisfy ∇×B = λB, checked by finite differences at three radii, so the current runs along the field everywhere and the field exerts no force on the plasma. At λa = 3 the axial field passes through zero at r = 0.802a and is reversed outside it. The reversal needs λa above 2.405, the first zero of J₀, and nothing was imposed at the edge to produce it. λa = 1.5: pinch parameter Θ = 0.75, reversal parameter F = 0.688. λa = 3: pinch parameter Θ = 1.50, reversal parameter F = -1.150.

The twist that outlives the turbulence

A plasma pinch driven hard enough goes violently unstable, and then settles into the same quiet state however it was started — with the field at its edge pointing backwards. The explanation is that turbulence destroys almost every constraint a perfect conductor obeys and spares one. The magnetic helicity, a measure of how twisted and linked the field is, decays far more slowly than the energy, and a field that has shed all the energy it can at fixed helicity has only one shape available to it.

astrophysics · Flux freezing A field that pushes harder than metal holds. The pressure a magnetic field exerts on whatever carries its current, B²/2μ₀, against field, beside the working strength of three conductor materials. One tesla pushes with four atmospheres; at 27 T the push equals what hard copper can bear, at 50 T what the strongest copper–niobium wire can bear, and at 100 T it is 4.0 GPa, beyond any conductor. A coil carrying its own field above these values needs something else to hold it together, and the something else is what a high-field magnet mostly is.

The mass a magnetic field has to be held in

A magnetic field pushes on the currents that make it with a pressure of B²/2μ₀ — four atmospheres at one tesla, four gigapascals at a hundred. So a strong magnet is a pressure vessel, and a theorem about pressure vessels applies to it: whatever its shape, the structure holding a field must carry at least the field's stored energy in tension. That fixes a least mass for every joule, and it is why the record fields are records in materials, held for microseconds by nothing but inertia.

electromagnetism · Field energy

Named alongside it

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

DissipationField energyFlux freezingHoop stressMagnetic energyMagnetic fluxMagnetic helicityMagnetic pressureMagnetic reconnectionMaxwell stress tensorPlasmaResistivity

All concepts