Toroidal and poloidal coordinates

The terms toroidal and poloidal refer to directions relative to a <a href="/facts/Torus/J9SkaV1W">torus</a> of reference. They describe a three-dimensional <a href="/facts/Coordinate_system/Mtd0q4SP">coordinate system</a> in which the poloidal direction follows a small circular ring around the surface, while the toroidal direction follows a large circular ring around the torus, encircling the central void.
The earliest use of these terms cited by the <a href="/facts/Oxford_English_Dictionary/qaxKX8Bc">Oxford English Dictionary</a> is by <a href="/facts/Walter_M._Elsasser/n3uT4wkY">Walter M. Elsasser</a> (1946) in the context of the generation of the <a href="/facts/Earth%2527s_magnetic_field/73G36wmx">Earth's magnetic field</a> by currents in the core, with "toroidal" being parallel to lines of constant <a href="/facts/Latitude/IBYqkjhU">latitude</a> and "poloidal" being in the direction of the magnetic field (i.e. towards the <a href="/facts/Geomagnetic_pole/Vc0Pc5RK">poles</a>).
The OED also records the later usage of these terms in the context of toroidally confined plasmas, as encountered in <a href="/facts/Magnetic_confinement_fusion/ThThVDpr">magnetic confinement fusion</a>. In the plasma context, the toroidal direction is the long way around the torus, the corresponding coordinate being denoted by z in the slab approximation or ζ or φ in magnetic coordinates; the poloidal direction is the short way around the torus, the corresponding coordinate being denoted by y in the slab approximation or θ in magnetic coordinates. (The third direction, normal to the magnetic surfaces, is often called the "radial direction", denoted by x in the slab approximation and variously ψ, χ, r, ρ, or s in magnetic coordinates.)

Toroidal and poloidal coordinates open-in-new

Toroidal and poloidal coordinates