• Toroid coils (Fig. 1) are inductors that confine the electromagnetic field of currents to the inner regions of the coils.

• For high-pressure NMR investigations, the use of toroid coils can be advantageous over the use of standard solenoid or Helmholtz saddle coils.

• The intrinsic high inductance (L) of toroid coils limits its use to lower NMR resonance frequencies (f):

Fig. 2 Toroid Cavity adapted from a toroid coil of many parallel-wound single-turn coils

• The inductance of toroid coils is reduced if the turns are wound in parallel. The area of the confined electromagnetic field, however, remains the same.

• A toroid cavity (Fig. 2) is derived from unifying many parallel-wound turns of a toroid coil to form a coaxial resonator.

The confined magnetic field (B) inside the toroid cavity is accurately quantified by the simple equation: 

where A is a proportionality constant (torus factor), and r is the radial distance from the long axis of the cavity.

The confinement of magnetic fields in toroid cavities is ideally suited for high-pressure NMR spectroscopy in metal autoclaves, while the unique field gradient facilitates rotating frame NMR imaging on the micrometer scale.